A method and system for detecting the quality of digital design of an oral prosthesis

Abstract

The application discloses a kind of oral prosthetic digital design quality detection method and system, obtain three-dimensional point cloud, form close deviation characteristics by edge contour bidirectional distance difference value discrimination outside protrusion and defect;Determine close reference according to clinical classification, obtain adaptive tightening dynamic detection reference value by combining curvature confidence weighting and item compensation;Based on the reference, interproximal space is subjected to region growth and contact density verification, and the deviation of interproximal contact is quantified and scored;By abutment axial surface normal, identify undercut, get the range of multiple teeth that can be positioned by step intersection, determine the permissible offset domain of positioning path by allowance correction and score;Finally, the sparse area is positioned, searched, filtered and merged, and the evaluation value is generated and collected as the evaluation completion amount, and the out-of-limit review is performed after the coverage ratio and the main score are weighted and merged, the quality detection result containing each dimension score and prompt is output, the objective quantitative evaluation of prosthetic fit, contact and wearing is realized.

Description

Technical Field

[0001] This invention relates to the field of digital dental restoration technology, and in particular to a method and system for quality inspection of digital design of dental restorations. Background Technology

[0002] With the widespread application of intraoral scanning and computer-aided design and manufacturing technologies in the field of dental prosthodontics, crowns, bridges, and other restorations are increasingly designed and fabricated using three-dimensional digital models. The long-term stability of a restoration in clinical use largely depends on the degree of fit between its margins and the abutment teeth, its contact relationship with adjacent teeth, and its ability to be smoothly inserted in the correct orientation. If these quality factors can be determined in advance from the digital model before formal fabrication, a significant amount of rework and chairside adjustments can be avoided.

[0003] However, current quality control of digital models of restorations still largely relies on visual inspection and experience-based judgment by designers, lacking unified and quantitative evaluation methods: fit is often judged only by whether the edges are roughly aligned, making it difficult to distinguish between two opposite deviations: protrusion and defects; contact relationships are mostly judged subjectively for tightness, failing to objectively differentiate the stress risks of point contact and surface contact; determining the insertion direction relies on repeated manual trial placement, which is time-consuming and prone to overlooking obstructive areas on individual abutment teeth. Furthermore, when scan data is missing in certain areas, current practices often indiscriminately use incomplete data to draw conclusions, resulting in insufficient support for the evaluation of some areas and making it difficult to guarantee the reliability of the judgment results. Summary of the Invention

[0004] This invention discloses a digital design quality inspection method and system for dental prostheses. The system aims to quantitatively evaluate the marginal fit, adjacent tooth contact, and placement direction of the prosthesis based on the three-dimensional point cloud of the prosthesis. The system obtains scores for each dimension through grading benchmarks and confidence weighting, and automatically supplements the evaluation of areas with insufficient coverage. Finally, after over-limit verification, the system outputs quality inspection results that combine quantitative conclusions and reliability indicators.

[0005] The first aspect of this invention proposes a method for quality inspection of digital design of dental prostheses, comprising: Acquire three-dimensional point cloud data of the oral prosthesis, and perform bidirectional nearest point distance difference direction discrimination on the three-dimensional point cloud data to form edge fit deviation features; The clinical grading of occlusion is determined by analyzing the edge occlusion deviation characteristics to establish an occlusion level benchmark. Based on the occlusion level benchmark, curvature confidence weighted deviation nodes are identified to obtain sub-item weight compensation values. The allowable fluctuation range of the occlusion level benchmark is verified by the sub-item weight compensation values ​​to determine the dynamic detection benchmark value. Based on the dynamic detection benchmark value, the gap region is grown to determine the adjacent contact area range. Based on the adjacent contact area range, the point-to-surface contact density is verified to obtain the adjacent contact deviation. Based on the adjacent contact deviation, the contact deviation is graded and scored to form the adjacent contact rating value. Based on the adjacent contact assessment value, the undercut area of ​​each abutment tooth axial surface is located to obtain the undercut distribution of the abutment teeth. The common undercut boundary of multiple teeth is analyzed through the undercut distribution of the abutment teeth to determine the permissible offset domain of the insertion path. Based on the permissible offset domain of the insertion path, the insertion path deviation angle cross-boundary verification is performed to form the insertion path assessment value. Based on the assessment value of the placement path, the non-compliant areas are marked to generate a set of marked areas. The marked areas are analyzed to form an evaluation completion amount for the missing areas covered by the evaluation. Based on the evaluation completion amount, the over-limit trigger review is performed to generate the quality test result of the oral prosthesis.

[0006] A second aspect of this invention provides a digital design quality inspection system for dental prostheses, comprising: The point cloud acquisition module is used to acquire three-dimensional point cloud data of oral prostheses and to perform bidirectional nearest point distance difference direction discrimination on the three-dimensional point cloud data to form edge fit deviation features. The fit scoring module is used to analyze the edge fit deviation characteristics to determine the clinical fit grading and fit level benchmark, identify curvature confidence weighted deviation nodes based on the fit level benchmark to obtain sub-item weight compensation values, and verify the allowable fluctuation range of the fit level benchmark through the sub-item weight compensation values ​​to determine the dynamic detection benchmark value. The adjacent contact verification module is used to determine the adjacent contact area range by growing the gap region based on the dynamic detection benchmark value, to verify the point-to-surface contact density based on the adjacent contact area range to obtain the adjacent contact deviation, and to perform contact deviation grading and scoring analysis based on the adjacent contact deviation to form an adjacent contact rating value. The positioning verification module is used to locate the undercut area of ​​each abutment tooth axial surface based on the adjacent contact assessment value to obtain the undercut distribution of the abutment teeth, analyze the common undercut boundary of multiple teeth through the undercut distribution of the abutment teeth to determine the permissible offset domain of the positioning path, and perform positioning path deviation angle cross-boundary verification based on the permissible offset domain of the positioning path to form the positioning path assessment value. The report output module is used to generate a set of marked areas by marking non-compliant areas based on the assessment value of the placement path, analyze the evaluation coverage missing areas of the marked area set to form an evaluation completion amount, and perform over-limit trigger review based on the evaluation completion amount to generate the quality test result of the oral prosthesis.

[0007] The beneficial effects of this invention are reflected in the following points: First, this invention designs the edge contour comparison as bidirectional, calculating not only the shortest distance from the surface of the restoration to the designed neck edge, but also, conversely, the shortest distance from the designed neck edge to the surface of the restoration. The sign of the difference between the two directions directly indicates whether the area is a protrusion or a defect. This directional discrimination result is further multiplied by the measurement confidence level of the curvature at that location, used to dynamically tighten or loosen the allowable fluctuation range of the fit grade. This allows areas with complex curvature and unstable measurements within the same batch to be given more lenient judgment leeway, while areas with gentle curvature and reliable measurements maintain strict standards, allowing the fit grade itself to have a judgment of its own reliability. Second, point contact and surface contact correspond to two different failure paths: the former concentrates the force at a single point, and the smaller the radius, the higher the stress; the latter nominally distributes the load over a region, but the more uneven the shape, the more easily the load concentrates on the narrower side, leading to premature failure. This invention verifies risk levels based on the equivalent radius or shape uniformity of each contact area, rather than using a single area threshold to measure all contact areas. This ensures that the judgment of adjacency quality is based on the critical conditions of two different mechanical consequences, rather than simply on the size of the contact area. Finally, the determination of the insertion direction and the completeness of the test data are integrated into the same process: the step-by-step calculation of undercuts in multiple abutments yields a feasible directional range for all abutments; the shrinkage margin correction incorporates the actual limitations of the material and bonding into this range; and the self-verification of the test coverage automatically locates areas with insufficient data, conducts supplementary tests, and labels their reliability in the supplementary evaluation stage. All three stages share the same coordinate and threshold system, ensuring that the test results provide both a quantitative score for the insertion direction and indicate which conclusions are based on complete data and which require manual verification, rather than presenting the two in a conflated manner. Attached Figure Description

[0008] Figure 1 This is a flowchart illustrating a digital design quality inspection method for dental prostheses according to the present invention.

[0009] Figure 2 This is a schematic diagram of the multi-tooth stepwise intersection operation and the generation of the positioning path permission offset domain of the present invention.

[0010] Figure 3 This is a structural block diagram of a digital design quality inspection system for dental prostheses according to the present invention.

[0011] Wherein: 1-Directional spherical projection; 2-Base tooth; 3-Infeasible direction sector; 4-Common undercut boundary of multiple teeth; 5-Maximum continuous positioning range; 6-Inscribed circle center; 7-Permitted offset reference domain; 8-Permitted offset domain of positioning path. Detailed Implementation

[0012] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0013] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0014] The technical solutions of the embodiments of this application will be described below.

[0015] like Figure 1 As shown, this embodiment of the invention provides a method for quality inspection of digital design of dental prostheses, including the following steps S101-S105: Step S101: Obtain three-dimensional point cloud data of the oral prosthesis, and perform bidirectional nearest point distance difference direction discrimination on the three-dimensional point cloud data to form edge fit deviation features.

[0016] Specifically, three-dimensional point cloud data of the dental prosthesis is acquired. The dental prosthesis is placed on the positioning platform of the structured light scanning system. The platform has three non-collinear positioning bosses. The outer contour of the cervical margin of the dental prosthesis is fitted and limited to the inner side of the bosses, thus restricting the angular offset introduced by manual placement within the gap between the bosses. The scanning head acquires data along the outer surface of the dental prosthesis at six angles according to a preset trajectory. Each angle projects a set of sinusoidal phase gratings and calculates the surface height. The point spacing per angle is 0.03 mm, covering the entire area of ​​the occlusal surface, proximal surface, and cervical margin. An overlap bandwidth of not less than 15% is reserved between adjacent angles. The local point sets calculated by each of the six angles are rigidly registered according to at least 200 common feature points within the overlap bandwidth. An angle with a registration error exceeding 0.01 mm is judged as an invalid angle, re-acquired, replaced, and then included in the merging. The 3D point cloud data was generated from six sets of registered points. Downsampling was performed with a voxel side length of 0.02 mm. Multiple original points within the same voxel were merged into a single representative point at the center of that voxel. This reduced the computational burden caused by excessively high point density in repeatedly scanned areas to a level similar to other areas. For each downsampled 3D point cloud, the average distance to its 30 nearest neighbors was calculated. Points whose distance exceeded the global mean plus three standard deviations were identified as outliers and removed. The threshold of three standard deviations was chosen because floating noise points generated by high-gloss reflections on the restoration surface typically deviate from the main surface by more than an order of magnitude; at this level, three standard deviations are sufficient to distinguish them from normal surface roughness fluctuations. The coordinate system of the 3D point cloud data uses the placement direction indicated in the restoration design document as the Z-axis. The XY plane orientation is determined by the least-squares fitting plane of all control points of the neck margin reference curve. Edge contour extraction is then performed directly within this coordinate system.

[0017] In some embodiments, the step of determining the direction of the bidirectional nearest point distance difference of the edge contour in the three-dimensional point cloud data to form an edge fit deviation feature includes: performing functional edge reverse positioning extraction on the three-dimensional point cloud data to obtain an edge contour point set; calculating the bidirectional nearest point distance based on the edge contour point set to generate a forward distance set and a reverse distance set; performing point-by-point difference calculation on the forward distance set and the reverse distance set to obtain a bidirectional distance difference distribution; and identifying edge overhang segments and underextended segments based on the bidirectional distance difference distribution to form an edge fit deviation feature.

[0018] Functional edge reverse localization extraction is performed on 3D point cloud data to obtain edge contour point sets. The neck margin reference curve generated during the prosthesis design stage is pre-discrete into a set of control points at equal intervals according to arc length. The order of the control points is consistent with the neck margin direction, with an interval of 0.1 mm. Each control point serves as an anchor point, and a reverse search is performed in the 3D point cloud data for the surface point with the closest spatial distance to it. The search radius is 0.2 mm, and the radius value corresponds to the superposition of scanning registration error and neck margin curvature change. Too small a radius will miss slightly off-center true neck margin points, while too large a radius will mistakenly include adjacent axial surface points. If no corresponding surface point is found for a control point within the search radius, it is determined that there is a scanning blind zone in the 3D point cloud data at that point. Instead, the spatial linear interpolation of the corresponding surface points of two adjacent successfully matched control points is used as the supplementary point. The nearest surface point corresponding to each anchor point in the 3D point cloud data also needs to be verified by local curvature: the principal curvature is calculated in a neighborhood with a radius of 0.15 mm centered on the anchor point. Matching points with principal curvature lower than the set lower limit are considered to fall on a smooth axial surface rather than at the neck edge turning point, and are discarded. The anchor point is then repositioned in the neighborhood according to the curvature maximum value. If there is still no point in the neighborhood that meets the curvature standard, the anchor point is processed by adjacent interpolation in the same way as the scanning blind zone and a curvature failure mark is added. The edge contour point set summarizes all surface points corresponding to the anchor points, and the order follows the original order of the control points. If the spatial distance between two adjacent points exceeds three times the control point interval, the segment is marked as a sparse segment. The sparse segment retains the original spacing and sparse mark in the edge contour point set, and the distance calculation is performed directly according to the actual point position. Each point in the edge contour point set carries its arc length position on the neck edge direction. This arc length position is directly inherited from the corresponding control point and is used for the corresponding pairing of the forward distance set and the reverse distance set at the same direction position.

[0019] Based on the edge contour point set, bidirectional nearest point distances are calculated to generate forward and reverse distance sets. The control point set of the neck margin reference curve and the edge contour point set each establish their own KD-tree spatial index. Both trees are in the same coordinate system, eliminating the need for additional coordinate conversion during mutual retrieval. For the forward distance set, each point in the edge contour point set is sent to the control point-side KD-tree to retrieve the nearest neighbor control point, and the Euclidean distance between them is recorded as the forward distance value at that location. The retrieval order is consistent with the original arrangement of the edge contour point set. Conversely, for the reverse distance set, each control point of the neck margin reference curve is sent to the edge contour point set-side KD-tree to retrieve the nearest scan point, and its Euclidean distance is taken. The two distance measurement directions are opposite. When a certain point on the neck margin of the restoration protrudes, the forward distance set value at that point is larger, while the reverse distance set value remains relatively unchanged. Conversely, when a certain point is defective, the reverse distance set value is larger, while the forward distance set is less affected. The two sets are only equal when the neck margin at that point exactly coincides with the design. In the forward distance set, edge contour point set members located within sparse sections inherit the sparse marker of that point in the edge contour point set. In the reverse distance set, the distance to the nearest scanned point of a control point within a sparse section is significantly greater than that of its adjacent control points; this value is also associated with the sparse marker. Both distance sets retain the actual larger values ​​to reflect the insufficiency of the point itself. There is no upper limit to the search radius; any distance value is accepted and recorded. If an upper limit is manually set and the excess portion is truncated, a significant deviation between the actual scanned surface at the neck edge and the designed neck edge will be mistakenly treated as a normal deviation within the normal range. The lengths of the forward and reverse distance sets correspond to the number of edge contour point sets and the number of control points on the neck edge reference curve, respectively. The number of points in both sets is generally equal but not mandatory; the arc length position label serves as the basis for the correspondence between the two sets of values.

[0020] The bidirectional distance difference distribution is obtained by performing point-by-point interpolation on the forward and reverse distance sets. The forward distance set is indexed by the number of points in the edge contour point set, and the reverse distance set is indexed by the number of control points in the neck edge reference curve. The number of points in the two sets is not required to be equal. Before the interpolation calculation, the data is resampled using the arc length position as the common coordinate, with a sampling interval of 0.1 mm, consistent with the original interval of the neck edge reference curve control points, to avoid introducing additional interpolation errors due to different intervals. After alignment, the two sets of values ​​correspond one-to-one at the same arc length position. The difference is calculated position-by-position using the formula ΔD_k=D_fwd_k-D_rev_k, where D_fwd_k is the forward distance set value after alignment at that position, D_rev_k is the reverse distance set value after alignment at the same position, and ΔD_k is the bidirectional distance difference at that position, with the unit being the same as both sets, in millimeters. Since the two sets are two directions of measurement of the same physical quantity, the subtraction does not involve dimensional conversion. A positive ΔD_k indicates that the restoration contour extends beyond the designed neck edge, corresponding to a deviation in the outward direction of the edge protrusion; a negative ΔD_k indicates that the restoration contour recedes within the designed neck edge, corresponding to a deviation in the under-extended direction of the edge. The sign is retained in subsequent calculations. The bidirectional distance difference distribution records ΔD_k for all arc length positions sequentially. When a resampling point falls outside the start and end points of the neck edge curve, the endpoint value is extrapolated instead of interpolated for that position. When both the forward and reverse distance set values ​​at a certain position carry sparse markers, ΔD_k is still calculated according to the formula and inherits the marker. The marker and the difference value are stored in the same position, so the difference value itself and its confidence level can be read simultaneously in the bidirectional distance difference distribution. The arrangement order of the bidirectional distance difference distribution is consistent with the original arc length order of the edge contour point set.

[0021] The characteristics of edge fit deviation formed by overhanging and underextended segments are identified based on the bidirectional distance difference distribution. The ΔD_k value at each location in the bidirectional distance difference distribution is first compared with two symmetrical thresholds. The absolute value of the thresholds is obtained from the statistical analysis of historical scan data of multiple clinically accepted restorations, taking the upper boundary of the normal fluctuation range of ΔD_k in that batch of data. Locations with ΔD_k exceeding the positive threshold are marked as overhanging candidate points, locations below the negative threshold are marked as underextended candidate points, and locations between the two thresholds are not marked. A segment is confirmed as an overhanging or underextended segment when four or more candidate points appear consecutively along the arc length. This threshold of 4 is derived from the ratio of the arc length sampling interval of 0.1 mm to the clinically identifiable minimum neck margin defect length of 0.4 mm. Candidate sequences shorter than four points are considered random fluctuations in measurement, and their ΔD_k values ​​remain in the bidirectional distance difference distribution. Candidate points carrying sparse markers are weighted at 0.5 when included in the continuous count. A continuous sequence consisting purely of sparse points within the same segment must reach eight to meet the weighted count threshold of not less than 4. If adjacent candidate point categories are directly flipped from overhang to underhang without passing through unmarked positions, the two sides are independently confirmed according to their respective categories. The sign change of the bidirectional distance difference distribution at that point is the true location of the boundary between the two types of deviations. All overhang and underhang segments after the edge-fitting deviation feature is confirmed are included and numbered sequentially according to their arc length. Each segment records its segment number, starting and ending arc length positions, and the location of the maximum absolute value of ΔD_k within the segment. The segment number is used in subsequent steps to associate the attribution of each deviation node within the segment, representing the deviation measured by the maximum absolute value of ΔD_k in that segment. A record is added for each confirmed segment of the edge-fitting deviation feature. The overhang and underhang segments within the edge-fitting deviation feature are arranged independently according to their own arc length positions.

[0022] Step S102: Analyze the edge fit deviation characteristics to determine the clinical fit grading benchmark, identify the curvature confidence weighted deviation nodes based on the fit grading benchmark to obtain the sub-item weight compensation value, and verify the allowable fluctuation range of the fit grading benchmark through the sub-item weight compensation value to determine the dynamic detection benchmark value.

[0023] Specifically, the clinical fit grading criteria are determined by analyzing the marginal fit deviation characteristics. The grading boundaries are taken from the existing four-level standard for clinical evaluation of cervical margin fit of dental prostheses: Grade I is less than 0.08 mm, Grade II is 0.08 to 0.15 mm, Grade III is 0.15 to 0.25 mm, and Grade IV is more than 0.25 mm. The four-level boundaries correspond to the existing division between "clinically acceptable" and "rework required" in this standard. Each overhang and underextended segment in the marginal fit deviation characteristics carries a representative deviation value. During analysis, the absolute values ​​of the representative deviation values ​​of all segments are first taken, and then the largest value is selected as the judgment deviation value of the prosthesis. The fit grade criterion is locked to the level in which the judgment deviation value falls. When the judgment deviation value is exactly equal to the boundary value of a certain level, the adjacent higher level with stricter judgment is used to avoid the boundary value being misjudged as the loose side. If two or more segments in the edge fit deviation feature have the same maximum representative deviation, the fit grade benchmark is still locked at that maximum value. However, the positional identifiers of all parallel segments are also associated for verification of the allowable fluctuation range of the dynamic testing benchmark value. The maximum value, rather than the average value, of the segment representative deviation in the edge fit deviation feature is used as the judgment criterion because clinical acceptance focuses on whether the most severe defect on the neck margin is acceptable. The average value would be lowered by a large number of slightly deviating segments, masking the fact that some severe segments have exceeded the acceptable range. The distance between the judgment deviation and the upper and lower boundaries of its grade is recorded together; the smaller the distance, the thinner the margin of the fit grade benchmark within the current grade.

[0024] In some embodiments, the step of identifying curvature confidence-weighted deviation nodes and obtaining sub-item weight compensation values ​​based on the fit level benchmark includes: performing deviation exceeding the limit judgment based on the fit level benchmark to obtain a set of deviation nodes; performing local curvature confidence assessment on the set of deviation nodes to form a measurement confidence distribution; performing confidence weighting on the set of deviation nodes using the measurement confidence distribution to form curvature confidence-weighted deviation nodes; and assigning sub-item weight compensation values ​​to the curvature confidence-weighted deviation nodes according to the deviation magnitude gradient.

[0025] A set of deviation nodes is obtained by performing deviation assessment based on the fit level benchmark. The boundary value between the current fit level benchmark and the next better level is taken as the assessment threshold for this assessment. The assessment threshold for level II is 0.08 mm, level III is 0.15 mm, and level IV is 0.25 mm. The assessment threshold is essentially the boundary that the restoration must be reduced to in order to advance to a better level. When the fit level benchmark is determined to be level I, there is no better level above it, so the assessment threshold is directly set to 0 mm, and any non-zero deviation position will be included in the deviation range. The assessment is performed position by position on the original bidirectional distance difference distribution on which the edge fit deviation feature is based. The absolute value of ΔD_k at each position is taken and compared with the assessment threshold. Positions that exceed the assessment threshold are marked as deviation candidates, and positions that do not exceed the threshold are not marked. Deviation candidates are not necessarily continuous along the arc length. If the adjacent positions before and after a single candidate position are not exceeded, the candidate is still valid. The deviation node set filters out all deviation candidate positions, recording their arc length position and corresponding original ΔD_k value one by one, with the recording order arranged according to arc length. If the same arc length position belongs to a certain overhanging segment or underextended segment, the position in the deviation node set is additionally associated with its segment number. Deviation candidates that do not belong to any confirmed segment are only recorded with their position and value. These unnumbered candidates were previously not confirmed as segments due to having fewer than 4 consecutive points, but now they emerge separately under a finer discrimination threshold. When the fit level benchmark is Level II or above, the discrimination threshold is relaxed with the level. Scattered points that were originally not segmented due to having fewer than 4 consecutive points fall more into the arc length range of confirmed segments under this threshold. Therefore, the number of candidate points with segment numbers is usually significantly greater than that of unnumbered candidates.

[0026] For example, the step of evaluating the local curvature confidence of the deviation node set to form a measurement confidence distribution includes: extracting local curvature values ​​based on the deviation node set to obtain a curvature feature set; adaptively classifying the curvature feature set and statistically analyzing the curvature dispersion within each class to generate an error characterization distribution; performing curvature error regression fitting on the error characterization distribution to generate an error fitting curve; and performing confidence-weighted mapping on the error fitting curve according to the fitting residuals to form a measurement confidence distribution.

[0027] Curvature feature set is obtained by extracting local curvature values ​​from the offset node set. For each position in the offset node set, the corresponding scanned surface point is located in the edge contour point set according to the arc length position label. Positions with curvature not reaching the target value are directly judged as insufficient samples and their curvature is not recalculated. A neighborhood with a radius of 0.15 mm is taken as the center of this surface point. A local quadratic surface is fitted to all points within the neighborhood. The curvature value is the average principal curvature of the quadratic surface at that point. The larger the average principal curvature, the steeper the bend. This value is significantly higher at the neck edge corner than in the flat axial surface area. When the number of points in the neighborhood is less than 10, it is determined that the curvature fitting sample is insufficient, the curvature value is changed to missing and associated with the insufficient sample label. A small number of neighborhood points usually occurs in members of the offset node set in sparse sections, where the forcibly fitted curvature value is inherently unreliable. When the quadratic surface fitting residual exceeds twice the average distance between neighborhood points, even if the number of points meets the target, the curvature value is still recorded as missing and associated with the fitting failure label, because the surface model clearly does not match the actual shape. The curvature feature set corresponds to each position in the deviation node set, arranged in order of the same arc length, with the total number of positions being exactly the same as the deviation node set. The curvature value itself only takes the average of the absolute values ​​of the principal curvatures; this step is concerned with the degree of curvature rather than the direction. Positions marked as empty in the curvature feature set are left as is. Each curvature value in the curvature feature set and its corresponding insufficient sample flag and fitting failure flag are stored in the same record. The simultaneous placement of both flags is common in sharp bends at the neck edge in sparse sections, where there are few neighborhood points and the shape changes abruptly. In subsequent weight reduction, the lower confidence value is taken based on both flags, so as not to miss any due to the absence of one flag.

[0028] The curvature feature set is adaptively categorized, and the curvature dispersion within each category is statistically analyzed to generate an error representation distribution. Locations in the curvature feature set marked with insufficient samples or failed fitting are first removed, and the remaining valid curvature values ​​are arranged in ascending order. Category boundaries are defined according to the equal-frequency principle, with each category accommodating one-tenth of the total valid curvature values. The number of categories automatically increases or decreases with the total valid values ​​rather than remaining fixed; this is the essence of "adaptive." The curvature at most neckline locations falls near common arc corners, with only a few sharp protrusions or polar planes deviating from this range. Fixed-width categorization easily results in gaps at both ends, while equal-frequency categorization ensures sufficient quantity within each category to support dispersion statistics. When the total valid values ​​are less than 30, the number of targets in each category is reduced to one-fifth of the total valid values; when less than 10, all valid values ​​are merged into a single category. In this case, the error representation distribution contains only one record, and the curvature dispersion reflects the overall fluctuation of curvature rather than the fluctuation of a narrow interval. The standard deviation of the curvature values ​​corresponding to the curvature feature set within each range is denoted as the curvature dispersion for that range. A larger standard deviation indicates more drastic fluctuations in the curvature measured at different locations within that curvature magnitude, indirectly reflecting poorer measurement repeatability for that magnitude of curvature. The error characterization distribution is arranged in ascending order, taking the mean of all curvature values ​​for each range as the representative curvature value. The representative curvature value and its corresponding curvature dispersion are recorded for each range, with a one-to-one correspondence; the range order itself corresponds to the curvature from smallest to largest. The curvature dispersion values ​​recorded for each range in the error characterization distribution retain their original dimensions, which are the same as the curvature—the reciprocal of the length.

[0029] Curvature error regression is performed on the error representation distribution to generate an error fitting curve. The representative curvature values ​​for each level of the error representation distribution are used as independent variables, and the corresponding curvature dispersion is used as the dependent variable. These two values ​​constitute all the input point pairs required for fitting. The number of point pairs equals the total number of levels in the error representation distribution; the more levels, the more point pairs are available for fitting. When the number of levels is 1, regression is not possible, and fitting is skipped; instead, the unique curvature dispersion value is used as the constant error level across the entire curvature range. When the number of levels reaches 3 or more, quadratic polynomial regression is used, in the form E(c) = a·c. 2E(c) = +b·c+e0, where c is the representative curvature value given by the error characterization distribution, E(c) is the fitting dispersion under that curvature, and a, b, and e0 are regression coefficients. The quadratic term allows the dispersion to show a non-monotonic trend of first decreasing and then increasing or first increasing and then decreasing as the curvature increases. On flat surfaces with extremely small curvature, scanning noise tends to dominate curvature estimation. At sharp corners with extremely large curvature, the fitting of quadratic surfaces is inherently unstable, and the dispersion at both ends is therefore too high. When the number of levels is 2, a linear fitting is used instead. Quadratic fitting will degenerate into a family of parabolas passing through the two points in the case of two points, and the coefficients are not unique, while linear fitting is uniquely determined. The regression coefficients are solved by least squares, that is, the sum of the squares of the differences between the predicted values ​​and the measured values ​​of curvature dispersion for all point pairs is minimized. The error fitting curve is based on the regression coefficients and covers a continuous interval from the minimum to the maximum representative curvature value. It can be calculated continuously within the interval. When the curvature value is equal to any value between two adjacent representative curvature values, the error fitting curve is directly substituted into the fitting formula to calculate the value. When the curvature value falls outside the interval, the fitting result corresponding to the nearest boundary value is used instead.

[0030] The measurement confidence distribution is formed by performing confidence-weighted mapping based on the fitting residuals using the error fitting curve. The representative curvature value for each level in the error characterization distribution is substituted into the error fitting curve to calculate the predicted dispersion for that level. The absolute value of the difference between the predicted dispersion and the measured curvature dispersion for that level is recorded as the fitting residual for that level. The larger the residual, the more significant the prediction deviation of the error fitting curve at that curvature level. The fitting residual is normalized to the maximum value of all levels. The normalized residual falls between 0 and 1. A normalized residual of 0 indicates that the prediction and measurement are perfectly matched for that level, while a normalized residual of 1 indicates that the residual for that level is the worst among all levels. The confidence weight is 1 minus the normalized residual; that is, the larger the residual, the lower the confidence weight. The weight value also falls between 0 and 1. This mapping relationship is the only weighting rule in this step, and the basic values ​​for each level of the measurement confidence distribution are directly adopted from this confidence weight. Locations in the curvature feature set that carry insufficient sample indicators or failed fitting indicators, or are not included in any grade, have a confidence weight of 0. This is because the error fitting curve cannot provide the predicted dispersion for these locations, and using the lowest confidence level is the most conservative approach when there is no data to reduce the weight. These locations also occupy one record in the measurement confidence distribution, with a fixed weight of 0. Each location in the deviation node set inherits the confidence weight of the grade corresponding to its curvature value, and all locations within the same grade share the same weight value. The measurement confidence distribution records the inherited confidence weights position by position according to the original arc length order of the deviation node set. Since all locations within the same grade share the weight of that grade, only the grade number and corresponding weight need to be filled in when recording, and the total number of locations is exactly the same as the deviation node set.

[0031] The set of deviation nodes is weighted using the measurement confidence distribution to form curvature confidence-weighted deviation nodes. The absolute value of the original ΔD_k at each position in the deviation node set is multiplied by the confidence weight at the same arc length position in the measurement confidence distribution. The product is denoted as the weighted deviation W_k at that position, calculated as W_k = |ΔD_k| × w_k, where w_k is the inherited confidence weight, ranging from 0 to 1. Therefore, W_k is no greater than the absolute value of the original deviation; the lower the confidence level, the more the weighted value is suppressed. For positions with a confidence weight of 0, W_k is directly set to zero. The curvature corresponding to these positions was previously unassessable due to missing values ​​or fitting failures, and the authenticity of their original deviation values ​​was already questionable. Setting it to zero makes it numerically equivalent to no deviation occurring, rather than artificially deleting the record at that position. The curvature confidence-weighted deviation node still retains this record completely, only its W_k remains constant at 0. The curvature confidence-weighted deviation node inherits the arc length position and segment number fields from the original deviation node set, and adds a new item: the weighted deviation W_k at each position. The arc length position, segment number, and W_k are combined and stored in the same record. The total number of records for the curvature confidence-weighted deviation node is exactly the same as the deviation node set, and the order remains unchanged. Under the same segment number, W_k at multiple positions may differ significantly. Curvature changes are uneven within the segment; positions near sharp transitions at the neck edge receive lower weights from the measurement confidence distribution, while positions near gentle transitions receive higher weights. Even when the original ΔD_k is similar, the weighted W_k will show significant differences. When the neck edge is a smooth surface with reliable scanning, the curvature is reliable everywhere, and the measurement confidence distribution weights are all 1. In this case, W_k degenerates into the absolute value of the original deviation itself.

[0032] For curvature confidence-weighted deviation nodes, a gradient weighting system is used to obtain sub-item weight compensation values ​​based on the deviation magnitude. The W_k values ​​at all locations within the curvature confidence-weighted deviation node are divided into four gradient intervals based on their numerical magnitude: level 1 for deviations not exceeding 0.05 mm, level 2 for deviations between 0.05 and 0.10 mm, level 3 for deviations between 0.10 and 0.20 mm, and level 4 for deviations exceeding 0.20 mm. The interval boundaries are not the same set of numbers as the four-level classification boundaries of the fit level benchmark; this is a finer distinction used to differentiate severity differences within the same level. Each gradient interval corresponds to a basic weighting coefficient: level 1 0.1, level 2 0.3, level 3 0.6, and level 4 1.0. The coefficient increases progressively from 0.1 to 0.3 to 0.6 to 1.0, with the weight increasing faster the deviation approaches the unacceptable range. The sub-item weight at each location within the curvature confidence-weighted deviation node is taken from the basic weighting coefficient of its corresponding gradient interval; different locations within the same interval have the same sub-item weight. The component weight compensation value is aggregating the component weights of all positions within the same segment according to the segment number. The maximum value is taken as the compensation value for that segment, rather than the average value. The reason is the same as in the determination of the closeness level benchmark: the compensation strength of a segment is determined by the most severe position within it. If there are both level 1 and level 4 positions within the same segment, the component weight compensation value is only taken as 1.0 corresponding to level 4. Whether a segment can be upgraded depends on the most difficult point to handle. Taking the highest level coefficient within the segment is precisely to prevent the severe position from being diluted. The low weights of other positions have no effect on lowering the upper limit. The gradient of the position where W_k is 0 must be level 1, and the component weight is fixed at 0.1. This position is still a true record in the curvature confidence weighted deviation node, but the deviation after weighting is exactly zero. Therefore, the component weight compensation value is still included in the contribution of its lowest level.

[0033] The dynamic detection benchmark value is determined by verifying the allowable fluctuation range of the fit level benchmark through the component weight compensation value. The fit level benchmark itself has an allowable fluctuation range. For levels I to III, it is one-tenth of the width between the upper and lower boundaries of the level. For level IV, the upper boundary is open and there is no finite width. The fluctuation range is changed to one-tenth of the lower boundary value of 0.25 mm, which is 0.025 mm. The fluctuation range was originally a fixed margin reserved to absorb the repeatability error of the scan itself. During verification, the maximum value among all segmented item weight compensation values ​​is taken as the verification coefficient. The verification coefficient is used to compress the original floating range proportionally: the compressed floating range is equal to the original floating range multiplied by (1 minus half the ratio of the verification coefficient to 1.0). The closer the verification coefficient is to 1.0, the more severe the segment is, and the greater the compression. When the distance between the judgment deviation and the grade boundary is less than one-tenth of the width of that grade, the margin is already very thin. The compressed floating range is then further narrowed by multiplying this ratio by one-tenth. After the two narrowings are superimposed, the lower limit is half of the original width, and it will not be narrowed further. The verification coefficient is taken from all segments, not just the segment on which the closeness grade is based, because the grading only cares about which grade the worst point falls into, while the floating range verification needs to consider whether other segments are also approaching the boundary. For example, if the cheek and tongue segments are both approaching the upper limit of their respective grades, they need to be considered as a whole. The current level of the fit rating benchmark is determined by the upper boundary value of that level. The compressed floating range expands symmetrically to both sides of this benchmark. The lower limit is the strict limit, and the upper limit is the relaxed limit. The verification coefficient is taken from the maximum value of the aforementioned sub-item weight compensation values. The sub-item weight compensation value is maximized once and becomes the verification coefficient for the compressed floating range. The dynamic detection benchmark value is thus determined as this pair of upper and lower limits, replacing the original fixed single boundary, and becoming the judgment line actually used in this detection.

[0034] Step S103: Based on the dynamic detection benchmark value, the gap region is grown to determine the adjacent contact area range. Based on the adjacent contact area range, the point-to-surface contact density is verified to obtain the adjacent contact deviation. Based on the adjacent contact deviation, the contact deviation is graded and scored to form the adjacent contact evaluation value.

[0035] Specifically, the interproximal contact area range is determined by growing the interproximal region based on dynamic detection benchmark values. The point cloud of the proximal surface of the restoration is registered with the point cloud of the proximal surface of adjacent teeth acquired by the intraoral scanner in the same sequence to the same coordinate system. The registration is based on the common feature points in the overlapping area of ​​the occlusal surfaces of the two teeth. The registration accuracy of the proximal surface itself inherits the registration result of the occlusal surface. The Euclidean distance from each point on the proximal surface of the restoration to the nearest point on the proximal surface of the adjacent tooth is calculated point by point to obtain the gap value at that point. All gap values ​​constitute a gap distribution map covering the entire proximal surface region. Region growth starts from the vertex of the contact ridge where the interproximal gap between the two teeth is narrowest and extends to the surrounding adjacent points: candidate point gap values ​​that do not exceed the growth threshold taken from the dynamic detection benchmark value are included in the current region; otherwise, the expansion in this direction is stopped. If there are two non-adjacent local minimum seeds, they are grown independently and then merged into the same connected region. The overlapping parts are not counted repeatedly. Region growing is performed twice: The first time, the stricter lower bound of the baseline value is used to obtain a conservative connected region, denoted as S_min; the second time, the more lenient upper bound is used to obtain a more lenient connected region, denoted as S_max, where S_max completely encompasses the region corresponding to S_min. The adjacent contact area interval records this pair of area values ​​[S_min, S_max] and their corresponding connected component point sets. The area values ​​define the upper and lower limits of the contact range, while the connected component point sets retain complete 3D geometry for subsequent projection density statistics. The inclusion of candidate points in region growing is independent of the traversal path: regardless of the direction from which the same candidate point is scanned, its gap value and the growth threshold have a fixed relationship, and the adjacent contact area intervals produced by different paths arriving at the point are identical.

[0036] In some embodiments, the step of verifying the point-to-surface contact density based on the adjacent contact area interval to obtain the adjacent contact deviation includes: performing axial projection density statistics on the adjacent contact area interval to generate a contact area density distribution; performing density concentration analysis based on the contact area density distribution to obtain point contact areas and surface contact areas; performing local stress concentration risk verification on the point contact areas and surface contact areas to form a risky contact area; and calculating the density deviation of the measured area of ​​the risky contact area based on the contact area density distribution to obtain the adjacent contact deviation.

[0037] For adjacent contact area intervals, occlusal axis projection density statistics are performed to generate contact area density distribution. The two connected domains corresponding to S_min and S_max given for the adjacent contact area intervals are each projected onto the same two-dimensional plane along the occlusal axis (restor placement direction). The projection plane is a cross-section perpendicular to the placement direction and passing through the middle height of the adjacent contact area. The boundaries of the connected domains do not move after projection; only the three-dimensional coordinates are compressed into two-dimensional coordinates. The projection plane is divided into square grids with a side length of 0.1 mm. The number of original three-dimensional points falling into each grid is counted, and the point density of that grid is obtained by dividing the number of points by the grid area, with the density unit being points per square millimeter. When a grid falls exactly on the boundary of the S_max connected domain and is cut into an incomplete part by the boundary line, the number of points in the grid is proportional to the actual portion falling into the grid. The grid division range is based on the circumscribed rectangle of the S_max connected domain. Grids outside S_max that do not belong to any connected domain are also included in the statistics, but the number of points in these grids is generally lower, used to contrast the contact area density distribution with the actual contact area. Within the same bounding rectangle, the grid covered by the S_min connected domain of adjacent contact area intervals is a subset of the grid covered by the S_max connected domain. The density values ​​of both in the contact area density distribution are taken from the same grid statistics. The contact area density distribution records the point density values ​​of each grid cell in the order of the two-dimensional coordinates of the grid. First, it is arranged cell by cell along the X-axis of the projection plane. After a row is finished, it moves to the Y-axis and proceeds. Traversing all the grid cells once constitutes a complete two-dimensional density map.

[0038] Density concentration analysis was conducted based on the density distribution of the contact area to determine the point contact area and the surface contact area. A three-tier classification system categorized all grids in the contact area density distribution according to their density level: grids with a density of 0 were classified as non-contact grids; grids with a density exceeding a local clinical experience threshold (the lower quartile of the measured density in the surface contact area of ​​similar accepted restorations) were classified as high-density grids; and grids with densities between these two levels were classified as transitional grids. Each high-density grid was examined in its eight-neighborhood. Grids with seven or more high-density grids in their eight-neighborhood were identified as concentrated core grids, while those with fewer than seven were identified as isolated high-density grids. Isolated high-density grids often correspond to pseudo-high density caused by scanning noise or localized micro-protrusions in the contact area density distribution, rather than true stable contact. Adjacent core grids are connected to form a single contiguous area. Each contiguous core grid set is designated as a candidate region. A candidate region is classified as a point contact region if its bounding rectangle has an aspect ratio of no more than 2:1 and an area less than 0.5 square millimeters. A region is classified as a surface contact region if its aspect ratio exceeds 2:1 or its area reaches 0.5 square millimeters or more. Meeting either aspect ratio or area criterion qualifies a region as a surface contact region. Isolated high-density grids and transitional grids are archived as background regions, with density values ​​for each grid cell saved sequentially according to coordinates. This data is used for subsequent risk verification to check the rationality of boundary delineation. Multiple point contact regions and surface contact regions can coexist on the same adjacent contact surface; they are not merged, and their grid coordinate ranges are recorded independently. If the background grid accounts for a high proportion of the contact region density distribution, it indicates that the overall density of the adjacent contact surface is low, and the number of candidate regions of both types will be correspondingly low.

[0039] Local stress concentration risk verification was performed on point contact areas and surface contact areas to form risk contact zones. First, a nominal occlusal load was allocated to all contact areas. The total load was taken as the average occlusal force under normal chewing at that tooth position, statistically derived from clinically measured occlusal forces. The load was not distributed proportionally by area; under elastic contact, the contact stiffness of the contact patch was proportional to its equivalent contact radius. Patches with greater stiffness received more load; therefore, the load was allocated according to the proportion of each area's radius to the sum of all area radii. The equivalent contact radius of each candidate area was uniformly calculated according to... In this conversion, S represents the measured area of ​​the region, and r represents the equivalent contact radius. The conversion involves transforming irregular contact patches into circles of the same area. Both point contact and surface contact areas participate in load distribution according to this formula. The load allocated to the point contact area is divided by the measured area to obtain the average contact stress. Substituting this into the aforementioned distribution relationship, we can see that the stress is inversely proportional to the equivalent contact radius; halving the radius doubles the stress. This inverse ratio is the root cause of the early failure of small-area contacts. Point contact areas with an equivalent contact radius less than 0.15 mm have stresses exceeding twice the average stress of all contact areas, thus being classified as high-risk and included in the risk contact zone. For surface contact areas, a different criterion is used: the rotating caliper method is used to calculate the minimum area of ​​the circumscribed rectangle along each candidate edge of the boundary. The ratio of the shorter side to the longer side is recorded as the shape uniformity. For surface contact areas with a shape uniformity below 0.4, where the load is concentrated in a narrow band on the shorter side and the band width is less than half that of the longer side, the surface contact degenerates into a line contact, and this is also classified as high-risk and included in the risk contact zone. Surface contact areas with a shape uniformity of not less than 0.4 and point contact areas with a radius of not less than 0.15 mm are classified as low-risk. Within the risk contact zone, each area maintains its original grid coordinate range and is marked separately according to the source of the point contact area and the source of the surface contact area.

[0040] The adjacent contact deviation is obtained by calculating the density deviation of the measured area of ​​the risk contact zone based on the density distribution of the contact area. Each high-risk candidate region has two area measures: one is the measured area A_j enclosed by the boundary, and the other is the density coverage area A_d, obtained by multiplying the number of non-zero density grids within the region by the area of ​​a single grid cell. The latter is accumulated cell by cell according to the grids in the contact area density distribution that the actual points fall into, reflecting the true contact range supported by the density distribution. Both area measures are in square millimeters. The relative difference δ_j is the absolute value of the difference between the two measures divided by the larger of the two. This comparison is performed independently for each high-risk candidate region. When δ_j exceeds 0.2, it indicates that the measured boundary of the region is inconsistent with the true contact range reflected by the contact area density distribution, which is likely because the boundary was drawn too wide or too narrow in the concentrated core grid determination stage of the contact area density distribution; when it does not exceed 0.2, the boundary delineation basically matches the density distribution. The deviation contribution of each high-risk candidate region is calculated by multiplying its measured area by δ_j, using the formula C_j = δ_j × A_j, where A_j is the measured area of ​​the j-th high-risk candidate region, δ_j is the relative difference of that region, and C_j is the deviation contribution of that region, all measured in square millimeters. The unit is still area; the larger the area, the greater the actual impact of the boundary delineation error. The adjacent-contact deviation is the sum of the deviation contributions of all high-risk candidate regions within the risk contact area. When summing, no distinction is made between candidate regions that were originally point contact or surface contact regions, as the deviation contribution is already an area value in the same unit, and no additional conversion is needed when adding across categories. The adjacent-contact deviation is driven by both the number of high-risk regions and the degree of deviation of each region's boundary. A severe deviation in a single large area and a slight deviation in multiple small areas may produce similar values, which will be used to convert subsequent grading and scoring into comparable percentage scores.

[0041] Contact deviation is graded and scored based on the amount of adjacent contact deviation to form an adjacent contact assessment value. The grading thresholds are divided into four segments according to the magnitude of the adjacent contact deviation: no more than 0.05 mm², 0.05 to 0.20 mm², 0.20 to 0.60 mm², and more than 0.60 mm². The absolute values ​​of these four thresholds are taken from previous acceptance records of adjacent contact surfaces of similar restorations, using the quartiles of the adjacent contact deviation distribution of clinically deemed acceptable samples. Each threshold corresponds to a base score of 95, 80, 60, and 35 points respectively. The difference between adjacent thresholds increases progressively from 15 to 20 points and then to 25 points, with greater score loss for each level of deviation. When the adjacent contact deviation falls within a certain threshold, the baseline score is linearly interpolated based on the actual position within the segment: if the deviation is located at the lower boundary of the segment, the baseline score for that segment is taken; if it is located at the upper boundary, the baseline score for the next segment is taken; and for other positions, the median value is taken proportionally. This interpolation ensures that restorations of different severity within the same segment do not receive the same score. The adjacent contact assessment value is the score after interpolation, rounded to one decimal place. Therefore, the score ranges from 35 to 95, with the highest score of 95 corresponding to the ideal state of zero deviation and the lowest score of 35 corresponding to the situation where the deviation exceeds the most stringent threshold. The adjacent contact assessment value only reflects the contact quality of the adjacent contact surface itself, and is separate from the neck margin fit, belonging to two independent dimensions. The two values ​​are not added together or averaged; each is retained as an independent conclusion. The original value of the adjacent contact deviation is archived along with the adjacent contact assessment value. When the same restoration has two adjacent surfaces, one mesial and one distal, a separate adjacent touch assessment value is calculated for each surface. The lower of the two values ​​is taken as the representative score for the adjacent touch dimension of the restoration. The score of the higher side is recorded along with the representative score in the adjacent touch assessment value record, so that the technician can determine which side of the adjacent surface needs to be adjusted.

[0042] Step S104: Based on the adjacent contact assessment value, locate the undercut area on the axial surface of each abutment tooth to obtain the undercut distribution of the abutment teeth. Analyze the common undercut boundary of multiple teeth through the undercut distribution of the abutment teeth to determine the permissible offset domain of the insertion path. Based on the permissible offset domain of the insertion path, perform the insertion path deviation angle cross-boundary verification to form the insertion path assessment value.

[0043] In some embodiments, the step of locating the undercut regions of each abutment tooth axial surface based on the adjacent touch assessment value to obtain the undercut distribution of the abutment teeth includes: determining the range of abutment teeth participating in the placement analysis based on the adjacent touch assessment value; calculating the normal vector of each abutment tooth axial surface within the range of the abutment teeth to generate an axial surface normal distribution; performing undercut angle over-limit identification based on the axial surface normal distribution to form undercut regions of each abutment tooth axial surface; and performing position integration for each undercut region of the abutment tooth axial surface to obtain the undercut distribution of the abutment teeth.

[0044] The abutment tooth range for placement analysis is determined based on the interproximal contact assessment values. The interproximal contact assessment values ​​calculated for each of the two proximal surfaces of the restoration are first compared to a score of 60. 60 is the baseline score corresponding to the third threshold in the contact deviation grading. A score below 60 indicates that the measured contact range on that side of the proximal surface significantly deviates from the actual contact reflected by density, and the constraint of adjacent teeth on the restoration in that area cannot be treated as ideal contact. For proximal surfaces with interproximal contact assessment scores below 60, the adjacent teeth, along with the prepared tooth covered by the restoration (i.e., the ground abutment tooth, whose axial point cloud is already included in the intraoral scan data), are included in the abutment tooth range. When the scores for both proximal surfaces are not lower than 60, the abutment tooth range only includes the prepared tooth itself; adjacent teeth only provide contact and do not constitute a physical obstruction in the placement direction. Each tooth included in the range must also meet a height requirement: if the effective height of its axial surface from the cervical margin to the occlusal surface is less than 1.5 mm, the directional constraint provided by that axial surface falls within the scanning angle resolution. After inclusion, noise is treated as a constraint, thus excluding it from the abutment tooth range. Effective height is calculated based on the range of coordinates of the tooth axial surface point cloud in the placement direction. Each tooth within the abutment tooth range is arranged sequentially according to its position on the dental arch, determined by the projection of the centroid of each tooth axial surface point cloud onto the midline of the dental arch. The distance between the centroid projections of adjacent teeth is calculated simultaneously. If the distance is less than the sum of the axial surface radii (equivalent circle radius of the axial surface point cloud cross-section), it is determined that the two tooth axial surfaces occlude each other in the placement direction. Since complete data cannot be obtained for the axial surface point cloud on the occluded side, this segment is marked separately within the abutment tooth range, and its normal vector is extrapolated from the neighboring points on the unoccluded side. Proximal surfaces with a contact score exactly equal to 60 are treated as having a score below 60. This treatment principle follows the same practice in S102 where the higher grade is used when the deviation reaches the grade boundary.

[0045] Normal vectors are calculated for each abutment tooth axial surface within the abutment tooth region to generate the axial normal vector distribution. The normal vectors are calculated point-by-point on each abutment tooth axial surface within the abutment tooth region: a neighborhood with a radius of 0.2 mm is taken centered at the current point. Principal component analysis is performed on all points within this neighborhood. The direction with the smallest eigenvalue among the three principal components is the direction of the normal vector at that point. The smallest eigenvalue means the point cloud spreads narrowest along this direction, and the normal vector of the fitted plane is precisely the direction of the narrowest point cloud spread. A radius of 0.2 mm is chosen because the abutment tooth axial surface itself has a convergence degree of approximately 2 to 6 degrees after preparation. If the radius is too large, the change in the convergence angle across the neighborhood will pull the normal vector towards the average tilt of the middle section of the neighborhood, masking the local true undulations; if the radius is too small, the number of neighborhood points is insufficient to support principal component decomposition. The normal vectors given by principal component analysis have two solutions, positive and negative. The solution pointing away from the centroid of the point cloud on the abutment tooth axial surface is taken, ensuring that all normal vectors within the abutment tooth region uniformly point towards the outer side of the tooth body. The ratio of the smallest eigenvalue to the second smallest eigenvalue reflects whether the neighborhood of a point is closer to a plane or a curve: when the ratio exceeds 0.3, the neighborhood extends along the edge but hardly expands laterally, and the fitted plane is not unique. The normal vector of this point is then obtained by averaging the distances of the points in the neighborhood with acceptable ratios. The weighting range is limited to the axial plane of the same tooth within the abutment tooth range. For segments occluded by adjacent teeth, the normal vector is obtained by spherical linear interpolation of the normal vectors of the unoccluded neighborhoods at both ends of the segment. The interpolation is performed along the great circle arc of a unit sphere to ensure that the result is still a unit vector. The axial plane normal distribution provides the unit normal vector of each point and its angular position on the dental arch. The angular position is measured along the direction of the dental arch with the dental arch midline as the zero-degree reference. In the axial plane normal distribution, the normal vectors of each tooth are grouped independently. Since the axial plane orientations of the three abutment teeth are different from each other, forced averaging would lose the independent constraint information of each tooth on the positioning direction.

[0046] Based on the axial normal distribution, undercut angle exceeding the limit is identified to form undercut regions on the axial surfaces of each abutment tooth. The essence of an undercut is that when a restoration is removed along a certain placement direction, a portion of the axial surface faces the removal direction, causing the restoration to become stuck. The criterion thus falls on the angle between the normal vector and the placement direction. The dot product n·d of the unit normal vector n at a point in the axial normal distribution and the unit vector d of the candidate placement direction is positive, indicating that the surface at that point is biased towards the opposite side of the removal direction and will come into contact with the tooth during removal. The undercut angle is calculated using θ=arcsin(n·d), where θ is the undercut angle at that point, and n·d takes a value between -1 and +1. θ falling within the range of ±90 degrees constitutes an undercut; a positive θ indicates a deeper undercut, and a larger absolute value indicates a deeper obstruction. Points with θ exceeding 2 degrees are considered exceeding the limit. 2 degrees is taken from the combined magnitude of the scanning angle resolution and the fitting residual of the normal vector. Positive undercut angles below 2 degrees cannot be distinguished from the calculation error of the axial normal distribution itself. Candidate direction d is not limited to a single one: Using the placement direction in the design document as the center, all directions within a 15-degree cone angle around it are sampled at 1-degree intervals on the direction sphere, and the above criteria are applied to each. Since the placement direction is precisely the quantity to be determined in this step, pre-determining a single direction would render the criteria meaningless. Exceeding limits are connected in adjacent angular positions given by the axial plane normal distribution. The connectivity criterion selects angular positions that differ by no more than one sampling interval and belong to the same tooth. Each connected exceeding limit point constitutes an undercut region on the axial surface of each abutment tooth. The undercut regions on the axial surfaces of the same tooth are different under different candidate directions. A one-degree deviation in direction can cause a small, originally conforming axial surface to become undercut. Each undercut region on the axial surface of the abutment tooth is given its angular position range, the start and end values ​​of its height along the placement direction, and the maximum value of θ within the range of its candidate direction.

[0047] The location of undercut regions on the axial surfaces of each abutment tooth is integrated to obtain the distribution of undercuts. The previous sub-step generated a set of undercut regions on the axial surfaces of each abutment tooth for each candidate placement direction. Integration first groups these regions together according to the candidate direction. Several undercut regions on the axial surfaces of the same abutment tooth under the same candidate direction and belonging to the same tooth are kept independent and unified under the local coordinate system of that tooth, with the origin at the centroid of the axial surface point cloud and the vertical axis at the placement direction. Integration is performed tooth by tooth: the angular position range of all undercut regions on the axial surfaces of the tooth is projected onto a circumferential unfolded diagram centered on the centroid. The unfolded diagram is flattened by cutting the three-dimensional axial surface along the cervical margin. The horizontal axis represents the angle around the tooth, and the vertical axis represents the height in the placement direction. The undercut regions appear as patches. Patches with consecutive angles and overlapping heights under the same candidate direction are merged into a continuous undercut band. Merging is only performed within a half-degree angular tolerance to avoid mistakenly merging two unconnected undercuts into one. The abutment tooth undercut distribution archives the positions and depths of all undercut zones on the circumferential unfolded diagram, classifying them by tooth and retaining the arch sequence of each tooth. The depth is based on the maximum value of the undercut angle θ, and each tooth is stored in layers according to candidate directions. The width of the undercut zone is also calculated, taking the angular span of the zone on the horizontal axis of the unfolded diagram. Narrow and deep undercut zones correspond to sharp local obstructions, while wide and shallow undercut zones correspond to large-area poor fit with gentle surfaces. The abutment tooth undercut distribution records the width and depth as two independent fields, which are only retained as morphological descriptions of the undercut zones along with the distribution for interpreting the cause of obstructions in the reporting process, and do not participate in the feasibility determination of intersection. The number and position of undercut zones in different candidate directions for the same tooth vary in the abutment tooth undercut distribution. The further the direction deviates from the designed placement direction, the more numerous and deeper the undercut zones. Subsequent tooth-by-tooth breakdown and hierarchical intersection are carried out layer by layer along these candidate directions.

[0048] In some embodiments, determining the permissible offset domain of the insertion path by analyzing the common undercut boundary of multiple teeth through the undercut distribution of the abutment teeth includes: splitting the undercut distribution of the abutment teeth into sets of single-tooth undercut zones according to the abutment teeth; performing a multi-abutment tooth stepwise intersection operation on the single-tooth undercut zone sets to determine the common undercut boundary of multiple teeth; extracting the maximum continuous insertable range based on the common undercut boundary of multiple teeth to form a permissible offset reference domain; and using the permissible offset reference domain to perform shrinkage margin correction to determine the permissible offset domain of the insertion path.

[0049] The undercut distribution of abutment teeth is broken down into individual tooth undercut bands. For example... Figure 2As shown, the undercut distribution of abutment teeth was previously a stacked whole, layered by tooth and then by candidate direction. This sub-step aims to cut it along the dimension of abutment tooth 2, making the undercut information of each abutment tooth 2 a separately usable copy. The splitting first reads the tooth position order in the abutment tooth undercut distribution. This order was previously determined by the projection of the centroid of each abutment tooth 2 onto the dental arch midline. The splitting is strictly performed in this order, and each split copy inherits its original order on the dental arch, with the adjacent relationships remaining locked before and after the splitting. For each tooth, the undercut bands of all candidate direction layers under its name are extracted. Although the position and depth of the undercut bands of the same tooth under different candidate directions are different, they share the same set of local coordinate systems of the tooth body. The coordinate system is also brought out during the splitting, so that the set of single-tooth undercut bands can still correspond back to the original axial point cloud of the tooth. For each tooth, an additional direction index table is attached. Each row in the table maps the sampling number of a candidate placement direction to the number and maximum depth of the undercut bands of that tooth under that direction. The direction index table allows for direct alignment of undercut bands of different teeth by direction sampling number when finding the common undercut boundary of multiple teeth. The retrieval path is shortened from traversing the entire distribution to looking up a single record in the table. The extracted single-tooth undercut band set is an independent component for each tooth, with each set containing its own coordinate system and a complete copy of the undercut band. The adjustment of an undercut band of a tooth only affects its own copy and is transparent to other teeth. Therefore, teeth can participate in successive intersections as independent operands. The same sampling number in the direction index table is universal across teeth. The number itself is taken from the sampling position of the candidate direction on the direction sphere and is consistent across teeth, ensuring that alignment by number corresponds to the same spatial direction rather than just the same position.

[0050] The common undercut boundary of multiple teeth is determined by a multi-tooth hierarchical intersection operation on the single-tooth undercut band set. For a candidate placement direction to become a feasible extraction direction, the single-tooth undercut band sets of all abutment teeth must be free of undercuts in that direction. If an undercut exists in the region of any tooth, extraction along that direction will be blocked by that tooth. Therefore, the hierarchical intersection is performed along the candidate direction dimension. For each candidate direction, the single-tooth undercut band set of each tooth is checked to see if there is an undercut below the direction layer. If there is an undercut in any tooth, the direction is determined to be infeasible. The hierarchical indexing operation proceeds sequentially according to the tooth sequence: first, the two teeth with the first position are selected, and it is determined whether they are simultaneously free of undercuts for each candidate direction, resulting in a table of feasible directions for two teeth; then, the feasible directions corresponding to the single-tooth undercut band set of the third tooth are intersected with this table to obtain a narrower table of feasible directions for three teeth; this process is repeated until all abutment teeth are included. Each tooth included only narrows the table, and each additional tooth adds a constraint. If the feasible direction list becomes empty after a certain level of intersection calculation, it means that there are no candidate directions that can simultaneously eliminate undercuts in the teeth that have been incorporated. The calculation stops immediately, and it is determined that the current combination of abutment teeth has no common feasible placement direction. Instead, the tooth that caused the list to become empty and its single-tooth undercut band set are output as the main obstacle. The multi-tooth common undercut boundary 4 is the boundary of the complement of the final feasible direction list on the direction spherical projection 1. The feasible directions form a connected region on the direction spherical projection 1. The outline of this connected region is the multi-tooth common undercut boundary 4. All directions within the outline are feasible, and the parts outside the outline that are pushed out by the undercut band of a single abutment tooth are the infeasible direction sectors 3. The multi-tooth common undercut boundary 4 records the direction coordinates of each point on the outline segment by segment and marks which tooth's infeasible direction sector 3 pushes out each segment of the boundary, so that every narrowing of the boundary can be traced back to the specific constraining tooth.

[0051] The maximum continuous positionable range is extracted based on the common undercut boundary of multiple teeth to form the permissible offset reference domain. The common undercut boundary of multiple teeth encloses one or more feasible directional connected areas on the directional sphere. If the restoration can be positioned from multiple unconnected directions, these directions appear as separate connected areas on the sphere. The extraction process first calculates the solid angle area of ​​each of these connected areas; the larger the area, the wider the permissible positional directional range. The area with the largest area is taken as the maximum continuous positionable range 5. Clinically, the restoration can only be positioned along a specific direction. Several unconnected feasible areas cannot transition continuously, and forcibly merging them will result in an unworkable positional path. The second largest feasible area that is discarded is still retained along with its solid angle area and marked as a candidate positional direction area. When the optimal area is narrowed to unusable due to margin correction, it can be used as a fallback. After determining the maximum continuous positioning range, the point with the largest geodesic distance from the boundary within the feasible area bounded by the common undercut boundary of the multi-tooth tooth is identified as the inscribed center 6. The direction of the inscribed center 6 is the direction least likely to slip off the boundary due to error, and is considered the optimal candidate for the design positioning direction. The permissible offset reference domain 7 is centered on the inscribed center 6 and has an angle equal to the radius of the inscribed circle, forming a disk on the direction sphere. Any direction within this disk falls within the feasible area bounded by the common undercut boundary of the multi-tooth tooth, allowing all abutment teeth to be positioned without undercuts. The radius of the permissible offset reference domain directly quantifies how many degrees the positioning direction can deviate from the optimal candidate while still being feasible. The larger the angle, the more lenient the accuracy requirements for the positioning direction during fabrication and insertion. At this point, the permissible offset reference domain only reflects geometric feasibility; the additional shrinkage caused by the material's elastic limit and the adhesive film thickness will be added in the margin correction.

[0052] The permissible offset reference domain is used to perform shrinkage margin correction to determine the permissible offset domain for placement. The permissible offset reference domain provides a purely geometrically feasible direction disk, without considering the actual constraints of the material and adhesive during placement. The correction is to convert these constraints into shrinkage of the disk angle. The first shrinkage comes from the adhesive film thickness: during placement, the adhesive layer occupies the gap between the restoration and the abutment tooth. The closer the placement direction is to the boundary of the feasible zone, the tighter the marginal fit, and the thinner the film thickness is compressed. When it becomes too thin, it cannot spread evenly. Therefore, the angular shrinkage is calculated by dividing the minimum reliable film thickness by the marginal placement path length and deducted from the radius of the reference domain angle. The second shrinkage comes from the elastic deformation tolerance of the restoration: the amount of elastic expansion that the metal or ceramic abutment can withstand during placement is limited. The further away from the optimal direction, the greater the instantaneous expansion required on the placement path. Directions exceeding the material's elastic limit, even if geometrically feasible, will result in porcelain chipping or permanent deformation during placement. Based on this, another shrinkage amount is deducted. The larger of the two contraction amounts is taken as the final contraction amount. Both constrain the same edge margin; the tighter one has already capped the usable angle, and the other, even if looser, cannot push the cap back. When the angle after contraction is less than 1 degree, the alternative positioning direction piece is checked: if the angle of the alternative piece is still greater than 1 degree after being corrected with the same margin, the alternative piece replaces the optimal piece and the positioning path allowable offset domain 8 is regenerated; if the alternative piece is also narrowed to within 1 degree or there is no alternative piece, the positioning path allowable offset domain 8 accurately gives the narrow angle of the optimal piece and adds a high-risk insertion label for the evaluation stage. The positioning path allowable offset domain is ultimately expressed by two items: the center direction and the angle radius. The former determines the positioning direction, and the latter determines the allowable offset margin in that direction.

[0053] Based on the permissible offset domain of the placement path, a deviation angle exceeding the limit is verified to generate the placement path evaluation value. The actual placement direction marked in the restoration design document is extracted and compared with the center direction of the permissible offset domain. The geodesic angle between the two on the direction sphere is recorded as the design deviation angle φ, which is the angle by which the actual designed placement direction deviates from the optimal candidate direction. The design deviation angle φ is compared with the angular radius φ_m of the permissible offset domain of the placement path: if it does not exceed φ_m, the designed placement direction falls within the permissible offset domain of the placement path, and placement is geometrically feasible with room for error; if it exceeds, it has exceeded the permissible range, and placement along this direction will encounter obstruction or material limitations. The verification is scored as follows: When the design deviation angle does not exceed φ_m, the positioning path evaluation value is calculated using the formula G=100-30×(φ÷φ_m), where φ is the design deviation angle, φ_m is the radius of the permissible offset domain of the positioning path, and G is the positioning path evaluation value. When φ is zero, G receives a full score of 100 points; when φ equals φ_m, G receives 70 points. If the design deviation angle exceeds φ_m, 5 points are deducted for every tenth of the excess, up to a minimum of 20 points. The more the deviation exceeds the limit, the greater the deduction, but a non-zero minimum is retained to distinguish different degrees of deviation. For repairs with a permissible offset domain angle of less than 1 degree, the permissible range is already extremely narrowed by the material allowance. In this case, even a small design deviation angle is prone to exceeding the limit. Verification will not provide sufficient additional positioning leeway, and the deduction will be based on the narrow feasible range rather than a large deviation in the design direction. The positioning path assessment value is calculated by rounding the above scores to one decimal place. The design deflection angle φ and the angular radius φ_m are appended to the positioning path assessment value so that reviewers can easily identify the extent of the violation without recalculation. The positioning path assessment value specifically characterizes the positioning direction dimension. Neck edge tightness and adjacent contact each have independent scores. The scores for these three dimensions are combined for the first time in the S105 violation review.

[0054] Step S105: Based on the evaluation value of the placement path, mark the unqualified areas to generate a set of marked areas, analyze the marked area set to form the evaluation completion amount for the missing areas covered by the evaluation, and perform over-limit trigger review based on the evaluation completion amount to generate the quality test result of the oral prosthesis.

[0055] Specifically, a set of marked areas is generated by marking non-compliant areas based on the in-situ path assessment value. The in-situ path assessment value, along with the adjacent contact assessment value, and the fit level benchmark and judgment deviation obtained in S102, are read in together. Each of the three dimensions has an independent pass line, with 70 points as the boundary. If the score of any dimension is lower than the pass line, a non-compliant marking is triggered. The score of the fit dimension is converted from the relative position of the judgment deviation within the corresponding level range: Level I corresponds to 95 to 80 points, Level II corresponds to 80 to 60 points, Level III corresponds to 60 to 35 points, and Level IV is fixed at 35 points. The closer the judgment deviation is to the upper boundary of the level, the closer the score is to the lower limit of the range. The conversion logic is consistent with the linear interpolation from the adjacent contact deviation to the adjacent contact assessment value. Thus, the fit score is on the same percentage scale as the other two dimensions. The annotation process doesn't simply label the entire restoration as unacceptable. Instead, it traces back to the specific geometric location upon which the score for that dimension was based. For example, an unacceptable fit is traced back to the lowest-scoring deviation segment on the cervical margin; an unacceptable proximal contact is traced back to the risk contact area; and an unacceptable placement path assessment is traced back to the undercut of the main obstructing tooth causing the design deviation to exceed the limit. Each traced geometric range constitutes an annotation unit. Each annotation unit records its corresponding dimension, its coordinate range on the restoration surface, and the triggering score. The coordinate range is uniformly converted to the overall scan point cloud coordinate system, allowing annotation units from different dimensions to be superimposed and displayed on the same 3D model. The same dimension may trigger multiple annotation units; for example, there might be several deviation segments on the cervical margin, each below the acceptable line. Each segment becomes an independent annotation unit and they are not merged when entering the annotation area set. The annotation area set gathers annotation units triggered by all dimensions, grouped by dimension, and within each group arranged from lowest to highest score, allowing the reviewer to first see the most problematic areas. Each labeled unit in the labeled area set also carries an over-limit range, which is the difference between the trigger score of the labeled unit and the pass line of its dimension. The over-limit range is only comparable within the same dimension.

[0056] In some embodiments, the step of parsing and evaluating the missing coverage areas of the labeled region set to form evaluation completion quantities includes: performing coverage density sparsity analysis on the labeled region set to obtain an uncovered evaluation dimension set; locating the corresponding regions of the uncovered evaluation dimension set to determine the evaluation coverage missing areas; performing supplementary evaluation operations on the evaluation coverage missing areas according to dimensions to generate missing area evaluation values; and aggregating the missing area evaluation values ​​according to dimensions to form evaluation completion quantities.

[0057] The set of uncovered evaluation dimensions is obtained by performing sparsity analysis on the marked area set. A complete list of evaluation dimensions is pre-defined for the entire test: cervical margin occlusion is divided into four equal zones (buccal, lingual, mesial, and distal) according to tooth anatomy, each counted as one dimension. The zone boundaries are defined by the four equal points of the cervical margin reference curve arc length. Proximal contact is counted as one dimension for the mesial and distal surfaces. The path of insertion is counted as a separate dimension, totaling seven evaluation dimensions. Each dimension corresponds to a specific spatial area on the restoration surface. The marked units in the marked area set are records of non-compliant areas. Conversely, if an area that should be covered by a certain evaluation dimension has no marked unit in the marked area set and the corresponding original score is missing, it indicates that this dimension was not effectively evaluated in this test. Sparsity analysis is performed dimension by dimension: the spatial area corresponding to the dimension is extracted, and the proportion of scan points falling within the area and actually participating in the scoring calculation is counted relative to the total number of points in the area. This is the coverage density of the dimension. If it is less than 0.6, it is considered sparse coverage, and this dimension is recorded in the uncovered evaluation dimension set. Sparsity often stems from missing point clouds in the scanned area or from skipping the scoring in a previous step due to insufficient samples. These dimensions often lack corresponding annotation units in the labeled area set. The uncovered evaluation dimension set collects all dimensions with sparse coverage, recording their dimension identifier, corresponding spatial region range, and measured coverage density for each dimension. This allows for priority processing of the dimensions with the lowest density and the greatest need for supplementary measurement during supplementary evaluation. Within the uncovered evaluation dimension set, dimensions are arranged from lowest to highest coverage density, with the lowest density being included in the supplementary evaluation first. Slight overlap between the spatial regions corresponding to each dimension is allowed. The buccal and mesial regions share a small band at the tooth surface corners. Scan points within the overlapping band are counted as complete in the coverage density of both related dimensions, with the same scan point contributing coverage to both dimensions simultaneously.

[0058] For example, the step of locating the corresponding region of the uncovered evaluation dimension set to determine the evaluation coverage missing area includes: generating a dimension region mapping table by matching the three-dimensional region type corresponding to each dimension of the uncovered evaluation dimension set; expanding the retrieval according to each three-dimensional region type based on the dimension region mapping table to obtain a candidate missing area set; performing isolated region filtering processing on the candidate missing area set to form a valid missing area set; and performing region merging based on the valid missing area set to determine the evaluation coverage missing area.

[0059] A dimension region mapping table is generated by matching the corresponding 3D region types for each dimension in the uncovered evaluation dimension set. Matching is performed dimension by dimension, taking the identifier and spatial range of that dimension from the uncovered evaluation dimension set, and comparing the geometry of the range with the four 3D region types divided according to the anatomical morphology of the overall 3D model of the restoration. The closest match is identified as the 3D region type corresponding to that dimension. Among the four 3D region types, the cervical margin ring type is a narrow ring surface within 0.5 mm above and below the cervical margin reference curve; the proximal plate type is an approximately planar plate with a normal deviation of more than 60 degrees from the insertion direction on both the mesial and distal sides; the axial cylindrical type is a cylindrical surface with a normal deviation between 30 and 60 degrees around the tooth; and the occlusal surface type is an undulating surface of the cusp and fissure with a normal deviation of no more than 30 degrees. This type is only used for partition complement and does not participate in any dimension matching. The narrow and long ring range of the cervical margin occlusion type matches the cervical margin ring type; the plate-like range of the proximal contact type matches the proximal plate type; and the insertion path type, which covers the entire axial surface, matches the axial cylindrical type. When a spatial dimension spans two shapes and cannot be fully accommodated by a single type, the type with the higher percentage of points within the range is identified as the primary type. Simultaneously, the secondary type is also recorded in the dimensional region mapping table to ensure that cross-type portions are not missed during retrieval. These cross-type dimensions often appear at tooth surface corners. The dimensional region mapping table records a dimension identifier and its associated 3D region type row by row, with primary and secondary types listed in separate columns. Each type also includes a retrieval threshold: 0.5 for annular shapes, 0.6 for sheet shapes, and 0.7 for cylindrical shapes. The rows are arranged in the same order as the dimensions in the uncovered evaluation dimension set. The ratio of the lengths of the three principal axes of the point cloud recorded in the uncovered evaluation dimension set is the basis for shape comparison: annular shapes show one long and two short axes connected end-to-end; sheet shapes show two long and one short axes; and cylindrical shapes have two axes close together and extend axially.

[0060] Based on the dimensional region mapping table, the search is expanded according to each 3D region type to obtain a set of candidate missing regions. The search is expanded dimensionally: the main type and subtype of the dimension are read from the dimensional region mapping table. The region corresponding to the main type is used as the main search range, and the region corresponding to the subtype is used as a supplementary search range. Together, they constitute the complete scanning interval of the dimension. The search proceeds within each type of 3D region according to the inherent direction of the type: for annular regions, the search is carried out segment by segment along the periodontal angle; for plate regions, the search is carried out block by block along the two orthogonal directions of the plane; and for cylindrical regions, the search is carried out grid by grid along the axial and circumferential directions. The direction conforms to the geometry of each type, avoiding the use of a uniform rectangular grid to cover regions with large shape differences, which would result in empty scanning at bends. At each location scanned, the local coverage ratio is calculated using the formula η = ρ_a ÷ ρ_t, where ρ_a is the measured effective point density at the current location, ρ_t is the theoretical full coverage density calculated based on the downsampled voxel side length (a voxel side length of 0.02 mm corresponds to a theoretical density of approximately 2500 points per square millimeter), and η is the local coverage ratio. Points with η lower than the preset retrieval threshold in the dimensional region mapping table for that type are marked as candidate missing points. The threshold is more lenient for annular types because the narrow neckline is difficult for the scanner to cover evenly, while it is more lenient for cylindrical types because the density baseline is higher when the axial plane faces the scanning head. Adjacent candidate missing points are connected along the retrieval direction to form a segment, and each segment constitutes a candidate missing region. If a single isolated candidate missing point has no adjacent missing points, it is not temporarily segmented and is left for the filtering stage to determine. The candidate missing region collection gathers candidate missing regions detected across all dimensions and the entire search range, recording each one's dimension, 3D region type, and start and end positions along the direction. Detections from the main and supplementary search ranges of the same dimension are stored side-by-side, without determining overlap. The candidate missing region set at this point is a coarse search result that has not been filtered, and it contains false missing regions caused by isolated noise points. The number of detected entries is usually more than the final number of entries.

[0061] The candidate missing region set is filtered to form a valid missing region set. Each candidate missing region within the set is verified to be a true missing region. The first filtering is based on area: the start and end positions of each candidate missing region are converted to their actual area. Regions with excessively small areas are mostly caused by individual noise points or scanning jitter. A lower limit for the area is set accordingly: approximately 0.3 mm arc length for ring-shaped regions, approximately 0.2 square millimeters for sheet-shaped regions, and somewhere in between for cylindrical regions. The lower limit corresponds to the minimum continuous sampling area required for normal evaluation of this type. Candidate missing regions with areas below the lower limit are considered isolated regions and are filtered out of the candidate missing region set. Filtering only affects the isolated region itself; the judgment of other regions in the candidate missing region set is independent. Candidate missing regions with the required area undergo an adjacency check: if they are densely surrounded by valid evaluation points but only have sporadic defects inside, it indicates that this is an occasional empty point in a fully evaluated area, and it is also filtered out. Retesting such areas does not improve overall coverage. Candidate missing regions that pass both filters retain their start and end positions, dimensions, and 3D region types as is, and are added to the valid missing region set. The valid missing region set records each filtered missing region and its area, allowing the region merging stage to prioritize merging missing regions with similar areas and adjacent locations. Missing regions detected in the main search range and supplementary search range within the same dimension are still listed separately here; the merging operation is handled uniformly by the region merging stage based on geometric adjacency. This stage is only responsible for screening for true and false regions on a region-by-region basis. Isolated regions that are filtered out, along with the filtering criteria, are separately added to the filtering log. Reviewers can use this log to trace why a particular region was not included in the supplementary test range. The filtering log is stored independently of the valid missing region set.

[0062] The evaluation coverage missing regions are determined by merging regions based on the effective missing region set. Missing regions in the effective missing region set come from different dimensions and search ranges, some of which are geometrically adjacent or even partially overlapping. Merging aims to combine these scattered records, which are essentially the same missing location, into a single complete region, preventing the same surface from being split into several pieces for supplementary measurement. Merging is performed pairwise based on geometric adjacency: if two missing regions in the effective missing region set share a boundary or the shortest distance between their boundaries is less than one sampling interval, they are considered adjacent and merged into a larger connected missing region. The boundary after merging is the outer contour of the union of the two boundaries; duplicate sampling points caused by internal overlap are only counted once. Merging is performed round by round. In each round, adjacent missing regions determined in that round are merged pairwise, and the result participates in the next round's evaluation, until no pair meets the adjacency condition in a certain round. This round-by-round process ensures that a series of consecutive missing regions are eventually merged into a single block. Isolated missing regions in the effective missing region set that never find adjacent merging objects are still directly included in the evaluation coverage missing region after all merging rounds. Cross-dimensional missing regions can be merged. At the corner of the same tooth surface, the cervical margin dimension and the adjacent contact dimension may each detect a missing region. Geometrically, they are the same location. After merging, they belong to the shared dimension, and a single supplementary scan can simultaneously satisfy two-dimensional coverage. To evaluate the coverage missing region, all remaining connected missing regions after merging are taken, and their complete boundaries, the set of dimensions covered, and the total area are given for each region. The boundary coordinates are still in the same system as the overall scan point cloud. The dimensional set of each region in the evaluation coverage missing region may contain one or more dimensions. The total area of ​​regions containing multiple dimensions is included in the supplementary measurements of all involved dimensions on a whole-region basis. A single supplementary scan can simultaneously fill multiple dimensional coverage gaps.

[0063] For areas with missing evaluation coverage, supplementary evaluation calculations are performed according to dimensions to generate evaluation values ​​for the missing areas. The outer layer traverses each region of the missing evaluation coverage, while the inner layer traverses each dimension within the set of dimensions contained in that region. Regions containing two dimensions undergo two independent evaluation calculations on the same surface. The number of regions and the set of dimensions together determine the total number of iterations. Before the calculation, all points within the boundaries of each block of the missing evaluation coverage are taken from the overall scan point cloud of the restoration as input. The original point cloud of the missing area surface has already been acquired in the six-view scan. Previously, the evaluation calculation could not be completed only due to insufficient local points, so the original points are retrieved and the calculation is repeated. Calculations are selected according to dimension category: the neck margin fit dimension is re-run to determine the bidirectional distance difference of the edge contour to obtain the fit deviation in the missing area; the adjacent contact dimension is re-run to verify the point-to-surface contact density to obtain the adjacent contact deviation at that location; and the placement path dimension is recalculated to determine the inverted concave angle of the axial surface towards the placement direction to obtain the degree of local placement obstruction. Each of the three types of operations uses the algorithms and thresholds already defined in its main step, but the input range is narrowed to the currently evaluated missing areas, ensuring consistency between the supplementary evaluation and the main evaluation criteria. The results can be directly incorporated into the original dimension scores without causing scale conflicts. The missing area evaluation values ​​are recorded block by block and dimension by dimension, including the calculated deviation, the converted percentage score, and the area of ​​the missing area. The conversion uses the same mapping curve from the deviation of the main step to the score for each dimension. The missing area evaluation values ​​only cover those sparsely evaluated parts, complementing and not repeating the scores calculated in the main step. When a missing area contains multiple dimensions, its missing area evaluation values ​​are split into multiple lines according to the dimensions, each line independently corresponding to one dimension, facilitating their incorporation back into the original score for that dimension.

[0064] The evaluation values ​​of missing areas are aggregated along dimensions to form the evaluation completion quantity. Aggregation gathers results scattered across various missing areas belonging to the same evaluation dimension, providing a complete supplementary conclusion for each evaluation dimension. A collection slot is built for each dimension: all missing area evaluation values ​​are traversed and placed into the corresponding slot according to their dimension label. Entries for the same dimension scattered across various missing pieces are thus grouped into one slot. Each entry is sorted according to the arc length of its corresponding missing piece on the cervical margin or proximal surface. End-to-end entries are pieced together to form a continuous supplementary evaluation coverage for that dimension. When multiple entries for the same dimension correspond to adjacent missing pieces, their evaluation conclusions are synthesized into a unified conclusion for that segment by weighted average of the missing piece area. Larger areas have higher weights and are more representative of the true situation for that segment. Missing pieces that are not adjacent retain their own independent conclusions, arranged in order of tooth surface position. The evaluation completion quantity provides the supplementary evaluation coverage and corresponding conclusion for each dimension. The coverage is expressed as the area ratio on the overall model; the ratio represents the proportion of the newly filled portion to the expected evaluation range of that dimension. A higher ratio indicates a larger gap in the previous evaluation of that dimension. The evaluation completion quantity and the original score of the main step belong to the same dimension and use the same criteria. During the data collection phase, they are presented side by side, with the main evaluation conclusion on the left and the supplementary evaluation conclusion on the right. Reviewers can immediately determine whether the conclusion of that dimension has changed direction after the gaps are filled. When the supplementary evaluation coverage of a certain dimension reaches more than 40% of the expected range, the evaluation completion quantity will be marked with a large-scale supplementary test indicator for that dimension, indicating that the previous main evaluation conclusion was based on less than 60% of the valid data, and its credibility needs to be reviewed together with the evaluation values ​​of the missing area.

[0065] The quality inspection results of the dental prosthesis are generated based on the evaluation completion quantity and the limit trigger review. The evaluation completion quantity is first merged with the original score of the main step by dimension, and weighted according to the coverage ratio of the supplementary evaluation: the higher the ratio, the greater the weight of the supplementary test conclusion; for dimensions with a very low ratio, the original score still dominates, and the supplementary test only makes minor adjustments. The two are weighted to synthesize the final dimension score for that dimension. Limit trigger review checks the final dimension score dimension by dimension: those below the pass line trigger a quality limit violation. Limit violation does not directly determine the scrapping of the prosthesis, but the dimension, along with the non-compliance geometric location and the limit violation range, is packaged into a review prompt. The limit violation range is taken from the merged final dimension score, not the main score. When the same prosthesis triggers multiple review prompts, they are arranged from largest to smallest limit violation range. The manual reviewer prioritizes the one with the largest deviation, and the prompt is included in the dental prosthesis quality inspection results. Even if the dimension with a large range supplementary test mark in the evaluation completion quantity does not violate the limit, a low confidence prompt is generated, indicating that the effective data on which the conclusion is based is insufficient and the reliability is low. The quality inspection results of dental prostheses are summarized across three dimensions: final score, review prompts, and low confidence prompts. An overall judgment is given, with the most severe judgment among the three dimensions: any dimension exceeding the limit requires rework; no limit exceeding the limit but a low confidence prompt requires review; all dimensions are acceptable with no prompts, indicating a pass. For example, a dental prosthesis quality inspection result might be: Occlusion dimension 78 points, acceptable; Proximal contact dimension 52 points, triggering a limit exceeding the limit, prompting a return to a risky contact area on the mesial proximal surface, suggesting adjustment of the proximal surface shape; Placement path dimension 85 points, acceptable but with a low confidence prompt, approximately 30% of the area depends on this retest; Overall judgment: rework required. The technician can then locate the mesial proximal surface in the design software using the prompted coordinates and make adjustments.

[0066] To implement the above-described method embodiments, a digital design quality inspection method for dental prostheses is proposed to achieve the corresponding functional and technical effects. See also... Figure 3 , Figure 3 This paper illustrates a structural block diagram of a digital design quality inspection system 300 for dental prostheses according to an embodiment of this application, comprising: The point cloud acquisition module 301 is used to acquire three-dimensional point cloud data of the oral prosthesis and to perform bidirectional nearest point distance difference direction discrimination on the three-dimensional point cloud data to form edge fit deviation features. The fit scoring module 302 is used to analyze the edge fit deviation characteristics to determine the clinical fit grading and fit level benchmark, identify curvature confidence weighted deviation nodes based on the fit level benchmark to obtain sub-item weight compensation values, and verify the allowable fluctuation range of the fit level benchmark through the sub-item weight compensation values ​​to determine the dynamic detection benchmark value. The adjacent contact verification module 303 is used to determine the adjacent contact area range by growing the gap region based on the dynamic detection benchmark value, to verify the point-to-surface contact density based on the adjacent contact area range to obtain the adjacent contact deviation, and to perform contact deviation grading and scoring analysis based on the adjacent contact deviation to form an adjacent contact evaluation value. The positioning verification module 304 is used to locate the undercut area of ​​each abutment tooth axial surface based on the adjacent contact assessment value to obtain the undercut distribution of the abutment teeth, analyze the common undercut boundary of multiple teeth through the undercut distribution of the abutment teeth to determine the permissible offset domain of the positioning path, and perform positioning path deviation angle cross-boundary verification based on the permissible offset domain of the positioning path to form the positioning path assessment value. The report output module 305 is used to generate a set of marked regions by marking unqualified areas based on the evaluation value of the placement path, analyze the evaluation coverage missing areas of the marked region set to form an evaluation completion amount, and generate the oral prosthesis quality test result by performing over-limit trigger review based on the evaluation completion amount.

[0067] The aforementioned digital design quality inspection system 300 for dental prostheses can implement a digital design quality inspection method for dental prostheses as described in the above-described method embodiments. The options in the above method embodiments are also applicable to this embodiment and will not be detailed here. The remaining contents of this application's embodiments can be referred to the contents of the above method embodiments, and will not be repeated in this embodiment.

[0068] The purpose of the above embodiments is to reproduce and derive the technical solution of the present invention by way of example, and to fully describe the technical solution, purpose and effect of the present invention. The purpose is to enable the public to have a more thorough and comprehensive understanding of the disclosure of the present invention, and not to limit the scope of protection of the present invention.

Claims

1. A method for quality inspection of digital design of dental prostheses, characterized in that, include: Acquire three-dimensional point cloud data of the oral prosthesis, and perform bidirectional nearest point distance difference direction discrimination on the three-dimensional point cloud data to form edge fit deviation features; The clinical grading of occlusion is determined by analyzing the edge occlusion deviation characteristics to establish an occlusion level benchmark. Based on the occlusion level benchmark, curvature confidence weighted deviation nodes are identified to obtain sub-item weight compensation values. The allowable fluctuation range of the occlusion level benchmark is verified by the sub-item weight compensation values ​​to determine the dynamic detection benchmark value. Based on the dynamic detection benchmark value, the gap region is grown to determine the adjacent contact area range. Based on the adjacent contact area range, the point-to-surface contact density is verified to obtain the adjacent contact deviation. Based on the adjacent contact deviation, the contact deviation is graded and scored to form the adjacent contact rating value. Based on the adjacent contact assessment value, the undercut area of ​​each abutment tooth axial surface is located to obtain the undercut distribution of the abutment teeth. The common undercut boundary of multiple teeth is analyzed through the undercut distribution of the abutment teeth to determine the permissible offset domain of the insertion path. Based on the permissible offset domain of the insertion path, the insertion path deviation angle cross-boundary verification is performed to form the insertion path assessment value. Based on the assessment value of the placement path, the non-compliant areas are marked to generate a set of marked areas. The marked areas are analyzed to form an evaluation completion amount for the missing areas covered by the evaluation. Based on the evaluation completion amount, the over-limit trigger review is performed to generate the quality test result of the oral prosthesis.

2. The method according to claim 1, characterized in that, The step of determining the direction of the bidirectional nearest point distance difference in the edge contour of the three-dimensional point cloud data to form edge fit deviation features includes: Functional edge reverse localization extraction is performed on the three-dimensional point cloud data to obtain an edge contour point set; Based on the edge contour point set, calculate the bidirectional nearest point distance to generate a forward distance set and a reverse distance set; The bidirectional distance difference distribution is obtained by performing point-by-point difference calculation between the forward distance set and the reverse distance set; Based on the bidirectional distance difference distribution, the edge overhang and underextended segments are identified to form edge sealing deviation characteristics.

3. The method according to claim 1, characterized in that, The step of identifying curvature confidence-weighted deviation nodes based on the tightness level benchmark to obtain sub-item weight compensation values ​​includes: Based on the aforementioned fit level benchmark, deviation exceeding the limit judgment is performed to obtain the deviation node set; A local curvature confidence assessment is performed on the set of off-nodes to form a measurement confidence distribution; The set of off-nodes is subjected to confidence weighting using the measured confidence distribution to form curvature confidence weighted off-nodes; For the curvature confidence weighted deviation nodes, the sub-item weight compensation value is obtained by assigning weights according to the deviation magnitude gradient.

4. The method according to claim 1, characterized in that, The step of verifying the point-to-surface contact density based on the adjacent contact area range to obtain the adjacent contact deviation includes: Perform axial projection density statistics on the adjacent contact area range to generate a contact area density distribution; Based on the density distribution of the contact area, a density concentration analysis is performed to obtain the point contact area and the surface contact area; Local stress concentration risk verification is performed on the point contact area and the surface contact area to form a risk contact zone; The adjacent contact deviation is obtained by calculating the density deviation of the measured area of ​​the risk contact zone based on the density distribution of the contact area.

5. The method according to claim 1, characterized in that, The step of locating the undercut regions on the axial surface of each abutment tooth based on the adjacent contact assessment value to obtain the undercut distribution of the abutment teeth includes: The range of abutment teeth participating in the placement analysis is determined based on the adjacent contact assessment values; Calculate the normal vector of each abutment tooth axial surface within the abutment tooth range to generate the axial surface normal distribution; Based on the axial normal distribution, undercut angle exceedance identification is performed to form undercut regions on the axial surface of each abutment tooth; The undercut distribution of the abutment teeth is obtained by integrating the positions of the undercut regions on the axial surfaces of each abutment tooth.

6. The method according to claim 1, characterized in that, The step of determining the permissible offset domain of the insertion path by analyzing the common undercut boundary of multiple teeth through the undercut distribution of the abutment teeth includes: The set of single-tooth undercut zones is obtained by separating the undercut distribution of the abutment teeth according to the abutment teeth; Perform multi-base tooth stepwise intersection operation on the single tooth undercut band set to determine the common undercut boundary of multiple teeth; Based on the common undercut boundary of the multi-tooth teeth, the maximum continuous positionable range is extracted to form the permissible offset reference domain; The allowable offset domain is determined by performing shrinkage margin correction using the allowable offset reference domain.

7. The method according to claim 1, characterized in that, The process of generating evaluation completion data for the missing regions covered by the labeled region set includes: The set of uncovered evaluation dimensions is obtained by performing coverage density sparsity analysis on the labeled region set. The missing evaluation coverage area is determined by locating the corresponding region of the uncovered evaluation dimension set. For the missing evaluation areas, perform supplementary evaluation operations according to dimensions to generate evaluation values ​​for the missing areas; The evaluation values ​​of the missing areas are aggregated by dimension to form the evaluation completion quantity.

8. The method according to claim 3, characterized in that, The step of performing local curvature confidence assessment on the set of off-nodes to form a measurement confidence distribution includes: Based on the set of off-nodes, local curvature values ​​are extracted to obtain a curvature feature set; The curvature feature set is adaptively categorized and the distribution of curvature dispersion generation error characterization within each category is statistically analyzed. Perform curvature error regression fitting on the error characterization distribution to generate an error fitting curve; The measurement confidence distribution is formed by performing confidence-weighted mapping on the fitting residuals using the error fitting curve.

9. The method according to claim 7, characterized in that, The step of locating the corresponding region of the uncovered evaluation dimension set to determine the evaluation coverage gap area includes: A dimension region mapping table is generated by matching the three-dimensional region type corresponding to each dimension according to the uncovered evaluation dimension set; Based on the dimensional region mapping table, a candidate missing region set is obtained by expanding and searching according to each three-dimensional region type; The candidate missing region set is subjected to isolated region filtering to form an effective missing region set; Based on the set of valid missing regions, perform region merging to determine the evaluation coverage missing regions.

10. A digital design quality inspection system for dental prostheses, characterized in that, include: The point cloud acquisition module is used to acquire three-dimensional point cloud data of oral prostheses and to perform bidirectional nearest point distance difference direction discrimination on the three-dimensional point cloud data to form edge fit deviation features. The fit scoring module is used to analyze the edge fit deviation characteristics to determine the clinical fit grading and fit level benchmark, identify curvature confidence weighted deviation nodes based on the fit level benchmark to obtain sub-item weight compensation values, and verify the allowable fluctuation range of the fit level benchmark through the sub-item weight compensation values ​​to determine the dynamic detection benchmark value. The adjacent contact verification module is used to determine the adjacent contact area range by growing the gap region based on the dynamic detection benchmark value, to verify the point-to-surface contact density based on the adjacent contact area range to obtain the adjacent contact deviation, and to perform contact deviation grading and scoring analysis based on the adjacent contact deviation to form an adjacent contact rating value. The positioning verification module is used to locate the undercut area of ​​each abutment tooth axial surface based on the adjacent contact assessment value to obtain the undercut distribution of the abutment teeth, analyze the common undercut boundary of multiple teeth through the undercut distribution of the abutment teeth to determine the permissible offset domain of the positioning path, and perform positioning path deviation angle cross-boundary verification based on the permissible offset domain of the positioning path to form the positioning path assessment value. The report output module is used to generate a set of marked areas by marking non-compliant areas based on the assessment value of the placement path, analyze the evaluation coverage missing areas of the marked area set to form an evaluation completion amount, and perform over-limit trigger review based on the evaluation completion amount to generate the quality test result of the oral prosthesis.

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