An orthodontic parameter analysis method and system based on three-dimensional tooth point cloud segmentation

Abstract

This invention provides a method and system for orthodontic parameter analysis based on three-dimensional tooth point cloud segmentation, belonging to the field of digital orthodontic technology. The method includes: acquiring point clouds of the entire dentition and point-level semantic labels, and single-tooth instance labels; extracting single-tooth point clouds and determining their centroids; extracting the occlusal plane based on the entire dentition point cloud, and projecting the centroids to obtain a two-dimensional sequence; fitting B-spline arch curves after sorting; using the first derivative of the curve as the mesiodistal direction, cross-multiplying it with the occlusal plane normal to obtain the buccal-lingual direction, and establishing a local orthogonal coordinate system; projecting along the mesiodistal and buccal-lingual directions and truncating bilaterally to obtain the mesiodistal diameter and buccal-lingual diameter; accumulating the mesiodistal diameters to obtain the necessary gap, calculating the arch curve arc length and adding endpoint compensation to obtain the usable gap, and obtaining the arch length discrepancy from the difference to quantitatively assess the crowding degree of the dentition. This solves the problem of inaccurate measurement of mesiodistal diameter, buccal-lingual diameter, and arch length discrepancy under noise, segmentation errors, and complex postures.

Description

Technical Field

[0001] This invention relates to the field of digital orthodontics technology, and more specifically, to an orthodontic parameter analysis method and system based on three-dimensional tooth point cloud segmentation. Background Technology

[0002] With the rapid development of intraoral scanning, 3D reconstruction, and artificial intelligence technologies, 3D digital dental arch models have gradually replaced traditional plaster models, becoming the core data foundation for clinical diagnosis, treatment planning, and efficacy evaluation in orthodontics. Compared to traditional plaster models, digital dental arch models offer significant advantages such as convenient storage, reusability, support for remote transmission, and automated computational analysis. They provide an efficient data carrier for measuring tooth geometry, analyzing dental arch morphology, and quantitatively assessing dental crowding. In routine orthodontic clinical analysis, the mesiodistal diameter, buccolingual diameter, and dental arch length discrepancy are the most commonly used key geometric parameters. Among these, the mesiodistal diameter directly reflects the space occupied by teeth along the dental arch alignment, serving as the core basis for tooth volume analysis, determining the degree of dental crowding, and formulating orthodontic space management strategies. The buccolingual diameter characterizes the lateral thickness of the crown, aiding in the analysis of crown morphology and occlusal relationships. Dental arch length discrepancy quantifies the capacity of the dental arch space to accommodate all teeth by comparing the available space in the dental arch with the space required for tooth alignment.

[0003] Currently, orthodontic parameter measurements for digital dental arch models are mainly divided into two categories: manual measurement and automatic measurement. Manual measurement relies on the operator manually selecting the crown measurement endpoints in 3D software to complete the size calculation. This method suffers from problems such as long operation time, measurement results being greatly affected by the operator's subjective experience, and insufficient repeatability between different operators and between different measurements by the same operator. Existing automatic measurement methods mostly use methods such as directional bounding boxes and extreme value search to estimate tooth size. Although these methods can reduce manual operation, they are easily affected by noise generated during point cloud acquisition, local outliers, scanning defects, and tooth segmentation boundary errors, resulting in overestimation of measurement results and poor stability. In addition, 3D tooth point cloud acquisition usually involves random scanning postures. Even if a single tooth instance point cloud has been obtained, if the measurement is performed directly in the global coordinate system or only based on the local principal axis of a single tooth, it will still be affected by factors such as tooth rotation, tilt, crowding, misalignment, and local morphological irregularities, making it difficult to stably determine the mesiodistal measurement direction and buccal-lingual measurement direction that conform to the orthodontic anatomy definition. Especially in common clinical scenarios such as severe crowding of teeth, close contact in the molar region, or slight misclassification of tooth boundaries, traditional automatic measurement methods cannot simultaneously ensure the degree of automation, accuracy, and stability of measurement, making it difficult to meet the needs of digital orthodontic clinics for efficient and reliable parameter analysis. Summary of the Invention

[0004] The purpose of this invention is to provide an orthodontic parameter analysis method and system based on three-dimensional tooth point cloud segmentation, which aims to solve the problem that existing three-dimensional tooth point cloud measurement methods are difficult to stably and accurately determine the mesiodistal diameter, buccal-lingual diameter, and arch length that conform to the orthodontic anatomical definition under noise, segmentation error, and complex tooth posture.

[0005] This invention is achieved through the following technical solution: An orthodontic parameter analysis method based on three-dimensional tooth point cloud segmentation includes the following steps: Obtain point cloud data of the entire dentition and its corresponding tooth segmentation results; wherein, the tooth segmentation results include at least point-level semantic labels and single-tooth instance labels; Based on the single tooth instance label, extract the single tooth point cloud corresponding to each single tooth instance from the full dentition point cloud data, and calculate the spatial centroid of each single tooth instance; The global occlusal plane is extracted based on the point cloud of the entire dentition, and the spatial centroid of each single tooth instance is projected onto the global occlusal plane to obtain a two-dimensional centroid projection sequence. Based on the two-dimensional centroid projection sequence, the topological sorting result of teeth along the dental arch direction is determined, and B-spline dental arch curves are fitted based on the sorted centroid sequence. The mesiodistal measurement direction is determined based on the first derivative of the B-spline arch curve at each tooth position. The buccal and lingual measurement directions are obtained by cross product of the mesiodistal measurement direction and the global occlusal plane normal vector and normalized. A single-tooth local orthogonal measurement coordinate system is constructed, consisting of the mesiodistal measurement direction, the buccal and lingual measurement direction and the global occlusal plane normal vector. Each single tooth point cloud is orthogonally projected along the mesiodistal measurement direction and the buccal-lingual measurement direction to obtain a one-dimensional projection sequence in the mesiodistal direction and a one-dimensional projection sequence in the buccal-lingual direction. Bilateral quantile statistical truncation is performed on the one-dimensional projection sequence in the mesiodistal direction and the one-dimensional projection sequence in the buccal-lingual direction, respectively, and the length of the effective projection interval after truncation is used as the mesiodistal diameter and buccal-lingual diameter of the single tooth instance. The required gap in the dentition is calculated based on the mesiodistal diameter of each single tooth example. The available gap in the dentition is calculated based on the arc length of the B-spline dental arch curve and endpoint compensation. The difference between the available gap and the required gap in the dentition is calculated to obtain the dental arch length inconsistency. The quantitative assessment results of dental crowding are output based on the discrepancy in the dental arch length.

[0006] Optionally, the full dentition point cloud data is obtained directly by an intraoral scanning device or by sampling a three-dimensional dentition triangular mesh model. The tooth segmentation results are obtained from the output of a 3D tooth point cloud semantic segmentation network, or from other 3D tooth row segmentation algorithms that have the ability to output point-level tooth semantic labels and single tooth instance labels. The tooth segmentation results are used to distinguish the gingiva and background from the point cloud regions of each single tooth, determine the range of each single tooth point cloud, and provide a data basis for subsequent orthodontic parameter measurements.

[0007] Optionally, the specific process of extracting the point cloud of each individual tooth from the point cloud data of the entire dentition based on the single tooth instance label, and calculating the spatial centroid of each single tooth instance is as follows: Traverse the point cloud data of the entire dentition, filter out the corresponding single tooth point cloud data according to the single tooth instance label, and form a single tooth point cloud set corresponding to each single tooth instance; Calculate the geometric centroid of a single tooth instance based on the single tooth point cloud set; Using the geometric centroid of a single tooth instance as a reference, the point cloud set of the single tooth instance corresponding to the single tooth instance is decentered to eliminate the translational offset of different scanning models in the global coordinate system.

[0008] Optionally, the specific process of extracting the global occlusal plane based on the point cloud of the entire dentition and projecting the spatial centroid of each single tooth instance onto the global occlusal plane to obtain a two-dimensional centroid projection sequence is as follows: Calculate the geometric center of the point cloud of the entire dentition, and use this geometric center as a reference to decenter the point cloud of the entire dentition to obtain the decentered point cloud of the entire dentition. Construct a covariance matrix of a decentralized full jaw point cloud, perform eigenvalue decomposition or singular value decomposition on the covariance matrix, and determine the unit eigenvector corresponding to the smallest eigenvalue as the normal vector of the global occlusal plane. By constructing two mutually orthogonal unit basis vectors in the global occlusal plane through Schmidt orthogonalization, a two-dimensional occlusal plane coordinate system is formed. The spatial centroid of each single tooth instance is projected onto the two-dimensional occlusal plane coordinate system to obtain a two-dimensional centroid projection sequence.

[0009] Optionally, the specific process of determining the topological sorting result of teeth along the dental arch direction based on the two-dimensional centroid projection sequence, and fitting the B-spline dental arch curve based on the sorted centroid sequence is as follows: Using the mean of all two-dimensional centroid projection points as the pole, the rectangular coordinates of each two-dimensional centroid projection point are converted into polar coordinates; Sort all polar coordinates in ascending order and calculate the polar angle difference between adjacent polar angles; The position with the largest polar angle difference is determined as the opening of the dental arch. The polar angle sorting sequence is then divided and recombined at this position to obtain the dental arch topological sorting result from the terminal teeth on one side to the terminal teeth on the other side. The distance between adjacent points is calculated based on the sequence of two-dimensional centroid projection points after topological sorting, and the cumulative chord length parameter is constructed and normalized to the interval [0,1]. The B-spline dental arch curve was obtained by fitting the normalized parameters with the corresponding two-dimensional centroid projection points using the least squares method.

[0010] Optionally, the specific process of the two-sided quantile statistical truncation is as follows: The one-dimensional projection sequences in the mesio-distal direction and the one-dimensional projection sequences in the buccal-lingual direction were sorted in ascending order, respectively. The preset low-resolution and preset high-resolution points of each sorted projection sequence are extracted as the effective measurement boundaries in the corresponding directions. Calculate the quantile difference between the preset high quantile and the preset low quantile, and use the quantile difference as the length of the effective projection interval in the corresponding direction.

[0011] Optionally, while obtaining the mesiodistal diameter and buccal-lingual diameter of a single tooth instance, the mesiodistal measurement endpoint and buccal-lingual measurement endpoint are calculated inversely based on the preset low quantile, preset high quantile, spatial centroid of the single tooth instance, and corresponding measurement direction vector, and three-dimensional measurement line segments corresponding to the mesiodistal diameter and buccal-lingual diameter are generated for three-dimensional visualization and manual verification of the measurement results.

[0012] Optionally, the required gap in the dentition is the sum of the mesiodistal diameters of each individual tooth instance participating in the analysis; the available gap in the dentition is the sum of the arc length of the B-spline arch curve between the first and last individual tooth instances participating in the analysis, and the compensation value of half the mesiodistal diameter of each of the first and last individual tooth instances participating in the analysis.

[0013] Optionally, the quantitative assessment result of dental crowding based on the arch length mismatch is as follows: when the arch length mismatch is positive, it is determined that there is remaining space in the arch or gaps between the teeth; when the arch length mismatch is negative, it is determined that there is insufficient space in the arch, and the dental crowding level is divided into four levels: basic coordination, mild crowding, moderate crowding and severe crowding based on the absolute value of the arch length mismatch.

[0014] Based on the same inventive concept, the present invention also provides an orthodontic parameter analysis system based on three-dimensional tooth point cloud segmentation, used to implement the orthodontic parameter analysis method based on three-dimensional tooth point cloud segmentation, including: a data acquisition and preprocessing module, a global benchmark construction module, a dental arch curve fitting module, a local measurement coordinate system construction module, a crown size measurement module, and a dental crowding assessment module. The output of the data acquisition and preprocessing module is connected to the input of the global benchmark construction module and the crown size measurement module, respectively. The output of the global benchmark construction module is connected to the input of the arch curve fitting module and the local measurement coordinate system construction module, respectively. The output of the arch curve fitting module is connected to the input of the local measurement coordinate system construction module and the dental crowding assessment module, respectively. The output of the local measurement coordinate system construction module is connected to the input of the crown size measurement module, and the output of the crown size measurement module is connected to the input of the dental crowding assessment module. The data acquisition and preprocessing module is used to acquire the point cloud data of the entire dentition and its corresponding tooth segmentation results, extract the point cloud of each tooth instance according to the single tooth instance label, calculate the spatial centroid of each single tooth instance, and perform decentralization processing on the single tooth point cloud based on the geometric centroid. The global benchmark construction module is used to extract the global occlusal plane based on the point cloud of the entire dentition, construct a two-dimensional occlusal plane coordinate system, project the spatial centroid of each single tooth instance onto the two-dimensional occlusal plane coordinate system, and obtain a two-dimensional centroid projection sequence. The dental arch curve fitting module is used to convert rectangular coordinates to polar coordinates with the mean of all two-dimensional centroid projection points as the pole, sort the polar coordinates and determine the opening of the dental arch, reorganize to obtain the dental arch topological sorting result, construct normalized cumulative chord length parameters based on the sorted centroid sequence, and use the least squares method to fit the cubic B-spline dental arch curve. The local measurement coordinate system construction module is used to calculate the first derivative of the cubic B-spline dental arch curve at each tooth position and normalize it to obtain the mesiodistal measurement direction. The mesiodistal measurement direction is then cross-multiplied with the global occlusal plane normal vector and normalized to obtain the buccal-lingual measurement direction. A single-tooth local orthogonal measurement coordinate system is constructed, consisting of the mesiodistal measurement direction, the buccal-lingual measurement direction and the global occlusal plane normal vector. The crown size measurement module is used to orthogonally project each single tooth point cloud along the mesiodistal measurement direction and the buccal-lingual measurement direction to obtain a one-dimensional projection sequence in the two directions. The projection sequence is subjected to bilateral quantile statistical truncation, and the effective projection interval length is used as the mesiodistal diameter and buccal-lingual diameter of the single tooth instance. The three-dimensional measurement endpoint is calculated inversely based on the quantile, the centroid of the single tooth space and the measurement direction vector. The dental crowding assessment module is used to accumulate the mesiodistal diameters of each single tooth instance to obtain the required dental space, calculate the arc length of the cubic B-spline arch curve between the first and last single tooth instances and superimpose the compensation value of half the mesiodistal diameter of each of the first and last single teeth to obtain the available dental space, calculate the difference between the available dental space and the required dental space to obtain the dental arch length discrepancy, and output the quantitative assessment result of dental crowding based on the absolute value of the dental arch length discrepancy.

[0015] Based on the same inventive concept, the present invention also provides an electronic device, including a memory and a processor, wherein the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to perform the above-described orthodontic parameter analysis method based on three-dimensional tooth point cloud segmentation.

[0016] Based on the same inventive concept, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described orthodontic parameter analysis method based on three-dimensional tooth point cloud segmentation.

[0017] The technical solution of the present invention has at least the following advantages and beneficial effects: By constructing a local orthogonal measurement coordinate system for a single tooth using the global occlusal plane and the B-spline arch curve, the mesiodistal and buccal-lingual directions can be adaptively determined based on the actual position and arrangement of the tooth in the dental arch. This effectively eliminates the interference of factors such as tooth tilting, rotation, crowding, and misalignment on the measurement direction, making the measurement results more consistent with the anatomical definition in orthodontic clinical practice.

[0018] The method of extracting effective projection intervals from one-dimensional projection sequences by using bilateral quantile statistical truncation can automatically filter out point cloud noise, scanning outliers, and abnormal data introduced by slight misclassification of tooth segmentation boundaries. It overcomes the problems of overestimation and large fluctuations in measurement values ​​that are easily caused by traditional extreme value methods or bounding box methods, and can still maintain stable and reliable measurement results in complex clinical scenarios with close contact and imperfect segmentation boundaries.

[0019] From inputting the point cloud and segmentation results of the entire dentition to outputting the assessment of mesiodistal diameter, buccal-lingual diameter, dental arch length discrepancy and crowding for each tooth position, no manual selection of measurement landmarks is required. This eliminates repeatability differences between and within operators, shortens measurement and analysis time, and ensures high repeatability of results.

[0020] Based on the B-spline arch curve arc length and endpoint compensation, the available space of the dentition is accurately calculated. Combined with the accumulated mesial and distal diameters of each tooth to obtain the necessary space of the dentition, the reliable quantification of arch length discrepancies is achieved. This provides an accurate and objective numerical basis for the determination of dentition crowding and is more suitable for clinical orthodontic needs such as severe crowding that require precise spatial analysis. Attached Figure Description

[0021] Figure 1 This is a flowchart illustrating the orthodontic parameter analysis method based on three-dimensional tooth point cloud segmentation according to an embodiment of the present invention. Figure 2 This is a schematic diagram of the orthodontic parameter analysis system based on three-dimensional tooth point cloud segmentation according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the extraction of the occlusal plane of the whole jaw point cloud and the projection of the centroid of a single tooth in an embodiment of the present invention; Figure 4 This is a schematic diagram of dental arch topology sorting and B-spline dental arch curve fitting in an embodiment of the present invention; Figure 5 This is a schematic diagram of the construction of a local orthogonal measurement coordinate system for a single-tooth example according to an embodiment of the present invention; Figure 6 This is a schematic diagram of the mesiodistal (MD) and buccolingual (BL) projection measurement process based on quantile statistics in an embodiment of the present invention. Figure 7 This is a schematic diagram of the dental crowding assessment process according to an embodiment of the present invention. Detailed Implementation

[0022] The following is a detailed description of the embodiments, in conjunction with the accompanying drawings.

[0023] Reference Figure 1 An orthodontic parameter analysis method based on three-dimensional tooth point cloud segmentation includes the following steps: Step 1: Obtain point cloud data of the entire dentition and its corresponding tooth segmentation results; wherein, the tooth segmentation results include at least point-level semantic labels and single-tooth instance labels.

[0024] In some embodiments, the full dentition point cloud data is obtained directly by an intraoral scanning device or by sampling a three-dimensional dentition triangular mesh model; The tooth segmentation results are obtained from the output of a 3D tooth point cloud semantic segmentation network, or from other 3D tooth row segmentation algorithms that have the ability to output point-level tooth semantic labels and single tooth instance labels. The tooth segmentation results are used to distinguish the gingiva and background from the point cloud regions of each single tooth, determine the range of each single tooth point cloud, and provide a data basis for subsequent orthodontic parameter measurements.

[0025] Step 2: Based on the single tooth instance label, extract the single tooth point cloud corresponding to each single tooth instance from the full dentition point cloud data, and calculate the spatial centroid of each single tooth instance.

[0026] In some embodiments, the specific process of extracting the point cloud of each individual tooth from the point cloud data of the entire dentition based on the single tooth instance label, and calculating the spatial centroid of each single tooth instance is as follows: Traverse the point cloud data of the entire dentition, filter out the corresponding single tooth point cloud data according to the single tooth instance label, and form a single tooth point cloud set corresponding to each single tooth instance; Calculate the geometric centroid of a single tooth instance based on the single tooth point cloud set; Using the geometric centroid of a single tooth instance as a reference, the point cloud set of the single tooth instance is decentered to eliminate the translational offset of different scanning models in the global coordinate system, so that subsequent geometric calculations are all completed under a unified local reference.

[0027] Step 3: Extract the global occlusal plane based on the point cloud of the entire dentition, and project the spatial centroid of each single tooth instance onto the global occlusal plane to obtain a two-dimensional centroid projection sequence.

[0028] In some embodiments, the specific process of extracting the global occlusal plane based on the full dentition point cloud and projecting the spatial centroid of each individual tooth instance onto the global occlusal plane to obtain a two-dimensional centroid projection sequence is as follows: Calculate the geometric center of the full dentition point cloud; use this geometric center as a reference to decentralize the full dentition point cloud to obtain a decentralized full dentition point cloud; construct the covariance matrix of the decentralized full dentition point cloud; perform eigenvalue decomposition or singular value decomposition on the covariance matrix; determine the unit eigenvector corresponding to the smallest eigenvalue as the normal vector of the global occlusal plane; construct two mutually orthogonal unit basis vectors within the global occlusal plane through Schmidt orthogonalization to form a two-dimensional occlusal plane coordinate system; project the spatial centroid of each individual tooth instance onto the two-dimensional occlusal plane coordinate system to obtain a two-dimensional centroid projection sequence.

[0029] Step 4: Based on the two-dimensional centroid projection sequence, determine the topological sorting result of the teeth along the dental arch direction, and fit the B-spline dental arch curve based on the sorted centroid sequence.

[0030] In some embodiments, the specific process of determining the topological sorting result of teeth along the dental arch direction based on the two-dimensional centroid projection sequence, and fitting a B-spline dental arch curve based on the sorted centroid sequence is as follows: Using the mean of all two-dimensional centroid projection points as the pole, the rectangular coordinates of each two-dimensional centroid projection point are converted into polar coordinates. All polar coordinates are sorted in ascending order, and the polar angle difference between adjacent polar angles is calculated. The position with the largest polar angle difference is determined as the opening of the dental arch. At this position, the polar angle sorting sequence is segmented and recombined to obtain the dental arch topology sorting result from the terminal teeth on one side to the terminal teeth on the other side. Based on the topology sorted two-dimensional centroid projection point sequence, the distance between adjacent points is calculated, and the cumulative chord length parameter is constructed. The cumulative chord length parameter is normalized to the interval [0,1]. The least squares method is used to fit the normalized parameter with the corresponding two-dimensional centroid projection point to obtain the B-spline dental arch curve.

[0031] Furthermore, referring to Figure 3 Let the input jaw point cloud be... ,in Indicates the first Three-dimensional points. First, the geometric center c of the full jaw point cloud is calculated, and a decentralized point set is constructed. Then, a covariance matrix is ​​constructed based on the decentralized point set, and eigenvalue decomposition or singular value decomposition is performed on this covariance matrix. Since the occlusal surface of the dental arch is approximately planar, the unit eigenvector corresponding to the smallest eigenvalue can be used as the normal vector of the occlusal plane. .

[0032] After obtaining the normal vector of the occlusal plane, two orthogonal unit bases in the occlusal plane are constructed through Schmidt orthogonalization. (Left and right base) and (Anterior-posterior base). For each single-tooth instance, calculate its spatial centroid. and map it to the and In the two-dimensional interlocking plane coordinate system, the two-dimensional centroid point is obtained. .

[0033] Since three-dimensional dental arches are typically arranged in a U-shape, the centroids of individual teeth can be approximated as forming an arc-shaped distribution in the two-dimensional occlusal plane. To obtain an ordered arrangement from the terminal teeth on one side to the terminal teeth on the other, the system uses the mean of all two-dimensional centroids as the pole and calculates the polar angle corresponding to each centroid. Then, the polar angles are sorted in ascending order and the difference between adjacent polar angles is calculated. The region with the largest difference is determined to be the opening of the dental arch. The sequence is cut and recombined at this position to obtain the dental arch topological sorting result.

[0034] Reference Figure 4 For the sorted two-dimensional tooth centroid sequence First, the cumulative chord length parameter is constructed based on the distance between adjacent centroids. This is then normalized to the [0,1] interval. Subsequently, a cubic B-spline curve is fitted using the least squares method. Figure 4 Conformal spline fitting curve This allows for a smooth depiction of the overall arc-shaped trajectory of the dental arch in the occlusal plane, resulting in the B-spline dental arch curve.

[0035] Step 5: Determine the mesiodistal measurement direction based on the first derivative of the B-spline arch curve at each tooth position. After cross-producting the mesiodistal measurement direction with the global occlusal plane normal vector, normalize it to obtain the buccal-lingual measurement direction. Construct a single-tooth local orthogonal measurement coordinate system composed of the mesiodistal measurement direction, the buccal-lingual measurement direction, and the global occlusal plane normal vector.

[0036] In some embodiments, refer to Figure 5 For the first Each tooth, the system in its corresponding cumulative chord length parameter Taking the first derivative with respect to the B-spline curve yields the two-dimensional tangential vector of the dental arch curve. Normalizing this vector and mapping it back to three-dimensional space gives the mesiodistal directions. Near and far directions It represents the local principal axis along the direction of tooth arrangement in the dental arch and can be used as the direction for measuring mesiodistal diameter.

[0037] In obtaining near and far directions and the normal vector of the occlusal plane Then, the system calculates the cheek-tongue direction using vector cross product. ,Right now .Depend on , and Together constitute the first A local orthogonal measurement coordinate system for each tooth, which simultaneously includes global dental arch structure constraints and local tooth orientation information, can reduce the impact of single tooth rotation, crowding, misalignment, and local geometric irregularities on measurement orientation estimation.

[0038] Step 6: Perform orthogonal projection of each single tooth point cloud along the mesiodistal measurement direction and the buccal-lingual measurement direction to obtain a one-dimensional projection sequence in the mesiodistal direction and a one-dimensional projection sequence in the buccal-lingual direction.

[0039] In some embodiments, refer to Figure 6 First, the system inputs the point cloud of the single tooth to be measured and its corresponding local measurement coordinate system. The local measurement coordinate system includes the mesiodistal direction and the buccal-lingual direction, used to determine the two orthogonal measurement principal axes (mesiodistal principal axis) for crown size measurement. and the cheek-tongue axis , refer to Figure 5 Subsequently, the system establishes an orthogonal projection model, projecting the single-tooth point cloud along the mesiodistal and buccal-lingual directions respectively, obtaining the mesiodistal projection sequence and the buccal-lingual projection sequence. Through this processing, the three-dimensional crown width measurement problem is transformed into the problem of calculating the interval length of two one-dimensional projection sequences.

[0040] Step 7: Perform bilateral quantile statistical truncation on the one-dimensional projection sequence in the mesiodistal direction and the one-dimensional projection sequence in the buccal-lingual direction, respectively, and use the length of the effective projection interval after truncation as the mesiodistal diameter and buccal-lingual diameter of the single tooth instance.

[0041] In some embodiments, the specific process of the two-sided quantile statistical truncation is as follows: The one-dimensional projection sequences in the near-to-far direction and the one-dimensional projection sequences in the cheek-tongue direction are sorted in ascending order, respectively. Preset low-quantile and preset high-quantile points are extracted from each sorted projection sequence as the effective measurement boundaries for the corresponding directions. The quantile difference between the preset high-quantile and preset low-quantile points is calculated, and this quantile difference is used as the length of the effective projection interval for the corresponding direction. In a preferred embodiment, referring to... Figure 6Low quantiles are selected from 1% of the quantiles, and high quantiles are selected from 99% of the quantiles, in order to remove a small number of outliers, scanning noise points, or boundary misclassification points at both ends of the projected sequence; among them, the mesial and distal diameters and the buccal and lingual diameters can be expressed as follows: in, The near and far diameters; This is a projection sequence in the near-far-mid direction; Near-to-far projection sequence The 99th percentile value, that is, the effective upper boundary of measurement in the near-far-mid direction; Near-to-far projection sequence The 1st percentile value, which is the lower boundary of the effective measurement in the near-to-far direction; The buccal-lingual diameter; Indicates the buccal-lingual projection sequence; buccal-lingual projection sequence The 99th percentile value, which is the effective upper boundary of measurement in the buccal-tongue direction; buccal-lingual projection sequence The 1% quantile value, which is the effective lower boundary of measurement in the buccal-tongue direction.

[0042] In some embodiments, while obtaining the mesiodistal diameter and buccal-lingual diameter of a single tooth instance, the mesiodistal and buccal-lingual measurement endpoints are calculated inversely based on preset low-quantile sites, preset high-quantile sites, the spatial centroid of the single tooth instance, and the corresponding measurement direction vectors. This generates three-dimensional measurement line segments corresponding to the mesiodistal diameter and buccal-lingual diameter for three-dimensional visualization and manual verification of the measurement results. Thus, the system can not only output numerical results for the mesiodistal diameter (MD) and buccal-lingual diameter (BL), but also provide visualized measurement results for clinical verification. By using quantile statistical truncation instead of traditional extreme value search, the impact of outliers, scanning noise, and segmentation boundary errors on the measurement results can be reduced, thereby improving the stability and robustness of automatic crown size measurement.

[0043] Step 8: Calculate the required gap of the dentition based on the mesiodistal diameter of each single tooth example, calculate the available gap of the dentition based on the arc length of the B-spline dental arch curve and endpoint compensation, and obtain the dental arch length mismatch by calculating the difference between the available gap and the required gap.

[0044] In some embodiments, the required dentition gap is the sum of the mesiodistal diameters of each individual tooth instance involved in the analysis; the available dentition gap is the sum of the arc length of the B-spline arch curve between the first and last individual tooth instances involved in the analysis, and the compensation value of half the mesiodistal diameter of each of the first and last individual tooth instances involved in the analysis.

[0045] Furthermore, referring to Figure 7The system acquires the dentition segmentation results and identifies the target teeth for dentition spatial analysis based on single-tooth instance labels. Subsequently, the system extracts the mesiodistal diameter (MD) values ​​of each target tooth and sums the MD values ​​of all target teeth to obtain the necessary spacing for dentition alignment. As shown in the following formula: in, This represents the total number of teeth in the current jawbone analysis. For the first The mesiodistal diameter of each tooth.

[0046] Furthermore, the system extracts the centroid sequence of the target tooth based on its spatial location and performs arch curve fitting on the centroid sequence to obtain a smooth curve characterizing the arch morphology. Preferably, the arch curve is fitted using a B-spline curve to reduce the impact of tooth misalignment, rotation, or local crowding on the arch length estimation.

[0047] After obtaining the dental arch curve, the system calculates the arc length of the arch curve between the first and last target teeth and uses this arc length as the main part of the available clearance. Considering that the dental arch curve usually passes through or is close to the tooth centroid, the space between the centroid of the first and last teeth and their distal margins may not be fully accounted for. Therefore, the system introduces endpoint half-tooth width compensation based on the arc length of the dental arch curve, that is, compensating for half the mesiodistal diameter of the first and last target teeth respectively, thereby obtaining the available clearance. .

[0048] Step 9: Output the quantitative assessment results of dental crowding based on the aforementioned arch length inconsistency.

[0049] In some embodiments, the quantitative assessment result of dental crowding based on arch length misalignment is specifically as follows: when the arch length misalignment is positive, it is determined that there is remaining space in the arch or interdental space; when the arch length misalignment is negative, it is determined that there is insufficient arch space, and the dental crowding level is divided into four levels: basic coordination, mild crowding, moderate crowding and severe crowding based on the absolute value of arch length misalignment.

[0050] Furthermore, after obtaining the necessary and available clearances, the system calculates the arch length discrepancy, as shown in the following formula: in, For dental arch length, the value is not adjusted; when When the available space in the dental arch is greater than the space required for tooth alignment, and there is remaining space or interdental spaces in the dentition, the amount of remaining space is called the dental arch space. The absolute value; when When the available space in the dental arch is less than the space required for tooth alignment, crowding is determined, and the degree of crowding is determined by... Absolute value quantization representation; when At that time, it was determined that the available space of the dental arch was completely matched with the space required for tooth arrangement, and the space of the dental arch was basically coordinated.

[0051] Finally, for crowded cases where the arch length misalignment is negative, the general clinical standards for systemic orthodontics are combined with... The absolute value is used to determine the dentition status, outputting assessment results such as basic harmony, mild crowding, moderate crowding, or severe crowding, and generating a structured analysis report including arch length misalignment value, dentition status, and crowding level. The arch length misalignment value, crowding level, and the three-dimensional measurement lines of the mesiodistal diameter and buccal-lingual diameter of each individual tooth generated in step seven are then integrated and displayed. The B-spline arch curve and the difference between the available and required spaces in the dentition are superimposed and displayed on the point cloud model of the entire dentition. Teeth with crowding or gaps are color-coded (e.g., red indicates severely crowded teeth, yellow indicates mildly crowded teeth, and blue indicates teeth with gaps). It supports interactive viewing of mesiodistal diameter, buccal-lingual diameter measurements, and three-dimensional measurement lines for any tooth position, facilitating manual review and verification by clinicians.

[0052] Automatically generate a structured report containing complete quantitative evaluation results. The report should include at least the following: Basic information: Patient number, scan date, jaw position analyzed (maxillary / mandibular), list of teeth involved in the analysis, and marking of missing teeth; Summary of single tooth parameters: Table of mesiodistal diameter and buccal-lingual diameter measurements for each tooth position; Dental arch space analysis: specific values ​​for required space in the dentition, available space in the dentition, and unadjusted value of dental arch length; Crowding assessment: Overall dentition status, crowding level, and corresponding clinical recommendations; Attachments: Screenshot of the point cloud of the entire dentition, dental arch curve fitting diagram, and visualization of the 3D measurement results.

[0053] If missing teeth, supernumerary teeth, or impacted teeth are detected during the analysis, the system will automatically perform the following operations: Mark the type and location of abnormal tooth positions in the tooth position list; When calculating the necessary space for the dentition, the standard mesiodistal diameter value corresponding to the missing tooth is automatically deducted, or the mesiodistal diameter value corresponding to the supernumerary tooth is added; The analysis report separately explains the impact of abnormal tooth positions on the calculation of arch length discrepancies and crowding assessment results, providing a reference for the design of clinical treatment plans.

[0054] Based on the same inventive concept, and corresponding to any of the above embodiments, refer to... Figure 2This invention provides an orthodontic parameter analysis system based on three-dimensional tooth point cloud segmentation, used to implement the aforementioned orthodontic parameter analysis method based on three-dimensional tooth point cloud segmentation, including: a data acquisition and preprocessing module, a global benchmark construction module, a dental arch curve fitting module, a local measurement coordinate system construction module, a crown size measurement module, and a dental crowding assessment module; The output of the data acquisition and preprocessing module is connected to the input of the global benchmark construction module and the crown size measurement module, respectively. The output of the global benchmark construction module is connected to the input of the arch curve fitting module and the local measurement coordinate system construction module, respectively. The output of the arch curve fitting module is connected to the input of the local measurement coordinate system construction module and the dental crowding assessment module, respectively. The output of the local measurement coordinate system construction module is connected to the input of the crown size measurement module, and the output of the crown size measurement module is connected to the input of the dental crowding assessment module. The data acquisition and preprocessing module is used to acquire the point cloud data of the entire dentition and its corresponding tooth segmentation results, extract the point cloud of each tooth instance according to the single tooth instance label, calculate the spatial centroid of each single tooth instance, and perform decentralization processing on the single tooth point cloud based on the geometric centroid. The global benchmark construction module is used to extract the global occlusal plane based on the point cloud of the entire dentition, construct a two-dimensional occlusal plane coordinate system, project the spatial centroid of each single tooth instance onto the two-dimensional occlusal plane coordinate system, and obtain a two-dimensional centroid projection sequence. The dental arch curve fitting module is used to convert rectangular coordinates into polar coordinates with the mean of all two-dimensional centroid projection points as the pole, sort the polar coordinates and determine the opening of the dental arch, reorganize to obtain the dental arch topological sorting result, construct normalized cumulative chord length parameters based on the sorted centroid sequence, and use the least squares method to fit the cubic B-spline dental arch curve. The local measurement coordinate system construction module is used to calculate the first derivative of the cubic B-spline dental arch curve at each tooth position and normalize it to obtain the mesiodistal measurement direction. The mesiodistal measurement direction is then cross-multiplied with the global occlusal plane normal vector and normalized to obtain the buccal-lingual measurement direction. A single-tooth local orthogonal measurement coordinate system is constructed, consisting of the mesiodistal measurement direction, the buccal-lingual measurement direction and the global occlusal plane normal vector. The crown size measurement module is used to orthogonally project each single tooth point cloud along the mesiodistal measurement direction and the buccal-lingual measurement direction to obtain a one-dimensional projection sequence in the two directions. The projection sequence is subjected to bilateral quantile statistical truncation, and the effective projection interval length is used as the mesiodistal diameter and buccal-lingual diameter of the single tooth instance. The three-dimensional measurement endpoint is calculated inversely based on the quantile, the centroid of the single tooth space and the measurement direction vector. The dental crowding assessment module is used to accumulate the mesiodistal diameters of each single tooth instance to obtain the required dental space, calculate the arc length of the cubic B-spline arch curve between the first and last single tooth instances and superimpose the compensation value of half the mesiodistal diameter of each first and last single tooth to obtain the available dental space, calculate the difference between the available dental space and the required dental space to obtain the arch length discrepancy, and output the quantitative assessment result of dental crowding based on the absolute value of the arch length discrepancy.

[0055] Based on the same inventive concept, corresponding to any of the above embodiments, the present invention provides an electronic device, including a memory and a processor. The memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to execute the orthodontic parameter analysis method based on three-dimensional tooth point cloud segmentation of the embodiment.

[0056] Alternatively, the aforementioned electronic device may be a server.

[0057] In addition, this embodiment also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the orthodontic parameter analysis method based on three-dimensional tooth point cloud segmentation of the embodiment.

[0058] It is understood that the processor in the embodiments of the present invention may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. The general-purpose processor may be a microprocessor or any conventional processor.

[0059] The method steps in the embodiments of the present invention can be implemented in hardware or by a processor executing software instructions. The software instructions can consist of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, portable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can reside in an ASIC.

[0060] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. A computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the flow or function according to the embodiments of the present invention is generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a storage medium or transmitted through a storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

Claims

1. A method for orthodontic parameter analysis based on three-dimensional tooth point cloud segmentation, characterized in that, Includes the following steps: Obtain point cloud data of the entire dentition and its corresponding tooth segmentation results; wherein, the tooth segmentation results include at least point-level semantic labels and single-tooth instance labels; Based on the single tooth instance label, extract the single tooth point cloud corresponding to each single tooth instance from the full dentition point cloud data, and calculate the spatial centroid of each single tooth instance; Based on the point cloud of the entire dentition, the global occlusal plane is extracted, and the spatial centroid of each single tooth instance is projected onto the global occlusal plane to obtain a two-dimensional centroid projection sequence. Based on the two-dimensional centroid projection sequence, the topological sorting result of teeth along the dental arch direction is determined, and B-spline dental arch curves are fitted based on the sorted centroid sequence. The mesiodistal measurement direction is determined based on the first derivative of the B-spline arch curve at each tooth position. The buccal and lingual measurement directions are obtained by cross product of the mesiodistal measurement direction and the global occlusal plane normal vector and normalized. A single-tooth local orthogonal measurement coordinate system is constructed, consisting of the mesiodistal measurement direction, the buccal and lingual measurement direction and the global occlusal plane normal vector. Each single tooth point cloud is orthogonally projected along the mesiodistal measurement direction and the buccal-lingual measurement direction to obtain a one-dimensional projection sequence in the mesiodistal direction and a one-dimensional projection sequence in the buccal-lingual direction. Bilateral quantile statistical truncation is performed on the one-dimensional projection sequence in the mesiodistal direction and the one-dimensional projection sequence in the buccal-lingual direction, respectively, and the length of the effective projection interval after truncation is used as the mesiodistal diameter and buccal-lingual diameter of the single tooth instance. The required gap in the dentition is calculated based on the mesiodistal diameter of each single tooth example. The available gap in the dentition is calculated based on the arc length of the B-spline dental arch curve and endpoint compensation. The difference between the available gap and the required gap in the dentition is calculated to obtain the dental arch length inconsistency. The quantitative assessment results of dental crowding are output based on the aforementioned arch length inconsistency.

2. The orthodontic parameter analysis method based on three-dimensional tooth point cloud segmentation as described in claim 1, characterized in that, The full dentition point cloud data is obtained directly by an intraoral scanning device or by sampling a three-dimensional dentition triangular mesh model. The tooth segmentation results are obtained from the output of a 3D tooth point cloud semantic segmentation network, or from other 3D tooth row segmentation algorithms that have the ability to output point-level tooth semantic labels and single tooth instance labels. The tooth segmentation results are used to distinguish the gingiva and background from the point cloud regions of each single tooth, determine the range of each single tooth point cloud, and provide a data basis for subsequent orthodontic parameter measurements.

3. The orthodontic parameter analysis method based on three-dimensional tooth point cloud segmentation as described in claim 1, characterized in that, The specific process of extracting the point cloud of each individual tooth from the point cloud data of the entire dentition based on the single tooth instance label, and calculating the spatial centroid of each single tooth instance is as follows: Traverse the point cloud data of the entire dentition, filter out the corresponding single tooth point cloud data according to the single tooth instance label, and form a single tooth point cloud set corresponding to each single tooth instance; Calculate the geometric centroid of a single tooth instance based on the single tooth point cloud set; Using the geometric centroid of a single tooth instance as a reference, the point cloud set of the single tooth instance corresponding to the single tooth instance is decentered to eliminate the translational offset of different scanning models in the global coordinate system.

4. The orthodontic parameter analysis method based on three-dimensional tooth point cloud segmentation as described in claim 1, characterized in that, The specific process of extracting the global occlusal plane based on the point cloud of the entire dentition and projecting the spatial centroid of each single tooth instance onto the global occlusal plane to obtain a two-dimensional centroid projection sequence is as follows: Calculate the geometric center of the point cloud of the entire dentition, and use this geometric center as a reference to decenter the point cloud of the entire dentition to obtain the decentered point cloud of the entire dentition. Construct a covariance matrix of a decentralized full jaw point cloud, perform eigenvalue decomposition or singular value decomposition on the covariance matrix, and determine the unit eigenvector corresponding to the smallest eigenvalue as the normal vector of the global occlusal plane. By constructing two mutually orthogonal unit basis vectors in the global occlusal plane through Schmidt orthogonalization, a two-dimensional occlusal plane coordinate system is formed. The spatial centroid of each single tooth instance is projected onto the two-dimensional occlusal plane coordinate system to obtain a two-dimensional centroid projection sequence.

5. The orthodontic parameter analysis method based on three-dimensional tooth point cloud segmentation as described in claim 1, characterized in that, The specific process of determining the topological ordering of teeth along the dental arch direction based on the two-dimensional centroid projection sequence, and fitting a B-spline dental arch curve based on the ordered centroid sequence is as follows: Using the mean of all two-dimensional centroid projection points as the pole, the rectangular coordinates of each two-dimensional centroid projection point are converted into polar coordinates; Sort all polar coordinates in ascending order and calculate the polar angle difference between adjacent polar angles; The position with the largest polar angle difference is determined as the opening of the dental arch. The polar angle sorting sequence is then divided and recombined at this position to obtain the dental arch topological sorting result from the terminal teeth on one side to the terminal teeth on the other side. The distance between adjacent points is calculated based on the sequence of two-dimensional centroid projection points after topological sorting, and the cumulative chord length parameter is constructed and normalized to the interval [0,1]. The B-spline dental arch curve was obtained by fitting the normalized parameters with the corresponding two-dimensional centroid projection points using the least squares method.

6. The orthodontic parameter analysis method based on three-dimensional tooth point cloud segmentation as described in claim 1, characterized in that, The specific process of the two-sided quantile statistical truncation is as follows: The one-dimensional projection sequences in the mesio-distal direction and the one-dimensional projection sequences in the buccal-lingual direction were sorted in ascending order, respectively. The preset low-resolution and preset high-resolution points of each sorted projection sequence are extracted as the effective measurement boundaries in the corresponding directions. Calculate the quantile difference between the preset high quantile and the preset low quantile, and use the quantile difference as the length of the effective projection interval in the corresponding direction.

7. The orthodontic parameter analysis method based on three-dimensional tooth point cloud segmentation as described in claim 1, characterized in that, While obtaining the mesiodistal diameter and buccal-lingual diameter of a single tooth instance, the mesiodistal measurement endpoint and buccal-lingual measurement endpoint are calculated inversely based on the preset low quantile, preset high quantile, spatial centroid of the single tooth instance, and corresponding measurement direction vector. The corresponding three-dimensional measurement line segments of the mesiodistal diameter and buccal-lingual diameter are generated for three-dimensional visualization and manual verification of the measurement results.

8. The orthodontic parameter analysis method based on three-dimensional tooth point cloud segmentation as described in claim 1, characterized in that, The required gap in the dentition is the sum of the mesiodistal diameters of all individual tooth instances involved in the analysis; the available gap in the dentition is the sum of the arc length of the B-spline arch curve between the first and last individual tooth instances involved in the analysis, and the compensation value of half the mesiodistal diameter of each of the first and last individual tooth instances involved in the analysis.

9. The orthodontic parameter analysis method based on three-dimensional tooth point cloud segmentation as described in claim 1, characterized in that, The quantitative assessment result of dental crowding based on the arch length mismatch is as follows: when the arch length mismatch is positive, it is determined that there is remaining space in the arch or gaps between teeth; when the arch length mismatch is negative, it is determined that there is insufficient space in the arch, and the dental crowding level is divided into four levels: basic coordination, mild crowding, moderate crowding and severe crowding according to the absolute value of the arch length mismatch.

10. An orthodontic parameter analysis system based on three-dimensional tooth point cloud segmentation, used to implement the orthodontic parameter analysis method based on three-dimensional tooth point cloud segmentation as described in any one of claims 1-9, characterized in that, include: The module includes data acquisition and preprocessing, global benchmark construction, dental arch curve fitting, local measurement coordinate system construction, crown size measurement, and dental crowding assessment. The output of the data acquisition and preprocessing module is connected to the input of the global benchmark construction module and the crown size measurement module, respectively. The output of the global benchmark construction module is connected to the input of the arch curve fitting module and the local measurement coordinate system construction module, respectively. The output of the arch curve fitting module is connected to the input of the local measurement coordinate system construction module and the dental crowding assessment module, respectively. The output of the local measurement coordinate system construction module is connected to the input of the crown size measurement module, and the output of the crown size measurement module is connected to the input of the dental crowding assessment module. The data acquisition and preprocessing module is used to acquire the point cloud data of the entire dentition and its corresponding tooth segmentation results, extract the point cloud of each tooth instance according to the single tooth instance label, calculate the spatial centroid of each single tooth instance, and perform decentralization processing on the single tooth point cloud based on the geometric centroid. The global benchmark construction module is used to extract the global occlusal plane based on the point cloud of the entire dentition, construct a two-dimensional occlusal plane coordinate system, project the spatial centroid of each single tooth instance onto the two-dimensional occlusal plane coordinate system, and obtain a two-dimensional centroid projection sequence. The dental arch curve fitting module is used to convert rectangular coordinates to polar coordinates with the mean of all two-dimensional centroid projection points as the pole, sort the polar coordinates and determine the opening of the dental arch, reorganize to obtain the dental arch topological sorting result, construct normalized cumulative chord length parameters based on the sorted centroid sequence, and use the least squares method to fit the cubic B-spline dental arch curve. The local measurement coordinate system construction module is used to calculate the first derivative of the cubic B-spline dental arch curve at each tooth position and normalize it to obtain the mesiodistal measurement direction. The mesiodistal measurement direction is then cross-multiplied with the global occlusal plane normal vector and normalized to obtain the buccal-lingual measurement direction. A single-tooth local orthogonal measurement coordinate system is constructed, consisting of the mesiodistal measurement direction, the buccal-lingual measurement direction and the global occlusal plane normal vector. The crown size measurement module is used to orthogonally project each single tooth point cloud along the mesiodistal measurement direction and the buccal-lingual measurement direction to obtain a one-dimensional projection sequence in the two directions. The projection sequence is subjected to bilateral quantile statistical truncation, and the effective projection interval length is used as the mesiodistal diameter and buccal-lingual diameter of the single tooth instance. The three-dimensional measurement endpoint is calculated inversely based on the quantile, the centroid of the single tooth space and the measurement direction vector. The dental crowding assessment module is used to accumulate the mesiodistal diameters of each single tooth instance to obtain the required dental space, calculate the arc length of the cubic B-spline arch curve between the first and last single tooth instances and superimpose the compensation value of half the mesiodistal diameter of each first and last single tooth to obtain the available dental space, calculate the difference between the available dental space and the required dental space to obtain the arch length discrepancy, and output the quantitative assessment result of dental crowding based on the absolute value of the arch length discrepancy.

Images