Pelvic floor muscle reconstruction and morphological parameter automatic measurement method based on point cloud data

Abstract

The application discloses a pelvic floor muscle group reconstruction and morphological parameter automatic measurement method based on point cloud data, relates to the technical field of image processing, and comprises the following steps: after target structure point cloud is acquired, the coordinate scale is unified, the density is balanced, and outlier points are removed; point-level reliability weight is generated according to the attenuation shadow clue and the geometric consistency clue and is woven into a reliability field; the missing section with insufficient coverage and low reliability is positioned on the initial boundary candidate according to the arc length, and the key section is determined by calculating the parameter sensitivity of the arc section disturbance, and the intersection of the two is taken as the repair domain; the robust completion is carried out in the repair domain according to the reliability weight, the topological closure and continuity constraint are applied to obtain the closed boundary, and the uncertainty representation is output; according to this, the area, the circumference and the diameter and other parameters are calculated and propagated to obtain the interval, the error source section is attributed in combination with the sensitivity and the uncertainty, so that the measurement drift caused by the artifact is reduced, and the consistency and the reviewability are improved.

Description

Technical Field

[0001] This invention relates to the field of image processing technology, specifically to a method for pelvic floor muscle group reconstruction and automatic measurement of morphological parameters based on point cloud data. Background Technology

[0002] Quantitative assessment of the three-dimensional morphology of pelvic floor muscles (such as the levator ani muscles) is primarily used for postpartum functional assessment, rehabilitation follow-up, and research statistics. Clinically, it is used to obtain volume via transperineal three-dimensional or four-dimensional ultrasound or pelvic magnetic resonance imaging. A standard plane is defined based on landmarks such as the pubic symphysis and anorectal angle. The boundaries of the hiatus, the course of muscle bundles, and the contours of surrounding soft tissues are then depicted on the standard plane or its approximate cross-section. Morphological parameters such as area, perimeter, radial distance, maximum diameter, and minimum diameter are calculated. To improve efficiency and accuracy, existing methods automate the positioning, segmentation, or contour extraction of the standard plane, and generate meshes or point clouds from the segmentation results for three-dimensional reconstruction and measurement. In dynamic sequences or under load, keyframes or key planes need to be selected for comparative measurements. Current workflows are generally cascaded, with plane positioning errors, segmentation errors, and reconstruction errors uploaded and superimposed onto the final parameters. Results are usually output directly in numerical form, making it difficult to promptly expose local boundary distortions.

[0003] In actual data acquisition, strong reflections caused by intestinal gas, sound beam obstruction, attenuation shadows, changes in tissue contrast, and changes in probe posture can lead to missing echoes at the trailing edge or deep areas of the target, blurred boundaries, or false contours. This can result in missing points in the point cloud or mesh stage, outlier clusters, uneven sampling density, local normal disturbances causing non-closed contours, topological anomalies, or incorrect closure across gaps under global smoothing or fitting constraints.

[0004] Key measurements of pore-like structures are extremely sensitive to the location and closure of the trailing edge. Local defects can cause systematic shifts in parameters such as area, perimeter, and diameter, making it difficult to align and compare results from different operators, different devices, or at different times. In actual workflows, manual verification, re-tracing, and re-collection are still required to confirm the reliability of the results, reducing the efficiency advantages and rework costs brought by automation. Moreover, there are hidden dangers that may seem reasonable but are difficult to detect when the data is not verified.

[0005] Therefore, the current technical problem is that when occlusion artifacts cause local missing and outlier points in the point cloud, and the target structure needs to maintain a closed topology to support morphological measurements, it is difficult to simultaneously obtain stable and repeatable boundary or surface representations and morphological parameter results that can trace the source of error. Summary of the Invention

[0006] (a) Technical problems to be solved To address the shortcomings of existing technologies, this invention provides a method for pelvic floor muscle group reconstruction and automatic measurement of morphological parameters based on point cloud data. It locates insufficiently covered and unreliable defective segments on initial boundary candidates by arc length, and determines key segments by calculating the sensitivity of parameters to arc segment perturbation. The intersection of these two methods forms the repair domain. Within the repair domain, robust completion is performed according to reliability weights, and topological closure and continuity constraints are applied to obtain closed boundaries, outputting an uncertainty characterization. Based on this, parameters such as area, perimeter, and diameter are calculated and propagated to obtain intervals. By combining sensitivity and uncertainty attribution error sources, measurement drift caused by artifacts is reduced, thus solving the technical problems described in the background art.

[0007] (II) Technical Solution To achieve the above objectives, the present invention provides the following technical solution: A method for pelvic floor muscle group reconstruction and automatic measurement of morphological parameters based on point cloud data includes: acquiring a three-dimensional point cloud of the target structure of the pelvic floor muscle group and performing scale coordinate unification, density equalization, outlier suppression, and estimation of geometric features; wherein the target structure of the pelvic floor muscle group includes at least the boundary of the pelvic floor muscle group or its closed contour; determining reliability weights and generating a reliability field based on attenuated shadow cues and geometric consistency cues, and outputting the point cloud with reliability weights and the reliability field; generating initial boundary candidates based on the point cloud with reliability weights, dividing the initial boundary candidates into arc segments according to arc length, and determining the missing segments by statistically analyzing the coverage and reliability weights; applying arc segment perturbation to the morphological parameters to obtain parameter sensitivity and determining key segments, and outputting the intersection arc segments; Within the intersection arc segment, weighted robust fitting or completion is performed based on reliability weights to generate error-corrected segments and replace them with the initial boundary candidates; topological closure and geometric continuity constraints are applied to the boundary to obtain the final closed boundary or closed surface, and the uncertainty characterization is output; morphological parameters of the target pelvic floor muscle group are calculated based on the final closed boundary or closed surface; uncertainty propagation is performed on the morphological parameters in combination with the uncertainty characterization and the parameter interval results are output; error source segments are determined and output by combining parameter sensitivity and uncertainty characterization.

[0008] Furthermore, the three-dimensional point cloud is obtained by combining the first set of points formed by voxel boundary sampling and the second set of points formed by isosurface sampling. Each point carries echo intensity, local contrast, sampling ray direction and time series frame number. After the point cloud is constructed, a unified scale and coordinate system, point density equalization and preliminary outlier removal are performed.

[0009] Furthermore, before generating reliability weights, the local normal consistency and local surface fitting residuals of the 3D point cloud computing are used as geometric consistency cues. Combined with the attenuation shadow cues of echo intensity and the stability cues corresponding to adjacent frames, the reliability weights of each point are determined. The reliability weights are limited to between zero and one.

[0010] Furthermore, the reliability field is output together with the point cloud with reliability weights and the point numbers are kept consistent. The reliability field records the reliability weight information with spatial location as the index, and when receiving the query location, it outputs the average reliability weight and point coverage of the points in the neighborhood based on the fixed radius neighborhood. The fixed radius is determined by the average point spacing after the point density is balanced.

[0011] Furthermore, the initial boundary candidate is the intersection profile of the initial surface and the measurement reference plane. The intersection profile is discretized into a continuous point sequence according to the arc length order, and the point coverage degree and average reliability weight corresponding to the point cloud with reliability weight are retained on the point sequence. Closed endpoint coincidence correction is performed on the continuous point sequence.

[0012] Furthermore, the continuous point sequence is divided into continuous small segments along the arc length direction of the initial boundary candidate. The point coverage of each small segment is statistically analyzed and the average reliability weight is calculated. The small segments with insufficient point coverage and low average reliability weight are merged in the arc length direction to obtain the missing segments, and the position range and length information of the missing segments on the initial boundary candidate are output.

[0013] Furthermore, for each morphological parameter, a minimum displacement is applied along the local normal direction on each continuous segment of the initial boundary candidate, and the morphological parameter is recalculated to obtain the sensitivity distribution of the parameter to the continuous segment; the key segment is determined based on the sensitivity distribution, and only the intersection of the missing segment and the key segment is determined as the intersection arc segment.

[0014] Furthermore, a robust fitting mechanism with reliability weighting is constructed within the repair domain corresponding to the intersection arc segment. The reliability weight is used as the weight of the data item, and an upper limit is set on the error contribution of outliers. Local error correction reconstruction is performed to complete the intersection arc segment. The boundary segments outside the repair domain maintain the original point order and only perform smoothing processing.

[0015] Furthermore, topological closure and geometric continuity constraints are applied to the completed boundary. These constraints include simple connected closed loop constraints, closure error threshold constraints, and no self-intersection constraints. The intersection arc segments and the boundary segments on both sides are required to be continuous in the tangential direction and have smooth curvature changes. When a break, hole, or multi-connected branch is detected, the problem area is automatically located and local corrections are performed.

[0016] Furthermore, uncertainty propagation includes sampling the repair domain multiple times to generate various feasible completion results, calculating morphological parameters separately, and statistically obtaining parameter interval results; uncertainty source attribution includes correlating sensitivity distribution with uncertainty characterization to calculate the contribution of each continuous segment to the parameter interval results, and outputting the continuous segment with the largest contribution as the error source segment and giving the parameter change before and after repair. In this application, the target structure refers to the closable contour object formed by the pelvic floor muscle group on the measurement reference plane or its approximate cross section, at least the boundary contour of the hiatus; the measurement reference plane can be obtained by pelvic floor anatomical landmarks such as the pubic symphysis and the anorectal angle; the subsequent initial boundary candidate, defect segment localization, intersection arc segment repair, and calculation of morphological parameters such as area, perimeter, and diameter are all based on the target structure of the pelvic floor muscle group as the measurement object.

[0017] (III) Beneficial Effects This invention provides a method for pelvic floor muscle group reconstruction and automatic measurement of morphological parameters based on point cloud data, which has the following beneficial effects: By unifying the scale coordinates, balancing the density, and suppressing outliers in the 3D point cloud of the target structure, reliability weights and reliability fields are generated based on attenuated shadow cues and geometric consistency cues. Artifacts can be queried and used as unified inputs and support for gating calculations. Arc segments are divided according to arc length on the boundary candidates. Missing segments are located based on point coverage and arc segment reliability. Then, controlled perturbations are applied to the arc segments to calculate the parameter sensitivity of morphological parameters and locate key segments. Simultaneously, the intersection of missing segments and key segments is used to determine the intersection arc segments. The repair domain is directly related to the target parameters. Within the repair domain corresponding to the intersection arc segments, robust fitting or completion is used according to reliability weights to form error-correcting fragments to fill the boundaries, limiting the contribution of outlier errors to suppress artifact traction. Outside the repair domain, only the boundary point order is smoothed to reduce global morphological shift.

[0018] The completed boundary is defined with a single connected closed loop, a closure error threshold, and a topological closure constraint that prohibits self-intersection. The repair segment is defined to be tangentially continuous and have smooth curvature with the boundary segments on both sides. When detecting breaks or multi-connected branches, the problem area is located and locally corrected so that the final closed boundary or closed surface meets the geometric premise of measurement and calculation.

[0019] While outputting the final closed boundary or closed surface, the system also outputs the uncertainty characterization of the repair domain. During the morphological parameter calculation process, the system generates multiple completion results for the repair domain and recalculates the parameters to propagate uncertainty, ultimately forming a parameter interval result. This allows the measurement output to have an interval and a verification entry point, facilitating follow-up audits and retest comparisons.

[0020] The parameter sensitivity and uncertainty characterization of step three are combined to output the attribution step four, which outputs the error source segment that contributes the most to the parameter interval and gives the parameter change before and after the repair. This allows the review to focus on the source segment and provide supplementary sampling guidance, forming reliability weight, sensitivity gating, local error correction and interval attribution. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the automatic measurement method for pelvic floor muscle group reconstruction and morphological parameters according to the present invention. Detailed Implementation

[0022] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] Please see Figure 1 This invention provides a method for pelvic floor muscle group reconstruction and automatic measurement of morphological parameters based on point cloud data, including: Step 1, before the point cloud enters the defect segment localization and key segment gating, explicitly writes the local unreliability caused by artifacts, attenuation and occlusion into the point cloud, so that the point cloud is transformed into a geometric observation with reliability weight, thereby providing a stable input for subsequent local error correction reconstruction around the key arc segment.

[0024] When the point cloud of the pelvic floor muscles is obtained through voxel boundary sampling, isosurface sampling, or dense contour sampling, it inherits the differences in sampling posture and voxel resolution, resulting in local over-dense, local under-dense, and isolated point clusters. If reliability calculations are directly performed under these conditions, outliers may form high-impact pseudo-hotspots, causing subsequent defect localization to misjudge uneven sampling as structural defects. Therefore, the point cloud is first converted into a scale-comparable, density-controllable, and outlier-suppressible representation to provide a reliable geometric basis for the generation of the reliability field.

[0025] Taking the target structure point cloud as input, the spatial position of each point is represented as a point coordinate vector. The echo intensity, local contrast, sampling ray direction, and time series frame number are organized into a point attribute vector. Then, coordinate scale normalization and attribute alignment are completed first, followed by density equalization. Finally, local geometric features are solidified and outliers are suppressed based on the equalization results, so that decay cues and geometric consistency cues fall within the same reference system.

[0026] Starting from the comparability of the same structure under different acquisition postures, a unified measurement reference coordinate is determined, so that the point cloud no longer depends on device coordinates or voxel coordinates. The key lies in the synchronous processing of point coordinate vectors and point attribute vectors, avoiding the misalignment where the coordinates have been unified but the ray direction remains stuck in the original coordinate system, thereby destroying the directionality of attenuation cues.

[0027] During execution, the scale is first unified based on the voxel spacing and the enclosing range of the target structure, and the reference origin is determined by the centroid of the target structure, so that the point coordinate vector... A consistent scale baseline is maintained across different individuals and under different conditions. Then, the point attribute vectors are... The sampling ray direction is transformed to the same reference coordinate, and the echo intensity and local contrast are normalized. In another embodiment, when the acquisition end does not provide probe attitude recording, a reference axis is established by aligning with the main direction of the point cloud to maintain consistency within the same dataset.

[0028] Where the point coordinate vector Perform uniform scaling and origin normalization on the point attribute vectors. The sampling ray direction and intensity fields are simultaneously mapped to the reference frame and intensity scale. Using the point cloud scale allows for comparison of the impact of scale differences on the localization of missing segments; the ray direction is aligned with the point coordinates, and the attenuation cues point to the true deep occlusion. Consistent intensity fields and reliability weights make local attenuation more sensitive and the overall gain more robust.

[0029] With the goal of ensuring the availability of geometrically consistent cues, density equalization is first performed spatially, followed by outlier suppression in the equalized point cloud using a bounded influence approach. Density equalization employs voxel rasterization resampling: the space is divided using a preset voxel edge length, each voxel retains a representative point, and detail points at boundary inflections are preserved during representative point selection. In another implementation, density equalization uses minimum distance-constrained subsampling, ensuring that the distance between any two points is not less than a preset minimum distance.

[0030] Outlier suppression employs a neighborhood-based quadratic surface fitting: for each point, a nearest neighborhood is established, and after fitting a quadratic surface, the directed distance from the point to the fitted surface is used as the residual. This residual is then mapped to residual weights to limit the pull of extreme residuals. To avoid dependence on standard deviation or variance, a cutoff scale is determined using a neighborhood residual quantile threshold, and a bounded influence function is employed.

[0031] Where: residual weight : Value Used to depict points The degree of conformity to the neighborhood geometry serves as the geometric consistency basis for subsequent reliability weights; residuals : Value , indicating a point The directed distance to its neighborhood fitted quadratic surface; cutoff scale : Value The residuals are determined by the preset quantiles of the neighborhood residuals; specifically, a density equalization strategy is first used to compress locally overly dense and overly sparse areas, and then a local quadratic surface is used to fit the residuals. Then use residual weights Suppress outliers and solidify local geometric consistency cues.

[0032] Neighborhood selection: point Use either a fixed number of nearest neighbors or a fixed radius; nearest neighbor search can be implemented using a ball tree or an octree. Local coordinates: based on points. Construct local plane coordinates based on the local principal directions (e.g., the principal component directions of neighboring points), and then project the neighboring points onto the local plane coordinates; residuals Defined as a point The sign of the difference between the local coordinate height and the fitted height is determined by the local normal consistency convention.

[0033] When used, the arc segment coverage is more uniform, avoiding false gaps caused by uneven sampling. Residual weights By significantly reducing the weight of outliers, reliability calculations focus more on structural continuity disruptions rather than isolated point clusters. Local geometry is solidified, making it easier to further distinguish between attenuation artifacts and geometric outliers.

[0034] Furthermore, in actual acquisition scenarios, the trailing edge and deeper parts of the target structure are more prone to occlusion attenuation and artifacts, resulting in localized point cloud gaps and erroneous point clusters. Using only geometric residuals can confuse real anatomical changes with acquisition artifacts, while using only intensity values ​​is susceptible to overall gain drift. To support subsequent defect localization and parameter sensitivity gating, ray attenuation evidence is used as the main thread, coupled with geometric consistency evidence and optional temporal consistency evidence to form point-level reliability weights and weave a reliability field. Unreliable regions can be queried in a spatially continuous banded form.

[0035] Using balanced point cloud and residual weights As input, a continuous attenuation segment of the ray attenuation consistency index is constructed along the sampling ray, and then combined with the residual weight. Reliability weights are obtained by entering the monotonically saturated mapping. If there are multiple frame point clouds, cross-frame drift constructs a temporal inconsistency penalty and enters the mapping. Finally, the discrete weights are organized into a reliability field by interpolation or rasterization, and the reliability changes can be continuously retrieved according to spatial location.

[0036] Based on the axial continuity of occlusion attenuation, instead of directly using single-point intensity, an energy comparison is formed in the axial neighborhood of the point. Axial integration averages speckle fluctuations, separating continuous attenuation from random texture fluctuations, and providing more stable attenuation evidence for reliability weights.

[0037] Point The axial position is represented as the ray positioning coordinate. The echo intensity on this ray is expressed as an echo intensity function. Take axial windows before and after the point, with the window length being the axial window length. And construct the ray attenuation consistency index:

[0038] Where: X-ray attenuation uniformity index : Value Used to characterize points Energy comparison between the forward window and the backward window; echo intensity function : , indicating the sampling ray in the axial coordinate The function of upper echo intensity; the integrand of the axial energy integral; in the point cloud export stage, each point records its source voxel index and the coordinates of the sampling ray in the probe coordinate system, i.e., each point can be returned to an axial sampling line in the volume data. Axial coordinates The echo intensity function represents the distance from the probe origin to the point along the sampling ray. The position of the volume data at that point is obtained by trilinear interpolation.

[0039] The axial integral is approximated by discrete summation: the axial window is... and The volume data is discretized into several sampling points based on the axial sampling step size, and the integral is replaced by the sum of the sampled values ​​multiplied by the step size. The calculations can be directly applied in engineering.

[0040] Furthermore, when generating the point cloud, the volume data coordinate index and sampling ray identifier are saved for each point; axial coordinates... Defined as the distance along the sampling ray from the probe origin to the point position. The result is obtained from the volume data using trilinear interpolation along the ray axis: let the axial step size be... :

[0041] in The same applies to back windows.

[0042] Ray axis coordinates : Position parameters along the sampling ray direction; ray positioning coordinates :for ,point Axial position along the sampling ray direction; axial window length : The stability term is determined by the axial resolution of the volumetric data and the thickness scale of the target structure. The range of values ​​is This avoids the denominator being zero and suppresses the divergence of the ratio at extremely low energies, ensuring logarithmic stability.

[0043] Among them, the ray positioning coordinates are determined based on the sampling ray direction. , with axial window length For echo intensity function Perform integration before and after the window, and then use the ray attenuation consistency index. Characterizes the axial attenuation mode.

[0044] In use, the attenuation cue is enhanced from single-point intensity to continuous axial evidence, reducing the interference of speckle on artifact detection. The ratio and logarithmic forms mitigate the impact of overall gain drift on the index. (Radiation attenuation consistency index) It can be directly referenced in subsequent weight mapping. Axial comparison is used to separate occlusion attenuation from texture noise, making the attenuation evidence stable for inclusion in weight calculation.

[0045] The attenuation evidence and geometric evidence are placed within a weighting system, with reliability serving as a direct weight for subsequent boundary fitting and defect segment statistics; residual weight... As a geometrically consistent basis, the ray attenuation consistency index As evidence of attenuation, timing inconsistency penalty Optional, timing inconsistency penalty Constructed from the cross-frame drift amplitude and saturated-truncated and mapped to The reliability weights are monotonically saturated.

[0046] Where: reliability weight : Value Used to characterize points The overall credibility level, and subsequent steps are weighted by reliability. As a data item weight, it participates in arc segment reliability aggregation and boundary fitting; attenuation contribution coefficient : Value This is used to adjust the strength of the influence of decay evidence in the reliability weight; Geometric contribution coefficient Values , representing the reliability weight for geometric outlier degree; time-series contribution coefficient. : Value , which represents the reliability weight for timing inconsistency penalty; a value of 0 indicates that timing clues are not used; ray attenuation consistency index. Values To obscure evidence of attenuation.

[0047] Residual weights : Value Used to provide evidence of geometric consistency; temporal inconsistency penalty : Value It is used to reduce the weight of unstable points across frames.

[0048] After obtaining the point-level reliability weights, the discrete weights are woven into a reliability field: the interpolation path uses moving least squares interpolation or radial basis function interpolation, and the nearest neighbor search uses ball tree index or octree index. In another embodiment, the reliability field is expressed in a rasterized manner, aggregating the reliability weights of points within each voxel and performing continuous processing on adjacent voxels.

[0049] First, the radiation attenuation consistency index is... Residual weights Timing inconsistency penalty Through attenuation contribution coefficient Geometric contribution coefficient Time-series contribution coefficient Mapped to reliability weights Then, the point-level weights are woven into a queryable reliability field using interpolation or rasterization, and a weighted point cloud is output.

[0050] When in use, reliability weight Coupling attenuation, geometric, and temporal evidence within the same mapping ensures that unreliable points are consistently weakened in subsequent fitting and statistical analysis. The reliability field provides spatially continuous queries, enabling stable aggregation of arc segment reliability within its neighborhood. The coexistence of weighted point clouds and the reliability field provides a consistent data foundation for subsequent point-level weighted fitting and arc-level defect determination.

[0051] Step 2: Construct initial boundary candidates and locate missing segments on the point cloud with reliability weights. Then, calculate the sensitivity of morphological parameters to arc segments and gate the output of intersection arc segments so that subsequent error-correcting reconstruction only occurs within the boundary range that is both unreliable and has the greatest impact on measurement.

[0052] Step one provides the reliability weights. While a reliability field is obtained, the point cloud remains an unordered, discrete observation. Directly searching for gaps in the point cloud can lead to misinterpretations of sparse sampling and local outlier clusters as structural defects. Therefore, the point cloud is first transformed into a closed and parameterizable initial boundary candidate, and then reliability weights are aggregated in units of arc segments. This transforms unreliable locations into locatable starting and ending points of the defective segment.

[0053] First, a set of candidate points within the thickness band of the plane is selected based on the measurement reference plane, and a closed profile is constructed. Then, the closed profile is divided into arc segments along the arc length direction, and reliability weights are aggregated within each arc segment. Simultaneously, coverage is statistically analyzed; finally, continuous arc segments with insufficient coverage and low arc segment reliability are merged into a missing segment output. This output also carries the contour position and spatial point index, ensuring that step three can be directly referenced and local error-correcting reconstruction can be carried out within a limited range.

[0054] First, a geometric carrier along the contour direction is provided for the location of the missing segment. The goal is not to obtain the final boundary in one go, but to obtain initial boundary candidates that can be closed, ordered, and reused. Without this carrier, the continuity, start and end positions, and arc segment affiliation of the missing segment cannot be defined consistently.

[0055] The measurement reference plane is provided as an external input, which can be selected manually or given by an external positioning algorithm; its minimal representation is a point on the plane and its normal vector. All subsequent projections, intersections, and direction sets can be calculated using this representation, and the planar positioning method does not need to be included in the scope of this invention.

[0056] During execution, a planar coordinate system is first established using the measurement reference plane, and the point coordinate vectors are then... Project onto a plane; then extract candidate points within the plane's thickness band and weight them with reliability. As fitting weights, the attenuation points are reduced. An adjustable concave hull is used for contour construction: after two-dimensional triangulation of the projection points, the outer edge is trimmed according to the side length threshold to obtain the concave hull boundary. Then, the boundary points are sorted according to the cumulative chord length to form a point sequence. Finally, a periodic spline curve is used to fit the point sequence and force the beginning and end to close. The weighted least squares fitting can be transformed into a sparse linear equation system and solved by a conjugate gradient solver. If an initial surface mesh is provided at the input, the mesh can be intersected with the measurement reference plane to obtain a closed intersection line, and the reliability weights are inherited at the sampling points of the intersection line. As boundary candidates, this ensures the existence of alternative engineering paths within the same terminology system. The edge length threshold is determined by statistical analysis of the nearest neighbor distances of the projected points: quantiles are calculated using the set of distances from each point to its nearest neighbors, and the higher quantile is selected as the triangulation clipping threshold; and reliability weights are used. Distance statistics are weighted to prevent the threshold from being amplified in low-reliability regions. The periodic closure constraint of spline fitting can be expressed by the equality of the first and last control points and the first derivative, ensuring closure and tangential continuity.

[0057] First, the coordinate vector of the projection point is projected in the coordinate plane of the measurement reference plane. Then, weighted by reliability Initial boundary candidates are obtained through concave shell construction and periodic spline fitting. Concave shell construction involves: performing two-dimensional triangulation of the projection points within the measurement reference plane; for each triangulated edge, edges with side lengths greater than a threshold and their associated triangles are removed; the outer boundary of the remaining connected triangle set is used as the concave shell profile. The side length threshold can be determined by the high quantile of the nearest neighbor distance set of the projection points.

[0058] In use, the initial boundary candidates provide stable point order and closure constraints, and arc segmentation and continuous gaps can be described. Reliability weights. After fitting, the pull of the attenuation zone points is weak, and the initial contour will pass through the gap and close incorrectly. The output contour and point index are consistent, which facilitates subsequent arc aggregation.

[0059] Furthermore, the point-level reliability weights The key to upgrading to arc-level decision quantity lies in simultaneously controlling arc coverage and arc reliability, thereby limiting the missing segment to a continuous segment rather than an isolated point. The decision result needs to be directly usable in step three, so the arc range and spatial point index must be output simultaneously.

[0060] During execution, the initial boundary candidates are divided into arc segments according to the cumulative chord length. The arc segment division can use a fixed arc length or a fixed number of points, and a point-arc segment assignment number is established for each point. Calculate the reliability of each arc segment for its index. :

[0061] Where: arc segment reliability : Used to characterize arc segment number The average confidence level is used for defect segment determination; stability term : To avoid the denominator being zero when the number of arc points is zero and to suppress numerical divergence caused by a very small number of points; reliability weight. : Value Used as a point-level trusted input for arc segment aggregation; point arc segment attribution number. A set of positive integers used for indexing points. Map to arc segment numbers to limit the aggregation range; Arc segment number : A set of positive integers used to index the arc segments after contour segmentation and as the decision unit; conditional expression : Limit the summation to point indices with the same arc segment index; point index : A set of positive integers that identify individual points in a point cloud with reliability weights and participate in arc aggregation; Determining the missing segment while simultaneously constraining the reliability of the arc segment The system counts arc points and verifies whether a continuous low-reliability band is formed in the neighborhood using a reliability field. Adjacent arcs that meet the conditions are merged into a missing segment, and the range of arc numbers, the start and end positions of the contour, and the set of spatial point indices for the missing segment are output. A kernel-weighted normalized continuous reliability field is defined for any query location's spatial coordinate vector. The reliability field is taken as a kernel-weighted average of the reliability weights of neighboring points:

[0062] Where: reliability field The range of values ​​is Its function is to output the query position. Local reliability; query location coordinate vector The value range is in three-dimensional real space, and its function is as the independent variable of the reliability field; point coordinate vector. The value range is in three-dimensional real space, and its function is to represent the first value in the point cloud. Spatial location of each point; reliability weight The range of values ​​is Its function is to input the point-level credibility level output from step one; Neighborhood point set The function of kernel functions is to limit the set of points participating in the interpolation; it can be obtained by using a fixed-radius neighborhood or a neighborhood with a fixed number of nearest neighbors. Its function is to attenuate the contribution of neighboring points according to distance, ensuring that nearby points have a greater impact and distant points have a smaller impact. (Stability term) The range of values ​​is Its purpose is to prevent the denominator from being zero when the neighborhood is empty or the kernel weights are extremely small. The kernel function is given in the following form: Gaussian kernel:

[0063] Where: distance The range of values ​​is Defined as Nuclear width The range of values ​​is Its function is to control the range of spatial smoothing; it can be taken as the median of the nearest neighbor distance of the point cloud or a multiple of the average point spacing after density equalization. Fixed radius: , where the radius Desirable to Fixed number of nearest neighbors: Take distance The nearest preset number of points. Neighborhood retrieval can be implemented using a ball tree, octree, or grid hash.

[0064] First, assign numbers to the point arc segments. Aggregate reliability weight Obtain the reliability of the arc segment Then, by combining the number of arc points and the continuity of the reliability field, adjacent low-reliability arcs are merged and output as a missing segment.

[0065] When using it, the output of the missing segment has a clear start and end range and a set of point indices, which can be directly referenced in step three. The reliability of the arc segment... Introducing a stable term The sparse arc segments can still be compared, avoiding the interruption of the judgment due to the denominator being zero. The continuity constraint of the reliability field reduces the risk of mistaking isolated low-weight points as missing segments.

[0066] As an example: The operator loads a point cloud with reliability weights onto the measurement workstation and determines the measurement reference plane, generating initial boundary candidates for the plane thickness band. The reliability of the arc segment is then calculated. And a continuous low-reliability arc segment at the trailing edge of the contour; the reliability field presents a strip-shaped low-reliability region at the same location, and the continuous arc segment is merged into a missing segment and the start and end positions and point indices are output within this processing range.

[0067] The missing segment does not necessarily significantly change the area, perimeter or diameter. Direct repair may introduce unnecessary morphological changes. Based on the missing segment, a local disturbance test is introduced to construct the parameter sensitivity spectrum, and the intersection arc segment is output in a gated manner, so that the subsequent error correction reconstruction is concentrated on the arc segment that is both low reliability and high sensitivity.

[0068] For each arc segment, a controlled perturbation is applied under closed constraints, and the morphological parameters are recalculated to obtain the parameter sensitivity. Then, a comprehensive sensitivity is formed through logarithmic exponential aggregation. and the reliability of the arc segment Commonly mapped to repair priority Finally, the intersecting arc segments within the missing segment set are output according to repair priority, along with information on affected parameters and a set of point indices for use in step three. To ensure consistency in perturbation recalculation, morphological parameter indices are... It can include area, perimeter, maximum diameter, minimum diameter and preset direction radius. The area and perimeter can be obtained by integrating closed polygons, and the diameter parameters can be obtained by the extreme distance of the direction projection, so that the sensitivity calculation does not depend on external annotation.

[0069] To quantify the unit perturbation response of a certain arc segment to a certain parameter, the key is that the perturbation must be controlled and kept closed to avoid introducing fractures or self-intersections into the sensitivity calculation. Therefore, the perturbation only acts on points inside the arc segment, and the endpoints are fixed and the tangential continuity constraint ensures natural splicing with adjacent arc segments.

[0070] During execution, a unit arc segment normal is constructed on each arc segment. This unit arc segment normal is obtained by cross product and normalization of the measurement reference plane normal and the arc segment tangent. Subsequently, the perturbation scale is set. Under the condition of fixing the two endpoints of the arc segment and maintaining tangential continuity, the perturbation profile is obtained by displacing the points inside the arc segment along the normal direction of a unit arc segment. The morphological parameter sequence is then considered. Calculate the parameter values ​​before the disturbance respectively With the parameter values ​​after the disturbance , obtain parameter sensitivity :

[0071] Where: parameter sensitivity : Value Characterizing the arc segment number For morphological parameter serial numbers Unit disturbance response intensity; arc segment number : A set of positive integers, indexing the arc segments after contour segmentation and used as the unit for sensitivity calculation; parameter number : A set of positive integers, indexing the morphological parameters involved in the gating; morphological parameter values The value depends on the parameter type and is used as the baseline parameter value before perturbation; for closed sampling point sequences The area parameter uses the polygon area formula; the perimeter parameter is the sum of the Euclidean distances between adjacent points; the diameter on a unit vector in a certain direction is the maximum value minus the minimum value of the projection; the maximum and minimum diameters take extreme values ​​on the direction set.

[0072] Parameter values ​​after disturbance The value depends on the parameter type, is used for the parameter values ​​after arc segment perturbation, and is used to form the difference; perturbation scale. : Value Used to set the arc segment perturbation amplitude and for sensitivity normalization; perturbation scale Take the median distance between adjacent points in the closed sampling point sequence and multiply it by a preset scaling factor; First, the normal of a unit arc segment is constructed, and under the constraints of fixed endpoints and continuous tangential direction, the perturbation scale is used. The parameter sensitivity is obtained by perturbing the arc segment and recalculating the parameters. .

[0073] In use, sensitivity is derived from controlled perturbations and maintains closed constraints to avoid breaks or self-contamination of sensitivity introduced by perturbations. The perturbation scale... Normalization makes sensitivity comparable across different contour scales; parametric sensitivity It provides computable input for subsequent multi-parameter aggregation and gating.

[0074] Furthermore, the multi-parameter sensitivity is unified into a comprehensive sensitivity, which, together with the arc segment reliability, generates a sortable gating quantity. Logarithmic exponential aggregation is used to highlight large sensitivity, while logarithmic compression of the dynamic range is used to maintain numerical stability. Subsequently, exponential normalization is used to form a repair priority, so that the selection of intersection arc segments has a clear order and can be verified.

[0075] Let the number of parameters be the number of parameters. For each arc segment number Calculate the overall sensitivity :

[0076] Where: Overall sensitivity : Characterizing the arc segment number The overall sensitivity to all parameters is used as the gating input; arc segment number. : A set of positive integers, indexing the arc segments after contour segmentation and using them as the unit for calculating overall sensitivity; aggregation scale : Value This is used to control the degree to which the polymerization emphasizes high sensitivity; Parameter sensitivity : Value , used as aggregate input; parameter number : A set of positive integers used to index morphological parameters; the number of parameters : is a positive integer used to limit the range of summation; Then, the reliability of the arc segment was considered. Construction Repair Priority :

[0077] Where: Repair priority : Value Used to indicate arc segment number The relative repair priority is used to determine the output order of intersection arc segments; arc segment number : A set of positive integers that index the arc segments after contour segmentation and serve as the output unit for repair priority; Gating scale :for Used to adjust the degree of differentiation in priority; arc segment reliability : Values Used to be unreliable The importance of amplifying low-reliability arc segments; Overall sensitivity : Value This is used to amplify the importance of highly sensitive arc segments; the total number of arc segments. : A positive integer used to limit the range of normalized summation; arc index : A set of positive integers used for normalized summation over all arc segments; Intersecting arc segments are selected only from the set of missing segments: within the missing segments, they are selected according to repair priority. Collect and merge continuous arc segments, and output the arc segment index range, contour start and end positions, and spatial point index set of the intersecting arc segments; simultaneously, consider the parameter sensitivity within the same arc segment. The parameter index corresponding to the maximum value is written into the output as the associated information of the affected parameters.

[0078] The overall sensitivity is first obtained by logarithmic exponential aggregation. Then, the reliability of the arc segment With overall sensitivity Mapped to repair priority Finally, within the set of missing segments, the information on the association between the intersecting arc segments and the affected parameters is output in order of priority.

[0079] When using, consider overall sensitivity. Reduce the impact of dimensional differences on multi-parameter synthesis and highlight key sensitive segments, prioritizing repair. By coupling low reliability with high sensitivity, the intersection arc is focused on the range most likely to cause measurement drift. The intersection arc carries a set of point indices, allowing step three to directly reference reliability weights within this range. Conduct localized error-correction reconstruction.

[0080] Step 3: Utilize reliability weights within the defined range of intersection arc segments. The error correction fragment is generated and replaced with the boundary candidate. Then, topological closure and self-intersection suppression constraints are applied to obtain a measurable closed boundary or closed surface, and the uncertainty characterization of the repair domain is output.

[0081] Outlier clusters may exist within the intersection arc segment, while the area outside the intersection arc segment contains highly reliable boundary information. If global fitting is used, local completion is easily pulled by global smoothing, resulting in overall drift; if fitting is only performed within the intersection arc segment without locking adjacent reliable segments, tangential breaks may occur between the completed segment and adjacent segments, inducing self-intersection. Therefore, the repair domain point index is first extracted and anchor point freezing constraints are constructed, and then robust fitting with reliability weighting is performed under the freezing constraints.

[0082] Using the range of arc segment indices and spatial point indices of the intersecting arc segments as the entry point, a set of repair point indexes is generated. And based on repair priority Add supporting arc segments to form a supporting domain; then extract the corresponding segments from the initial boundary candidates and construct anchor point sequences at both ends of the segments. The anchor point sequences are obtained by projecting the high reliability points selected by the reliability field; then construct the reliability-weighted robust energy under the anchor point freezing constraint and solve the control points to obtain the error correction segments; finally, replace the error correction segments back with the initial boundary candidates to output the intermediate results of the error correction boundaries, which are used for topology closure verification and secondary correction.

[0083] To transform the intersecting arc segments into a solvable repair domain and adjacent reliable segments into anchor point freezing constraints, and to avoid outlier clusters dominating the fitting within a local area, anchor points are not determined by single points, but rather by the spatial continuity of the reliability field. The anchor point set is then projected onto the measurement reference plane to form an anchor point sequence, ensuring that the anchor point sequence is naturally distributed along the boundary direction. Control points within the repair domain are allowed to move, ensuring that the endpoint positions and endpoint tangential directions remain consistent when the error-corrected segments are replaced back to the original boundary.

[0084] During execution, first determine the arc segment's assigned number. Extract a set of repair point indices from a point cloud with reliability weights. Subsequently, repair priority was assigned. Select supporting arc segments and limit the cumulative chord length of the supporting arc segments to ensure that the supporting arc segments cover the endpoint neighborhood; then, perform a fixed-radius query on the endpoint neighborhood in the reliability field to filter reliability weights. Points above the threshold are projected onto the measurement reference plane to obtain the anchor point sequence; finally, the boundary points corresponding to the anchor point sequence are located on the initial boundary candidates and their positions and tangential unit vectors are frozen. The freezing method adopts consistency constraints and is written into the constraint set of the solver.

[0085] In engineering implementation, neighborhood queries can use octree indexes, tangential unit vectors can be obtained by boundary point order difference and normalization, and constraint solutions can be achieved using the augmented Lagrange method.

[0086] First, the point arc segment is assigned a number. Extract the set of repair point indices Then, support arc segments are added, and high-reliability points are selected from the reliability field to form an anchor point sequence and the position and tangential constraints are frozen.

[0087] The repair domain and the support domain correspond to the point index set and the arc range, respectively, so that the solution range in step three has a verification boundary; anchor point freezing writes the reliable segment into the boundary condition, and the endpoints are continuous and tangentially continuous after the error correction segment is replaced. The reliability field screening does not select isolated outliers to be added to the anchor point sequence, reducing the probability of endpoint constraints being contaminated by noise.

[0088] Generate error correction segments under anchor point freeze constraints, and assign reliability weights. Data terms are introduced to reduce the contribution of decaying artifact points, and a saturation-type error morphology is used to limit the impact of large residuals. This allows the geometric trend of adjacent reliable segments to be continued at points where the point cloud is missing without bridging across artifacts. During execution, the error-corrected segments are represented as control points. The parameter curve, the set of repair point indices The directed distance from each point within the curve is denoted as the residual. Build robust energy :

[0089] In the formula: robust energy : Value Used as the solution objective to generate error-corrected segments; set of repair point indices : Finite set, used to limit data items to only come from the repair domain and the support domain; point index : Positive integer, used for index repair points; reliability weight : Value Used to weight point residual terms; residual : Value Used to characterize the directed distance error from a point to a curve; Curve representation: Error correction segments can be represented by control points. The cubic spline or polygonal line approximation; the nearest point rule: for each point Find the line segment closest to the point in the set of broken line segments and take the distance from the foot of the perpendicular as the distance to the point. Sign rule: Within the measurement reference plane, take the tangential unit vector of the nearest line segment, rotate it 90 degrees clockwise to obtain the normal unit vector, and determine the sign based on the half-plane of the point relative to the line segment. The symbols are locally continuous.

[0090] Robust Scale : Value It is used to control the transition of error from quadratic growth to saturation growth; smoothing coefficient : Value Used to adjust the intensity of second-order difference smoothing; control points : Values ​​are taken in a two-dimensional vector space and used as free variables for the curve; control point number : The value is a positive integer and satisfies Used to index internal control points; total number of control points : is a positive integer and satisfies , used to limit the length of the control point sequence; The solution is obtained in two stages: first, the parameters are fixed and the solution is obtained using Gauss-Newton iteration. Then update the parameters and repeat the iteration; the Jacobian can be obtained using analytical derivatives or finite differences, with the finite difference step size and robust scale being determined. Linkage is used to avoid numerical jitter. If the reconstructed object is a surface segment, the control points are expanded into a control mesh and expressed as tensor product splines. The second-order difference is applied simultaneously in two parameter directions, which can still form a sparse structure and be solved using a conjugate gradient solver.

[0091] First, the reliability weight is obtained. and robustness scale The saturated data terms are composed of second-order difference smoothing terms, forming robust energy. Then, the control points are solved under the anchor point freezing constraint. It also outputs the error-corrected segment.

[0092] When in use, reliability weight After its addition, the impact of decay artifact points on the error correction segment is systematically reduced, the saturated error morphology limits large residuals, outlier clusters no longer affect control point updates, and the tendency to bridge gaps is reduced. The synergy between second-order difference smoothing and anchor freezing ensures that the curvature change is continuous when the error correction segment is replaced back to the original boundary.

[0093] For example: The operator inserts a key cloud with reliability weights and loads the intersection arc segment. Initial boundary candidates and sections to be repaired appear on the measurement reference plane. The system selects high-reliability points at both ends based on the reliability field to form an anchor point sequence and lock the boundary points. Then the system solves the robust energy and outputs the error correction segment. After the error correction segment replaces the initial boundary candidate, the endpoint contour is continuous.

[0094] The intermediate results of the error correction boundary may still contain close-range crossings, self-intersecting thin loops, or multi-connected segments, which can cause ambiguity in the area integration path of step four and affect the location of the diameter extremum. Therefore, it is necessary to solidify the simply connected closed loops and output the uncertainty characterization and candidate completion set of the repair domain.

[0095] First, the closure and connectivity of the error correction boundary are checked. If multiple connected segments appear, the main boundary connected to the anchor point sequence is retained and isolated segments are removed. Then, under the anchor point freezing constraint, the endpoint consistency and self-intersection suppression potential is applied to the error correction segment and the solution is solved twice to make the boundary satisfy a single connected closed loop. Subsequently, the arc-level uncertainty radius is constructed by weighting the residuals of the repair points, and a feasible complete set is generated as the output under the control of the uncertainty radius, which provides a direct input for the uncertainty propagation in step four.

[0096] The topology closure requirement is transformed into a solvable potential energy, and only the error correction segment is corrected while keeping the anchor points frozen. The endpoint consistency potential energy ensures that the beginning and end of the error correction segment are connected in a consistent manner, and the self-crossing suppression potential energy ensures that the separation between non-adjacent sampling points is kept to a minimum. To control the computational scale, self-crossing suppression is only calculated for sampling point pairs that may cross at close range, and a set of point pairs is generated by spatial grid hashing.

[0097] Furthermore, sampling points are obtained by uniformly sampling along the error correction segment during execution. And construct a set of non-adjacent sampling point pairs. Reconstruct the topological closed potential energy :

[0098] Where: Topological closed potential energy : Value Used to constrain endpoint consistency and suppress self-intersection; sampling points : Values ​​are taken in a two-dimensional vector space, used for the discrete representation of error-correcting segments and for potential energy calculation; sampling point number , : Values ​​are positive integers used to index the set of point pairs Total number of sampling points The range of values ​​is a positive integer and satisfies Used to determine endpoint sampling points and ; Point-to-point set The value is a finite set, used to limit the calculation of repulsive potential energy only on non-adjacent but spatially close point pairs; potential energy coefficient. : Values Used to adjust the intensity of self-pollination inhibition; stabilizing term : Values This is used to prevent the denominator from being zero and to create strong repulsion. The second-order correction employs sequential quadratic programming or the augmented Lagrange method: using control points Minimize robust energy for initial conditions With topological closed potential energy The weighted sum is used while keeping the anchor point frozen constraint unchanged; the gradient can be obtained analytically by the chain derivative or by finite difference. Sampling points are first obtained by uniform sampling. And generate a set of point pairs using spatial raster hashing. Then, using topological closed potential energy Drive secondary correction while keeping the anchor point freeze constraint unchanged.

[0099] In use, endpoint consistency terms solidify closed connections, ensuring the unique closure of the integral paths for area and perimeter calculations. Barrier potential energy creates repulsion at close-range crossing point pairs, suppressing self-intersections during the solution phase without relying on post-processing shearing. (Point pair set) Generated by spatial grid hashing, the computational scale of self-intersection suppression is controllable and easy to implement in engineering.

[0100] Furthermore, a propagable uncertainty characterization is provided for step four. It uses the weighted quantile of the residual amplitude as the arc-level uncertainty radius, thus linking uncertainty with reliability weights. Robustness Scale Furthermore, the residual fitting error after anchor point freezing remains homogeneous and independent of variance or standard deviation. Subsequently, the perturbation amplitude of the control points along the normal to a unit arc segment is limited by the uncertainty radius, and a topological closure potential is applied after each perturbation. The rapid correction ensures that the candidate complement always satisfies endpoint consistency and self-intersection inhibition.

[0101] The set of repair point indices will be used during execution. By arc segment number Divided into a set of indices of points inside the arc segment Recalculate the residuals And construct the uncertainty radius :

[0102] Where: Uncertainty radius : Value Used to specify the arc segment number Geometric oscillation amplitude and drive candidate completion generation; arc segment number : Positive integer, used to index arc segments; quantile operator : Used to return the first digit of the input sequence The quantile value is formed by sorting the input sequence in ascending order and taking the quantile number as the quantile value. Element; quantile coefficient values , Controlling quantile position and degree of conservatism, residuals Values The amplitude of the uncertainty radius is the source of the set of indices of points within the arc segment. , is a finite set used to limit the number of points in quantile calculations; the floor operator. It maps quantile positions to integer indices, taking values ​​from a finite sequence, where the sequence length is... The value range is positive integers, and the quantile number is obtained from the number of points within the arc segment.

[0103] Subsequently, the uncertainty radius was used. As the upper limit of the amplitude, for control points A controlled perturbation is performed along the normal direction of a unit arc segment to generate candidate error correction segments. Each candidate segment is then passed through a topological closed potential after generation. Rapid correction of solidified endpoint consistency and self-crossing suppression; the number of candidates is determined by repair priority. The allocation process generates more candidates for higher-priority arc segments. If the reconstructed object is a surface segment, a perturbation is applied to the displacement of the surface vertices along the local normal, and after each perturbation, Laplacian smoothing and topological closure potential are combined. Make corrections to maintain the continuity of the facets and prevent them from crossing over.

[0104] First, the quantile operator is used. Calculate the radius of uncertainty And then Limiting Disturbance Control Points and through topological closed potential energy Quickly correct and generate feasible complete sets And output it. As a supplement, for each arc segment number... Define a set of fixed amplitude coefficients (e.g., three values: negative, zero, positive), and multiply the amplitude coefficients by the uncertainty radius along the normal of the control point along a unit arc segment. Disturbance; for high repair priority Choose more combinations of amplitude coefficients for the arc segment, for low The arc segment selection has fewer combinations. A topological closure potential energy is performed once after each generation. The rapid correction eliminates candidates that do not meet the closure or self-inhibition requirements, and the remaining candidates constitute .

[0105] When using it, the uncertainty radius Characterizing the substitutable magnitude of the repair domain in quantile form ensures that the uncertainty expression aligns with the residual source, enabling feasible completion of the complete set. After each generation, endpoint consistency and self-intersection suppression are satisfied to prevent the interval propagation in step four from introducing topologically unqualified candidates. Repair priority. Participating in candidate allocation makes the candidate coverage of high-sensitivity arcs more comprehensive and facilitates source attribution.

[0106] Step 4: Unify the point estimation of the closed boundary and the interval propagation of the candidate completion into the same measurement operator, and locate the interval fluctuation to a specific arc segment to form a verifiable and traceable measurement output.

[0107] Step three ensures closure and no self-intersections, but interval propagation requires the same sampling rule, the same direction definition, and the same discrete integration path. If the candidate completion and the final boundary are inconsistent in sampling density or point order direction, the interval width will be mixed with discrete errors. Therefore, the closed sampling point sequence must be solidified. The generation rules and direction set are determined, and a sequence of candidate sampling points is generated under the same rules. With candidate parameter values .

[0108] Among them, a closed sampling point sequence is generated from the final boundary. Then, arc length resampling is performed, and then the area, perimeter, maximum diameter, minimum diameter and preset direction radius are calculated within the measurement reference plane to obtain morphological parameter values. Then, a feasible complete set was added. Each candidate completion is converted into a candidate sampling point sequence according to the same arc length and direction set rule. And recalculate the candidate parameter values. Provides input from the same source.

[0109] The final boundary is solidified into a discrete object that can be repeatedly measured, and the direction search of diameter-type parameters is fixed on a direction set. The order is as follows: first, the closure and point sequence direction are unified; then, the arc length is homogenized; finally, the direction set is bound to a preset direction radius, so that the diameter meaning of different candidate completions is consistent.

[0110] During execution, the final boundary is represented as a sequence of closed sampling points. Total number of sampling points A preset integer is used; arc length resampling employs piecewise linear interpolation or cubic spline interpolation, with periodic extension at the closed endpoints to maintain consistency. The point sequence direction is then determined by the directed area sign, and the point sequence is reversed if necessary to unify the direction. Next, the direction set is locked: the direction set consists of unit vectors within the measurement reference plane, with angular intervals consistent with the preset direction radii; the maximum and minimum diameters are obtained on this direction set using the difference of projected extreme values. Optionally, when the maximum distance from a boundary point to its convex hull boundary is lower than a preset threshold, the convex hull is first calculated, and a rotating caliper is used to reduce the number of direction traversals.

[0111] First, a closed sampling point sequence is constructed. Then, the point order direction and arc length density are unified, the direction set is locked, and the diameter parameters are calculated accordingly.

[0112] When using it, the closed sampling point sequence The uniformity of arc length ensures that the discrete accumulation of perimeter and area has a consistent scale, the unification of point order and direction ensures that the vector measurement convention is consistent, avoiding ambiguity of parameter signs, and the locking of direction set ensures that the maximum diameter and the minimum diameter have the same search domain, which facilitates interval propagation and attribution alignment.

[0113] Complete the feasible set Convert it into a set of candidate parameter values ​​and use the quantile operator Generate the interval boundaries. This depends on the uncertainty radius obtained in step three. The corresponding candidate morphological differences do not introduce second-order moment statistics, thus maintaining the geometric interpretability of the interval.

[0114] The feasible complete set will be completed during execution. Each candidate completion tag in the middle is marked with a candidate number. Total number of candidates The value is a preset positive integer; each candidate is padded to generate a candidate sampling point sequence. The arc length and direction set rules of technical point four are followed; then the candidate parameter values ​​are calculated. And according to parameter number Grouping. Quantile operator Linear interpolation quantiles can be used to reduce the impact of the total number of candidates. Boundary jumps caused by finiteness can be addressed by setting candidate weights and performing weighted quantiles during candidate completion. The lower and upper bounds of the interval are defined as follows:

[0115] Where: lower bound of the interval The value range varies depending on the parameter index. Dimensional determination; upper bound of the interval The value range varies depending on the parameter index. Dimensional determination is used for higher quantile boundaries; quantile operators : Used to return the first Percentage value, in the form of ascending sort and then taking the index. The elements; sort the input sequence in ascending order to obtain Take the serial number as elements As the output. If linear interpolation is used, linear interpolation is performed between adjacent indices, but the output is still considered as... The implementation method.

[0116] quantile coefficient The range of values ​​is Used with Together, upper and lower bounds are determined; candidate parameter values The value depends on the parameter number. Dimensional determination, used for quantile input; morphological parameter sequence number : Values ​​are a set of positive integers used to index the area, perimeter, maximum diameter, minimum diameter, and preset direction radii; candidate index : The value is a positive integer and satisfies Used for index candidate completion; total number of candidates : Positive integer, used to limit the candidate size and participate in quantile position calculation; floor operator : Used to map quantile positions to integer indices; where, first, candidate parameter values ​​are obtained. Then use the quantile operator Output the lower bound of the interval and the upper bound of the interval .

[0117] When using, candidate parameter values Generated under the same measurement operator, making the interval boundaries correspond to candidate geometric differences, quantile operator It directly applies to a finite number of candidate sequences, facilitating engineering implementation and maintaining interval verifiability; the interval boundaries can be correlated with the candidate sequence numbers. Binding outputs provides a traceability entry point for subsequent attribution.

[0118] Interval boundaries do not directly indicate the source of error. Step two provides parameter sensitivity. Step 3 provides the uncertainty radius. And fix priority Since the gating information has been fixed, sub-step 402 couples the three into arc segment contribution weights. The attribution results are packaged together with the differences before and after the repair to support the review and supplementary sampling decisions.

[0119] Furthermore, define the set of repair arc segments. For each parameter index, the set of arc segment indices covered by the intersection arc segments is given. Calculate the contribution weight of the arc segment It then outputs the range of the continuous arc segment that contributes the most. Subsequently, it calculates the parameter values ​​before repair using the same measurement operator. Compared with the repaired parameter values Difference and the difference Interval boundaries, range of error source arc segments, candidate sequence number With candidate parameter values The output is encapsulated. Finally, the normal is derived from the boundary tangent within the error source arc range, and then combined with the reliability weight. The spatial descent direction provides an indication of the replenishment direction.

[0120] Sensitivity, oscillation amplitude, and gating strength are combined into a sortable attribution factor, and exponential normalization is used to ensure the comparability of contribution weights. Its output is the range of continuous error sources combined by arc segment number, which can be directly mapped to a closed sampling point sequence. During execution, the set of repaired arc segments is... Inner arc segment number Calculate the contribution weight of the arc segment :

[0121] Where: arc segment contribution weight : Values Used for relative contribution of arc segments and for ranking; attribution scale : Values Used to adjust the sharpness of the distribution; repair priority : Values Used for injecting gating information; radius of uncertainty : Values Used to characterize the amplitude of arc segment oscillation; parameter sensitivity : Values , used to characterize the intensity of parameter response; Repair arc segment set : Values ​​are taken from a finite set, used to limit the scope of attribution; arc segment number : The value is a set of positive integers used to index arc segments; parameter number : Values ​​are a set of positive integers used for indexing parameters; arc segment index : The set of values ​​is a positive integer, used for normalized summation index; Based on this, the contribution weight is determined by the arc segment. Sort and merge the error source ranges of consecutive arc segments; to maintain continuity, perform a one-dimensional convolution smoothing on the arc segment index, with the total sum of the convolution kernels being one. Exponential function. It can be replaced by a positive value mapping of a power function and normalized, as long as the sum of the monotonically increasing coupling quantity and the normalization is kept to be one.

[0122] First, the arc segment contribution weight is calculated. Then, sort and merge the error source ranges of continuous arc segments, and assign weights to the arc segments. Simultaneously, coupling repair priority Uncertainty radius and parameter sensitivity Attribution, gating, and completion of oscillating links are of the same origin; exponential normalization is on the same scale; sorting and merging are performed; and the range of error sources is mapped to the closed sampling point sequence. , supplementary sampling direction indication and verification positioning.

[0123] Furthermore, the point estimate, interval, attribution range, and variance are organized into a single output package, providing indications for re-sampling direction for field execution. The core principle is to explicitly record the remediation impact as a variance. and with reliability weight The spatial descent direction constrains the direction of supplementary mining.

[0124] Calculate the parameter values ​​before repair during execution. Compared with the repaired parameter values And obtain the difference quantity Output packet write parameter values Lower bound of the interval Upper bound of the interval Error source range, arc segment contribution weight Sort list, candidate number With candidate parameter values The supplementary sampling direction indicator is obtained by differentiating the unit tangent from adjacent sampling points within the error source range, then rotated 90 degrees in the measurement reference plane to obtain the unit normal, and a fixed-radius neighborhood query is performed on both sides of the normal to compare reliability weights. The aggregate value is used to select the side with the smaller aggregate value as the indication direction; if the input is a surface, the local surface normal is used instead of the plane normal and the same reliability comparison is performed.

[0125] Among them, the difference was obtained. After being loaded into the output packet, the re-sampling direction is obtained by comparing the normal configuration with the reliability. Difference quantity The repair process is linked to the final output, which facilitates the verification of actual changes in parameters. The output package binds the interval, attribution range and candidate index. The source of the interval can be traced back to the candidate completion and arc range. The supplementary sampling direction is determined by the geometric normal and reliability comparison. The direction and reliability evidence are from the same source and are easy to operate.

[0126] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0127] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0128] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0129] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0130] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for pelvic floor muscle group reconstruction and automatic measurement of morphological parameters based on point cloud data, characterized in that: include, A 3D point cloud of the target structure of the pelvic floor muscles is acquired and subjected to scale coordinate unification, density equalization, outlier suppression, and geometric feature estimation. The target structure of the pelvic floor muscles includes at least the boundary of a fissure formed by the pelvic floor muscles or its closed contour. Reliability weights are determined based on attenuated shadow cues and geometric consistency cues, and a reliability field is generated. The point cloud with reliability weights and the reliability field are output. Initial boundary candidates are generated based on the point cloud with reliability weights. The initial boundary candidates are divided into arc segments according to arc length, and the coverage and reliability weights are statistically analyzed to determine missing segments. Arc segment perturbations are applied to morphological parameters to obtain parameter sensitivity and determine key segments. Intersecting arc segments are output. Within the intersection arc segment, weighted robust fitting or completion is performed based on reliability weights to generate error-corrected segments and replace them with the initial boundary candidates; topological closure and geometric continuity constraints are applied to the boundary to obtain the final closed boundary or closed surface, and the uncertainty characterization is output; morphological parameters of the target pelvic floor muscle group are calculated based on the final closed boundary or closed surface; uncertainty propagation is performed on the morphological parameters in combination with the uncertainty characterization and the parameter interval results are output; error source segments are determined and output by combining parameter sensitivity and uncertainty characterization.

2. The method for automatic measurement of pelvic floor muscle group reconstruction and morphological parameters according to claim 1, characterized in that: The three-dimensional point cloud is obtained by combining the first set of points formed by voxel boundary sampling and the second set of points formed by isosurface sampling. Each point carries echo intensity, local contrast, sampling ray direction and time series frame number. After the point cloud is constructed, a unified scale and coordinate system, point density equalization and preliminary outlier removal are performed.

3. The method for automatic measurement of pelvic floor muscle group reconstruction and morphological parameters according to claim 2, characterized in that: Before generating reliability weights, the local normal consistency and local surface fitting residuals of the 3D point cloud computing are used as geometric consistency cues. Combined with the attenuation shadow cues of echo intensity and the stability cues corresponding to adjacent frames, the reliability weights of each point are determined. The reliability weights are limited to between zero and one.

4. The method for automatic measurement of pelvic floor muscle group reconstruction and morphological parameters according to claim 3, characterized in that: The reliability field and the point cloud with reliability weights are output together and the point numbers are kept consistent. The reliability field records the reliability weight information with spatial location as index, and when receiving the query location, it outputs the average reliability weight and point coverage of the points in the neighborhood based on the fixed radius neighborhood. The fixed radius is determined by the average point spacing after the point density equalization.

5. The method for automatic measurement of pelvic floor muscle group reconstruction and morphological parameters according to claim 4, characterized in that: The initial boundary candidate is the intersection profile of the initial surface and the measurement reference plane. The intersection profile is discretized into a continuous point sequence according to the arc length. The point sequence retains the point coverage degree and average reliability weight corresponding to the point cloud with reliability weight, and the continuous point sequence is corrected for closed endpoint coincidence.

6. The method for automatic measurement of pelvic floor muscle group reconstruction and morphological parameters according to claim 5, characterized in that: The continuous point sequence is divided into continuous small segments along the arc length direction of the initial boundary candidate. The point coverage of each small segment is statistically analyzed and the average reliability weight is calculated. The small segments with insufficient point coverage and low average reliability weight are merged along the arc length direction to obtain the missing segment. The location range and length information of the missing segment on the initial boundary candidate are output.

7. The method for automatic measurement of pelvic floor muscle group reconstruction and morphological parameters according to claim 6, characterized in that: For each morphological parameter, a minimum displacement is applied along the local normal direction on each continuous segment of the initial boundary candidate, and the morphological parameter is recalculated to obtain the sensitivity distribution of the parameter to the continuous segment; the key segment is determined based on the sensitivity distribution, and only the intersection of the missing segment and the key segment is determined as the intersection arc segment.

8. The method for automatic measurement of pelvic floor muscle group reconstruction and morphological parameters according to claim 7, characterized in that: A robust fitting mechanism with reliability weighting is constructed within the repair domain corresponding to the intersection arc segment. The reliability weight is used as the weight of the data item, and an upper limit is set on the error contribution of outliers. Local error correction reconstruction is performed to complete the intersection arc segment. For boundary segments outside the repair domain, the original point order is maintained and only smoothing is performed.

9. The method for automatic measurement of pelvic floor muscle group reconstruction and morphological parameters according to claim 8, characterized in that: Topological closure and geometric continuity constraints are applied to the completed boundary. The constraints include simple connected closed loop constraints, closure error threshold constraints, and no self-intersection constraints. The intersection arc segments and the boundary segments on both sides are required to be continuous in the tangential direction and have smooth curvature changes. When a break, hole, or multi-connected branch is detected, the problem area is automatically located and local corrections are performed.

10. The method for automatic measurement of pelvic floor muscle group reconstruction and morphological parameters according to claim 9, characterized in that: Uncertainty propagation involves sampling the repair domain multiple times to generate various feasible completion results, calculating morphological parameters for each, and then statistically obtaining the parameter interval results. Uncertainty source attribution involves correlating the sensitivity distribution with the uncertainty characterization, calculating the contribution of each continuous segment to the parameter interval results, and outputting the continuous segment with the largest contribution as the error source segment and providing the parameter changes before and after repair.

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