A method for constructing a spatial measurement reference based on a three-dimensional organ model

Abstract

The application discloses a kind of space measurement benchmark construction methods based on three-dimensional organ model, to solve the problem of lack of anatomical explainability and insufficient robustness to biological individual differences due to dependence on external morphology or overall registration in prior art.Methods include: collecting voxel data of target three-dimensional organ model and coordinates and topological relationship of internal inherent anatomical feature points;Based on anatomical prior knowledge, define a hierarchical benchmark space network containing topological layer, geometric constraint layer and coordinate system layer;The anatomical feature point set of target model is mapped and adapted to the benchmark network, and the coordinate transformation relationship is established.The application constructs the benchmark by taking the internal stable anatomical structure network as the skeleton, significantly improves the adaptability to morphological variation, gives the spatial coordinates clear anatomical semantics, and realizes the whole traceability of the measurement process, providing a reliable foundation for precision medical research and multi-source biological space data integration.

Description

Technical Field

[0001] This invention relates to the field of space measurement technology, and in particular to a method for constructing a space measurement benchmark based on a three-dimensional organ model. Background Technology

[0002] With the rapid development of spatial measurement technology and bioinformatics, obtaining high-resolution three-dimensional digital models of human organs has become a reality. These three-dimensional organ models are playing an increasingly important role in disease diagnosis, surgical planning, drug development, and basic biological research. For example, large-scale international scientific projects such as the Human Biomolecular Atlas Project (HuBMAP) are dedicated to integrating massive amounts of three-dimensional spatial data from different individuals and organs to construct a complete human cellular atlas. In such research and applications, a fundamental and crucial step is establishing a unified spatial measurement benchmark, enabling the precise location, measurement, and comparison of three-dimensional models and their internal tissue and cellular features from different sources, under different imaging conditions, and even from different individuals.

[0003] However, spatial measurement based on 3D organ models currently faces several significant technical challenges. First, the biological variability of organs themselves and the deformation introduced by the imaging process make it extremely difficult to establish a stable and universal measurement benchmark. Different individuals and the same organ exhibit natural differences in size, shape, and internal structure; even within the same individual, organs can change under different physiological or pathological conditions. Furthermore, the image data used to construct 3D models (such as tissue sections, CT scans, and MRI scans) inevitably introduce errors such as translation, rotation, scaling, and non-rigid deformation during acquisition, processing, and 3D reconstruction. Existing techniques typically employ simple methods based on external markers or global image registration to align the model. The former relies on artificially added physical markers on or around the organ surface, which are often difficult to implement in clinical or experimental settings or can damage the sample; the latter attempts to globally match the entire 3D model with an idealized template, but this method is ineffective for organs with complex and variable morphologies (such as cerebral sulci and liver lobes), easily generating large registration errors in local areas, leading to distortion of the spatial correspondence of detailed structures.

[0004] Secondly, existing methods fail to fully utilize the inherent anatomical structures within organs. An organ is not a homogeneous geometry; it contains a complex topological network composed of blood vessels, nerves, functional zones, and other structures. While the morphology of these structures varies between individuals, their topological connections and relative spatial layouts generally maintain a high degree of conservation. Examples include the vascular tree of the kidney (the branching pattern of the renal arteries and veins) or the Couinaud segmentation system of the liver. Current methods for constructing measurement benchmarks mostly focus on the overall shape or surface features of organs, failing to use this inherent, stable anatomical network as the framework for benchmark construction. This results in the loss of spatial constraint information that best represents the essence of the organ, leading to insufficient biological significance and poor robustness of the established benchmarks.

[0005] Finally, existing measurement benchmarks suffer from weak interpretability and traceability. Many coordinate mapping relationships established based on complex mathematical transformations (such as higher-order Bézier surfaces and large-deformation differential homeomorphisms), while achieving high-precision alignment between models, are themselves highly nonlinear "black boxes." Users struggle to understand the specific anatomical significance of a particular spatial point's coordinates in the new coordinate system within the original organ. Furthermore, this transformation process is difficult to reverse engineer or perform error propagation analysis. When cross-scale measurements are required (e.g., relating the location of a specific cell population from the overall organ scale) or to verify the reliability of measurement results, existing benchmark systems fail to provide a clear and traceable path.

[0006] In summary, existing technologies for constructing spatial measurement benchmarks for 3D organ models suffer from three main interrelated technical problems: insufficient robustness to biological variations and imaging deformations, failure to effectively utilize the stable anatomical network within organs, and poor interpretability and traceability of the constructed benchmarks. These issues severely limit the in-depth application value of 3D organ models in fields such as precision medicine, comparative anatomy, and developmental biology. Summary of the Invention

[0007] To achieve the above objectives, the present invention provides a method for constructing a spatial measurement benchmark based on a three-dimensional organ model, the method comprising the following steps:

[0008] Step 1: Collect voxel data of the target three-dimensional organ model, and identify and extract the three-dimensional coordinate data and topological connection relationship of multiple anatomical feature points inside the target three-dimensional organ model to form a target anatomical feature point set;

[0009] Step 2: Based on prior anatomical knowledge, define a hierarchical reference space network that is independent of specific three-dimensional organ models. The hierarchical reference space network includes a topological layer that defines node types, a geometric constraint layer that defines the relative spatial relationships between nodes, and a coordinate system layer that defines the absolute spatial reference.

[0010] Step 3: Map and adapt the target anatomical feature point set to the hierarchical reference space network, and obtain the coordinate transformation relationship from the original space of the target three-dimensional organ model to the standard coordinate system of the hierarchical reference space network through optimization solution;

[0011] Step 4: Based on the coordinate transformation relationship, a three-dimensional continuous coordinate mapping field covering all voxels of the target three-dimensional organ model is constructed using a spatial interpolation algorithm. The three-dimensional continuous coordinate mapping field is used to map the original coordinates of any voxel in the target three-dimensional organ model to the standard coordinate system.

[0012] Step 5: Output the parameterized organ model carried in the standard coordinate system and the coordinate mapping parameter set that records the coordinate transformation relationship and the parameters of the three-dimensional continuous coordinate mapping field.

[0013] Preferably, step 1, which involves identifying and extracting multiple anatomical feature points within the target three-dimensional organ model, specifically includes:

[0014] The anatomical feature points are selected from the inherent anatomical structural landmarks within the target three-dimensional organ model. These anatomical structural landmarks include the bifurcation points of the vascular tree, the entry points of nerve bundles, the geometric centroids of specific anatomical functional zones, and the opening points of glandular ducts.

[0015] The identification and extraction process is completed by combining an automatic image segmentation algorithm with manual correction. The automatic image segmentation algorithm locates candidate regions of feature points based on the voxel intensity gradient, local texture features, and a pre-trained deep learning model of the target three-dimensional organ model. The manual correction is performed by domain experts who verify, adjust, and confirm the algorithm's localization results based on anatomical knowledge.

[0016] For each identified and extracted anatomical feature point, its three-dimensional Cartesian coordinates in the original space of the target three-dimensional organ model are recorded. Based on the physiological connection relationship between the anatomical structure landmark points, an undirected graph describing the point-to-point connection relationship or a directed graph describing the branch flow relationship is constructed to formally record the topological connection relationship.

[0017] The number of anatomical feature points in the target anatomical feature point set shall not be less than 8, and the anatomical feature points shall be distributed in at least three different main anatomical sub-regions of the target three-dimensional organ model to ensure the breadth and representativeness of spatial distribution.

[0018] Preferably, the hierarchical reference space network defined in step 2 is constructed as follows:

[0019] The topology layer consists of multiple abstract network nodes, each of which corresponds to a type of feature point with universal anatomical significance. The connection edges between the abstract network nodes are defined according to the physiological structural connectivity relationships recorded in standard anatomical atlases.

[0020] The geometric constraint layer assigns a set of relative geometric constraint parameters to each connection edge in the topology layer. These parameters describe the allowable range of the azimuth angle, zenith angle, and relative distance ratio of the child node relative to its parent node in spherical coordinates. The boundary values ​​of these allowable ranges are obtained through statistical learning on a 3D organ model database containing multiple standard samples. The statistical learning calculates the mean and standard deviation of the geometric relationship between all corresponding feature point pairs in the database, and uses the mean plus or minus three times the standard deviation as the initial boundary of the allowable range.

[0021] The coordinate system layer establishes the absolute origin, axis, and scale of the standard coordinate system by assigning fixed three-dimensional calibration coordinates to three pre-selected non-collinear key abstract network nodes in the topology layer. The selection of the three key abstract network nodes must meet the requirement of uniquely determining a spatial rectangular coordinate system.

[0022] Preferably, step 3, which maps and adapts the target anatomical feature point set to the hierarchical reference space network, specifically includes the following sub-steps:

[0023] Step 3.1: Based on the anatomical semantic consistency, match each anatomical feature point in the target anatomical feature point set with the corresponding abstract network node in the hierarchical reference space network topology layer to establish a one-to-one mapping pair;

[0024] Step 3.2: Using the geometric constraint layer parameters of the hierarchical reference space network as soft constraints, construct a nonlinear optimization objective function. The first part of the objective function minimizes the sum of Euclidean distances between the coordinates of the target anatomical feature points after global rigid body transformation and the ideal coordinates of the corresponding abstract network nodes in the standard coordinate system. The second part of the objective function applies a penalty term to cases where the relative geometric constraint parameters are violated after transformation. The weight coefficient of the penalty term is proportional to the degree of violation.

[0025] Step 3.3: Solve the nonlinear optimization objective function using an iterative optimization algorithm, including the Levenberg-Marquardt algorithm, to obtain the optimal global rotation matrix, translation vector, and anisotropic scaling factor, which together constitute the initial rigid body transformation component in the coordinate transformation relationship;

[0026] Step 3.4: Based on the initial rigid body transformation, a thin plate spline transformation that allows local elastic deformation is introduced as a non-rigid correction component to further eliminate the residual local registration error between the target anatomical feature point set and the hierarchical reference space network, and finally form a complete coordinate transformation relationship containing rigid and non-rigid components, and calculate its inverse transformation.

[0027] Preferably, in step 4, the construction of the three-dimensional continuous coordinate mapping field adopts a thin-plate spline interpolation method based on radial basis functions. The specific process is as follows:

[0028] All anatomical feature points that have been mapped and adapted in step 3 are used as control points for thin-plate spline interpolation. The coordinates of the control points in the original space of the target three-dimensional organ model constitute the source point set, and the coordinates in the standard coordinate system constitute the target point set.

[0029] The thin-plate spline interpolation method solves for a mapping function that makes the mapping error of all control points zero, and at the same time minimizes the bending energy function of the mapping function over the entire space. The bending energy function is the integral of the square of the second-order partial derivative of the mapping function, which is used to ensure the smoothness and physical rationality of the mapping.

[0030] The coefficients of the thin plate spline interpolation function are obtained by solving a system of linear equations, the construction of which combines the correspondence of the control points with the condition for minimizing bending energy.

[0031] For any non-control point voxel in the target three-dimensional organ model, its original coordinates are input into the solved thin plate spline interpolation function. By calculating the radial distance between the voxel and all control point source points and performing a weighted summation, the coordinates of the voxel in the standard coordinate system are directly output, thereby realizing continuous coordinate mapping of the entire model space.

[0032] Preferably, after constructing the three-dimensional continuous coordinate mapping field, the method further includes a global optimization step of the mapping field based on tissue type consistency:

[0033] Obtain the tissue type label of each voxel in the target three-dimensional organ model. The tissue type label is obtained through image segmentation and includes cortical tissue, medullary tissue, epithelial tissue, or connective tissue.

[0034] Define an organization deformation consistency constraint term, which calculates the coefficient of variation of the distance between adjacent voxels of the same organization type label in the standard coordinate system relative to their corresponding distance in the original space, and promotes the coefficient of variation to approach zero.

[0035] The tissue deformation consistency constraint term is used as a regularization term and added to the objective function when constructing the thin plate spline interpolation function. Together with the bending energy function, they constitute the overall optimization objective. By resolving the constrained optimization problem, an optimized three-dimensional continuous coordinate mapping field is obtained. The optimized three-dimensional continuous coordinate mapping field ensures that the spatial continuity within the same tissue is better maintained during the mapping process while maintaining accurate mapping of anatomical feature points.

[0036] Preferably, the coordinate mapping parameter set output in step 5 is a structured data file, which contains the following traceable information:

[0037] The first module records the complete definition of the hierarchical reference space network, including the type list and connection matrix of all abstract network nodes in the topology layer, the specific values ​​of all relative geometric constraint parameters in the geometric constraint layer, and the calibration coordinates of the three key abstract network nodes in the coordinate system layer.

[0038] The second module records the mapping correspondence table between the target anatomical feature point set and the hierarchical reference space network, as well as all parameters of the final coordinate transformation relationship obtained by optimization in step 3. All parameters include the rotation and translation matrix of the global rigid body transformation, the anisotropic scaling factor, and the coefficient matrix of the non-rigid transformation of the thin plate spline.

[0039] The third module records the core interpolation parameters of the three-dimensional continuous coordinate mapping field constructed in step 4. When thin plate spline interpolation is used, the core interpolation parameters include the source coordinates and target coordinates of all control points, as well as the corresponding thin plate spline coefficient weight vector.

[0040] The fourth module records the quality assessment indicators generated during the mapping process, including the average positioning error and maximum positioning error after mapping the target anatomical feature point set, as well as the statistical value of the Jacobian matrix of the deformation field of the three-dimensional continuous coordinate mapping field in the non-control point region, which are used to evaluate the local reversibility and biomechanical rationality of the mapping.

[0041] Preferably, the method further includes a step of fine-tuning the hierarchical reference space network by individualized geometric constraints between step 3 and step 4:

[0042] After completing the initial mapping adaptation in step 3, calculate the actual relative geometric relationship of all mapping point pairs in the target anatomical feature point set under the standard coordinate system, including the actual azimuth angle, actual zenith angle, and actual relative distance ratio.

[0043] The calculated actual relative geometric relationship is compared and analyzed with the preset allowable range in the hierarchical reference space network geometric constraint layer. If the statistical distribution of the actual relative geometric relationship of a certain type of connecting edge is significantly concentrated in a sub-interval of the allowable range, then the fine-tuning procedure is started.

[0044] The fine-tuning program uses multiple sample data from a specific population or disease cohort to which the target 3D organ model belongs as the learning object, recalculates the geometric constraint parameters of the connection edges, and replaces the original preset parameters in the hierarchical reference space network with the updated geometric constraint parameters to form an adaptive reference space network. This network is used to guide the subsequent construction of references for the same type of 3D organ model, making the constructed references more reflective of the anatomical commonalities of a specific group.

[0045] Preferably, the standard coordinate system and the coordinate mapping parameter set constructed by the method are used to realize cross-sample spatial data integration and analysis, and specific application methods include:

[0046] For the second three-dimensional organ model to be analyzed, repeat steps 1 to 5 to map it to the same standard coordinate system to generate the second parameterized organ model;

[0047] Under the standard coordinate system, the differences in anatomical morphology, tissue density, or functional characteristics between the first and second parametric organ models at corresponding spatial locations are directly and quantitatively compared, and the corresponding spatial locations are defined by the same standard coordinate system.

[0048] Alternatively, multiple three-dimensional organ model data from different imaging modalities, including computed tomography, magnetic resonance imaging, and tissue slice images, can be mapped to the standard coordinate system. Pixel-level or feature-level fusion of the multimodal data can be performed in the standard coordinate system to generate a comprehensive organ atlas containing multimodal attributes.

[0049] Preferably, the entire process of defining and optimizing the coordinate transformation relationship in the method incorporates a multi-level error propagation and uncertainty quantification model:

[0050] The uncertainty quantification model models the localization error of the anatomical feature point identification and extraction in step 1, the range error of the geometric constraint layer parameters based on statistical learning in step 2, and the residual error of the optimization solution in step 3 as a Gaussian distribution with zero mean and specific variance.

[0051] In the process of constructing the coordinate mapping field in step 4, the error is transmitted through the coefficients of the linear equation system of the thin plate spline interpolation function, and finally the confidence interval of each voxel coordinate value in the standard coordinate system is calculated.

[0052] The confidence interval is represented in the form of an elliptic. The three principal axes and length of the elliptic are determined by the eigenvectors and eigenvalues ​​of the covariance matrix of the voxel coordinates, and are saved as metadata along with the parameterized organ model output in step 5.

[0053] When spatial distance or volume measurement is performed in the standard coordinate system, the uncertainty of the measurement result can be calculated and reported according to the coordinate confidence interval of the voxels involved, using the error propagation law, thereby realizing the full-process uncertainty quantification from raw data to final measurement result.

[0054] The beneficial effects of this invention are:

[0055] 1. This invention establishes a spatial benchmark with high robustness to morphological variations and imaging deformations in biological individuals. Traditional methods rely on the variable external contours of organs or artificially added markers, which are sensitive to individual differences and preparatory deformations. This invention creatively uses an inherent, topologically stable network of anatomical feature points within organs as the "skeleton" for constructing the benchmark. By defining a hierarchical benchmark spatial network and utilizing its geometric constraints for mapping and adaptation, the establishment of the benchmark is independent of the overall shape, thereby significantly reducing the negative impact of differences in individual size and shape or non-rigid deformations generated during sample processing, achieving a stable and consistent measurement basis in real biological variation scenarios;

[0056] 2. This invention endows spatial measurement coordinates with explicit anatomical semantics, greatly enhancing the interpretability and practicality of measurement results. The standard coordinate system constructed in this invention is directly rooted in formalized anatomical prior knowledge, with each spatial region associated with a specific internal anatomical structure. This means that any measurement point or region coordinate obtained under this benchmark is no longer a purely mathematical expression, but carries direct anatomical meaning. This characteristic allows clinicians or biologists to intuitively understand the measurement results without complex reverse mapping interpretation, greatly promoting the direct application value of this method in disease diagnosis, surgical planning, or biological discovery.

[0057] 3. This invention provides a fully traceable and verifiable technical path from raw data to standard measurement results. Not only does it output the final standard coordinate model, but more importantly, it simultaneously outputs a complete set of coordinate mapping parameters, meticulously recording every step of the parameters and intermediate results from feature point extraction, network matching, transformation solving to full-field interpolation. This design achieves "white-box" measurement, allowing for reverse tracing of any measurement point to pinpoint its exact location in the original sample, and enabling step-by-step analysis of uncertainties such as positioning errors and registration residuals. This unprecedented traceability meets the stringent requirements of precision medical research for data reliability and result verifiability, laying a foundation of trust for the integration and comparison of high-quality biospatial data. Attached Figure Description

[0058] To more clearly illustrate the technical solutions in this invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, those skilled in the art can obtain other drawings based on these drawings without creative effort.

[0059] Figure 1 This is a flowchart of the steps of the method of the present invention;

[0060] Figure 2 This is a flowchart illustrating the steps of the method of the present invention to perform global optimization of the mapping field based on organizational type consistency.

[0061] Figure 3 This is a flowchart illustrating the steps of individualized geometric constraint fine-tuning in the method of the present invention. Detailed Implementation

[0062] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. It should also be noted that, to make the embodiments more comprehensive, the following embodiments are the best and preferred embodiments, and those skilled in the art can use other alternative methods to implement some well-known technologies; moreover, the accompanying drawings are only for more specific description of the embodiments and are not intended to specifically limit the present invention.

[0063] Please see Figures 1-3 This invention provides a method for constructing a spatial measurement benchmark based on a three-dimensional organ model. The method first involves data acquisition and feature point extraction. Three-dimensional image data of biological organ samples are acquired using microcomputed tomography (CT) technology, with a scanning resolution set at 5 micrometers per voxel. Three-dimensional reconstruction software synthesizes the two-dimensional image sequence into a mesh model containing approximately 20 million voxels, each recording its spatial coordinates and grayscale value. A pre-trained deep convolutional neural network is used to segment the model, identifying stable anatomical structures within the target organ, such as vascular trees.

[0064] Subsequently, the segmentation results are subjected to skeletal analysis to automatically locate key anatomical feature points, including branch points, terminal points, and centroids of specific regions. This process simultaneously records the three-dimensional Cartesian coordinates of all feature points and constructs an undirected graph representing topological connectivity based on physiological connections. This step ensures that subsequent benchmark construction is based on biologically conserved internal structures, providing accurate and meaningful input data for establishing robust spatial benchmarks. The combination of automatic and semi-automatic feature point identification effectively overcomes the efficiency bottlenecks and subjective errors associated with manual labeling.

[0065] In one possible implementation, the hierarchical reference space network is defined based on a standard anatomical knowledge base. This network comprises a topology layer, a geometric constraint layer, and a coordinate system layer. The topology layer abstracts network nodes corresponding to a class of anatomical feature points, and the connecting edges between nodes are defined according to the connectivity relationships in the standard anatomical atlas. The parameters of the geometric constraint layer are obtained through statistical learning: a standard model database containing 20 normal samples is collected, and the relative azimuth, zenith angle, and distance ratio between all corresponding feature point pairs in the database are calculated; the mean and standard deviation of each geometric parameter are calculated, and the range of the mean plus or minus three times the standard deviation is set as the allowable boundary value for that parameter, forming quantified constraints.

[0066] The coordinate system layer establishes an absolute right-handed Cartesian reference coordinate system by assigning fixed three-dimensional calibration coordinates to three non-collinear key nodes in the network. These three nodes are typically chosen as the organ entry point and two distal feature points with the greatest difference in distribution direction. This hierarchical definition transforms fuzzy anatomical knowledge into computable mathematical constraints, giving the baseline network both universality and individual adaptability, serving as a bridge connecting abstract anatomical concepts and concrete digital models.

[0067] In one possible implementation, the mapping and adaptation of the target model's feature point set to the baseline network is achieved through a multi-step optimization process. First, graph isomorphism matching is performed, mapping specific feature points to abstract network nodes one-to-one based on anatomical semantics. Then, a nonlinear optimization objective function is constructed, which includes a distance term and a constraint term. The distance term requires that the transformed feature point coordinates be as close as possible to the ideal coordinates of the network nodes. The constraint term penalizes violations of the allowable ranges for relative orientation, angle, and distance ratios in the geometric constraint layer, with the penalty weight proportional to the degree of violation. The Levenburg-Marquardt algorithm is used to iteratively optimize this function, solving for the optimal global rigid body transformation parameters, including the rotation matrix, translation vector, and scaling factor.

[0068] Subsequently, thin-plate spline transformation is introduced as a non-rigid correction component to eliminate local registration residuals, ultimately obtaining a complete, smooth, and reversible coordinate transformation relationship from the original model space to the standard coordinate system. The core of this step is to incorporate statistical constraints into the optimization process, ensuring that the mapping result satisfies both overall alignment and the relative spatial relationships between anatomical structures, thereby achieving a balance between mathematical optimality and biological rationality.

[0069] In one possible implementation, the continuous coordinate mapping field is constructed using a thin-plate spline interpolation method with feature points as control points. The coordinates of the feature points that have completed the mapping adaptation are used as the source and target point sets for interpolation, respectively. The thin-plate spline function is constructed as a weighted sum of an affine transformation and a series of radial basis functions, where the radial basis functions adopt a function form specific to thin-plate splines. All coefficients of the function are determined by solving a system of linear equations that force the function to pass precisely through all control points while minimizing the bending energy integral of the function over the entire space, thus ensuring the smoothness and physical plausibility of the mapping.

[0070] For any voxel that is not a control point in the model, its original coordinates are input into this function. By calculating its distance to all control points and performing a weighted sum, its coordinates in the standard coordinate system can be obtained. The advantage of this method is that it can derive a smooth coordinate transformation field covering the entire continuous three-dimensional space based on a finite number of precise control points, realizing the key transition from discrete feature matching to mapping of the entire voxel space.

[0071] In one possible implementation, after the initial coordinate mapping field is constructed, a global optimization based on tissue type consistency is further performed. First, the tissue type segmentation label for each voxel on the target 3D organ model is obtained; for example, the kidney is distinguished into cortex, medulla, and renal pelvis using image grayscale and texture features. A tissue deformation consistency constraint is defined, which calculates the coefficient of variation of the distance ratio (standard spatial distance divided by the original spatial distance) between all adjacent voxel pairs belonging to the same tissue type in the standard coordinate system.

[0072] The optimization objective is to minimize the weighted sum of bending energy and its coefficient of variation while maintaining the accuracy of the thin-plate spline function's mapping to control points. The parameters of the thin-plate spline function are fine-tuned using a gradient descent algorithm, ensuring that the spatial structure within the same tissue maintains more uniform scaling or deformation during coordinate transformations, avoiding unnatural local distortions. This optimization step enhances the biological plausibility of the mapping results, ensuring that tissue regions with similar properties maintain intrinsic morphological consistency in standard space, and improving the reliability of subsequent quantitative measurements.

[0073] In one possible implementation, the output coordinate mapping parameter set is organized into a structured data file containing multiple independent modules. The first module fully records the topology of the reference space network, the specific values ​​of the geometric constraint parameters, and the coordinate system definition. The second module records the mapping correspondence table between the target model feature points and network nodes, as well as all parameters of the final coordinate transformation matrix obtained through optimization. The third module stores the core interpolation parameters required to construct the continuous mapping field. The fourth module saves quality evaluation indicators of the mapping process, such as the feature point residuals and the statistical eigenvalues ​​of the deformation field Jacobian matrix.

[0074] This modular and structured parameter archiving method fully encapsulates all transformation information from the raw data to the standard space, making the entire mapping process completely reproducible and auditable. Any analysis result in the standard space can be traced back to the precise spatial location and context of the original data by reversing the call to these parameters, achieving full traceability of the measurement and analysis process.

[0075] In one possible implementation, an individualized fine-tuning mechanism for the geometric constraints of the baseline network is introduced after the initial mapping. The statistical values ​​of the geometric relationships of the target model's feature point set after the actual mapping are calculated and compared with the network's preset general constraint range. If a stable distribution pattern deviating from the general range is found for the geometric relationships of a specific connection edge in a specific population sample, the learning process is initiated. Using a new database containing multiple samples from that population, the relevant geometric parameters are re-statistically analyzed, and the corresponding allowable ranges in the baseline network's geometric constraint layer are updated accordingly.

[0076] For example, for a particular mouse strain, the angle of a certain branch of the renal blood vessels may be generally smaller. After fine-tuning, a dedicated baseline network adapted to that strain can be generated. This mechanism enables the baseline network to adaptively evolve from general to specific, allowing its geometric constraints to more accurately reflect the anatomical commonalities of a specific population or pathological state while maintaining the core topology unchanged. This provides a higher-precision spatial benchmark in more specific application scenarios.

[0077] In one possible implementation, a constructed standard coordinate system is used to integrate cross-sample data. A second, different 3D organ model is mapped to the same standard coordinate system using the same method, generating a second parametric model. Since the two models share the same spatial reference, their corresponding spatial locations have completely consistent anatomical definitions. Therefore, pixel-level or feature-level comparative analysis can be performed directly in the standard coordinate system, quantitatively calculating the volume differences, average density differences, or signal intensity differences between the two models within a specific anatomical region.

[0078] This application method completely solves the problem of data comparability caused by individual differences in samples, imaging angles, or resolutions. Multimodal data, such as structural information from computed tomography scans and gene expression information from tissue sections, can also be mapped to a standard space and then precisely overlaid and fused to construct a comprehensive biological atlas containing multi-level information, providing a powerful spatial data integration platform for systems biology research.

[0079] In one possible implementation, the entire mapping process is nested within a multi-level error propagation and uncertainty quantification model. This model models feature point identification errors, geometric constraint statistical errors, and optimization residuals as independent Gaussian distributions. When constructing the continuous coordinate mapping field, the aforementioned source errors are propagated to the uncertainty estimation of each voxel coordinate in the standard coordinate system through the linear error propagation law. Ultimately, the uncertainty of each voxel coordinate is represented by a confidence interval in the form of a three-dimensional ellipsoid, the principal axis direction and size of which are determined by the covariance matrix of the estimated coordinates of that point. These confidence intervals are stored as metadata along with the standard spatial model.

[0080] When a user performs any distance, area, or volume measurement in a standard space, the system can automatically calculate the overall uncertainty range of the measurement result based on the confidence intervals of the voxel coordinates involved and generate a report. This mechanism, for the first time, achieves quantitative characterization of uncertainty throughout the entire process from raw data to final analysis results in the standardization of anatomical space, significantly improving the scientific rigor and reliability of the measurement results.

[0081] Example: Construction and application of standardized spatial benchmarks for a three-dimensional mouse kidney model;

[0082] Step 1: Collect voxel data and internal anatomical feature data of the target 3D organ model;

[0083] First, a complete kidney sample was obtained from an 8-week-old male C57BL / 6J mouse. The sample was imaged using microcomputed tomography (CT) at a resolution of 5 micrometers per voxel. The obtained two-dimensional image sequence was then reconstructed into a three-dimensional voxel grid model using 3D reconstruction software. This model contains approximately 20 million voxels, each storing its spatial coordinates and grayscale intensity value.

[0084] Next, internal anatomical feature points are identified and extracted from the 3D model. In this embodiment, the extracted feature points focus on the renal arterial vascular tree system because its branching pattern has high topological stability across individuals. The specific identification process is as follows:

[0085] Automatic segmentation: A deep learning model based on 3D U-Net was used to automatically segment the renal arteries. This model was trained on a dataset containing 50 mouse kidney microCT scans and was able to segment the complete renal artery and its main branches from voxel data.

[0086] Feature point extraction: Automated analysis of the segmented 3D vascular skeleton. The endpoints of the vascular skeleton are defined as "terminal points," and the center points connecting three or more branches in the skeleton are defined as "bifurcation points." In this embodiment, a total of 23 anatomical feature points were identified, including 1 renal artery inlet point, 7 major bifurcation points (corresponding to the primary and secondary branches of the renal artery, respectively), and 15 terminal points (corresponding to the ends of the interlobular arteries).

[0087] Manual correction and verification: The 23 automatically identified feature points were reviewed jointly by a renal pathologist and an anatomist. Experts verified the anatomical significance of each point in a 3D visualization environment; for example, the hilum point closest to the medial side of the kidney was identified as the "renal artery inlet point," and the hierarchical level of the bifurcation points was confirmed according to standard renal vascular anatomy atlases. Experts manually fine-tuned the positions of two bifurcation points that were slightly off-target in the automatic identification.

[0088] Data recording: Record the three-dimensional coordinates of each feature point. For example, the coordinates of the renal artery inlet point are... Simultaneously, based on the connectivity of the vascular skeleton, a connection graph with feature points as nodes and vascular segments as edges is constructed to formally record the topological connectivity. All 23 feature points cover the cortical, medullary, and hilar regions of the kidney, satisfying the requirement of extensive spatial distribution.

[0089] Step 2: Define a hierarchical baseline space network that is independent of the specific model;

[0090] Based on standard anatomical knowledge of mouse kidneys, an abstract hierarchical reference spatial network is defined. This network serves as a unified spatial reference framework for all mouse kidney models.

[0091] Constructing the topology layer: The network is defined to contain 23 abstract nodes, with node types strictly corresponding to the feature point types extracted in the first step. For example, node types include "renal artery entry (RA_Entry)," "first-order anterior bifurcation (P1_Bifurcation)," and "second-order superior bifurcation (S2_Bifurcation)," etc. The connection edges between nodes are determined according to the standard vascular tree branching atlas, forming a directed acyclic graph, with the direction representing the blood flow direction.

[0092] Define a geometric constraint layer: Assign relative geometric constraint parameters to each connection edge in the topology layer. For this, a database containing 20 standard models of normal mouse kidneys was used. Taking the edge from the "renal artery inlet" node to the "first-order anterior bifurcation" node as an example:

[0093] Calculate the relative geometric relationship between these two corresponding points for all 20 samples in the database.

[0094] Azimuth: Calculate the azimuth (φ) of the child node (first-level fork) in the local spherical coordinate system with the parent node (entrance) as the origin. Calculate the mean φ value from 20 samples. Degree, standard deviation Degrees. The allowable range of the azimuth angle is defined as... That is, approximately Spend.

[0095] Zenith angle: Similarly, calculate the zenith angle (θ) and obtain the mean. Degree, standard deviation Degree. The allowable range is set as follows: Spend.

[0096] Relative distance ratio: Calculate the Euclidean distance between the child node and the parent node, then divide by the estimated diameter of the blood vessel at the parent node (in this example, the diameter of the renal artery inlet) to obtain the ratio value r. Statistical analysis yields... , The permissible range is defined as follows: .

[0097] Repeat this statistical process for all connected edges to generate a complete table of geometric constraint parameters.

[0098] Establishing the coordinate system layer: Three non-collinear key nodes are selected to fix the standard coordinate system. In this embodiment, the "renal artery inlet point" is selected as the coordinate origin. Select a specific terminal point, the "cortical terminal point," located on the outermost cortex of the kidney, and place it on the positive direction of the X-axis in a standard coordinate system, with coordinates as follows: , The standard unit of length is used; another specific terminal point located on the dorsal side of the kidney, the "postcortical terminal point," is selected and placed in the first quadrant of the XY plane, with coordinates as follows: , where α is a small positive angle. Thus, the right-handed Cartesian reference coordinate system of the standard coordinate system is uniquely determined by the coordinates of these three points.

[0099] Step 3: Map and adapt the anatomical feature point set of the target model to the baseline spatial network;

[0100] This step aims to accurately map the 23 specific feature points obtained in the first step onto the abstract network defined in the second step.

[0101] Node matching: Based on anatomical semantics, the “renal artery entry point” of the target model is matched with the “RA_Entry” node of the baseline network, the “first-level anterior bifurcation point” is matched with the “P1_Bifurcation” node, and so on, to establish 23 one-to-one mapping pairs.

[0102] Constructing the objective function: This involves creating a nonlinear optimization objective function. .

[0103] ;

[0104] Distance Term : .in These are the original coordinates of the i-th feature point in the target model. The global rigid body transformation to be determined is (rotation R, translation t, scaling s). These are the ideal coordinates of the corresponding nodes in the baseline network (from the coordinate system layer definition).

[0105] Constraints : 2. For each connecting edge j, calculate its actual geometric parameters after transformation. (e.g., azimuth angle) exceeds the allowable range of the geometric constraint layer. The degree of punishment is determined by the square of the penalty. This is the weight of the constraint; in this embodiment, the constraint on the critical branch is given a higher weight.

[0106] and These are the weighting coefficients for balancing the two terms. In this example, after preliminary testing, they are set to... , .

[0107] Optimization Solution: Using the Levenberg-Marquardt algorithm to optimize the objective function. Optimization was performed. The optimization variables were the 12 parameters of the rigid body transformation (9 elements of the rotation matrix, 3 elements of the translation vector, and scaling was simplified as isotropic). After 50 iterations, the optimization converged, yielding the optimal rigid body transformation parameters R, t, and s.

[0108] Non-rigid correction: After applying the rigid body transformation described above, the average residual between 23 point pairs is calculated to be 12 micrometers. To further reduce the error, a thin-plate spline transformation is used for non-rigid correction. Using the points after the rigid body transformation as the source points and the reference network coordinates as the target points, a TPS transformation is solved. Finally, the complete coordinate transformation relationship is as follows: And calculate its numerical inverse transform. After this step, the mapping error of the 23 control points was reduced to near zero.

[0109] Step 4: Construct a continuous and reversible coordinate mapping field covering the entire organ voxels;

[0110] The goal is to assign standard coordinates to all 20 million voxels in the kidney model.

[0111] Thin-plate spline interpolation: The 23 feature points precisely mapped in step three are used as control points. The form of the thin-plate spline mapping function F(x) is:

[0112] ;

[0113] in, These are the original spatial coordinates. It is an affine matrix. It is a translation vector. These are the source coordinates of the control points. It is a weight vector. These are radial basis functions. They are determined by solving a system of linear equations. This system of equations requires The target coordinates of the control points are equal, while minimizing bending energy. .

[0114] Global optimization for tissue consistency: The kidney has been segmented into three main tissue regions: cortex, medulla, and renal pelvis. A tissue deformation consistency constraint is introduced. The optimization objective is defined as:

[0115] ;

[0116] in, ;

[0117] β is the coefficient of variation of the distance ratio between all adjacent voxel pairs within the same tissue region, expressed in standard space and original space. β is the weight, set to 0.2 in this example. By fine-tuning the parameters of the TPS function using gradient descent, the spatial continuity within the cortex and medulla is improved (i.e., the CV value is reduced) while maintaining the accuracy of control point mapping. After optimization, the distance ratio coefficient of variation in the cortical region decreased from 0.15 to 0.09.

[0118] Generating a continuous mapping field: The function FF after solving is the final continuous coordinate mapping field. For any voxel, simply change its original coordinates... Substituting FF into the equation will output its standard coordinates. Its inverse function can be calculated using numerical methods (such as Newton's iteration method). .

[0119] Step 5: Output the parametric organ model in the standard spatial coordinate system and the complete set of coordinate mapping parameters;

[0120] Generate a parametric model: Combine the grayscale values ​​and tissue labels (cortex / medulla / renal pelvis) of each voxel in the original model with the standard coordinates calculated in step four. This leads to the formation of a new, parameterized kidney model defined in the standard coordinate system.

[0121] Generate coordinate mapping parameter set: Output a structured JSON file containing the following modules:

[0122] Network definition module: Completely records the topology of the reference spatial network, all geometric constraint parameters (such as: "edge_RA_to_P1":{"phi_range":[5.9,24.5],"theta_range":[68.1,96.9],"r_range":[1.2,3.0]}) and the calibration coordinates of the three key nodes.

[0123] Mapping Relationship Module: Records the original coordinates, standard coordinates, and corresponding node IDs of 23 feature points.

[0124] Transformation Parameter Module: Records the rigid body transformation matrices R, t, s obtained in the third step and all coefficients of the TPS transformation. .

[0125] Quality assessment module: Records the final residual of the control point (0.5 micrometers in this embodiment), the mean (1.02, close to 1 indicates good volume retention) and minimum (0.88, indicating slight local compression) of the determinant of the Jacobian matrix of the entire deformation field.

[0126] Uncertainty module: Based on the feature point positioning error (estimated at ±3 micrometers) and the statistical variance of geometric constraints, the error propagation model calculates that, in the standard coordinate system, the 95% confidence interval radius of most voxel coordinates within the model is less than 8 micrometers.

[0127] Effect verification and comparative analysis:

[0128] To verify the effectiveness of the method in this embodiment, it was compared with two conventional methods. The same target kidney model and five other different test kidney models were used as benchmarks.

[0129] Comparative Example 1 (Traditional Surface Registration Method): This method employs the commonly used registration method based on the best fit of the organ's outer surface. Using the iterative nearest-point algorithm, the target model is rigidly registered with a standard kidney outer surface template. Then, a non-rigid B-spline transformation is used for refinement, aligning the two surfaces as closely as possible.

[0130] Comparative Example 2 (Simple Feature Point Rigid Body Transformation Method): Using only the 23 internal feature points extracted in the first step of this embodiment, a global rigid body transformation is calculated through Protodyakonov analysis (rotation and translation only, no scaling, ignoring geometric constraints), transforming all voxels to the space with the feature point centroid as the origin.

[0131] Evaluation metrics: Fifty corresponding microanatomical landmarks (such as specific renal corpuscle centers) were manually labeled in the cortical and medullary regions of each test kidney model. These points were mapped to standard space using three different methods, and the average and maximum registration errors between them and their corresponding points in the standard atlas were calculated. The results are shown in Table 1.

[0132] Table 1

[0133] Method Name Average registration error (micrometers) Maximum registration error (micrometers) Cortical area error (micrometers) Medullary region error (micrometers) Coordinate interpretability Method of this invention 8.7 22.3 8.1 9.5 Strong (coordinates can be directly linked to the vascular branch level) Comparative Example 1: Traditional Surface Registration Method 25.4 68.9 19.8 35.7 Weak (only mathematical coordinates, no clear anatomical meaning) Comparative Example 2: Simple Feature Point Rigid Body Transformation Method 18.6 45.2 16.9 21.5 (Based solely on point sets, lacking network structure constraints)

[0134] Results analysis:

[0135] Accuracy Comparison: The method in this embodiment of the invention achieved the highest registration accuracy, with an average error of only 8.7 micrometers, significantly lower than the two comparative examples. This demonstrates that utilizing the hierarchical constraints of the internal anatomical network can more effectively overcome the influence of variations in the overall morphology of organs, achieving more precise alignment of internal structures.

[0136] Regional stability comparison: Comparative Example 1 (surface registration) showed significantly higher errors in the medullary region than in the cortex region. This is because the medulla is located inside the organ, and its deformation is less correlated with surface deformation. In contrast, the methods of this invention and Comparative Example 2 showed relatively balanced errors in both the cortex and medulla, but this invention demonstrated higher accuracy. This indicates that methods based on internal features are inherently more advantageous, and the network constraints of this invention further enhance this advantage.

[0137] Interpretability Comparison: The standard coordinate system constructed in this invention is directly rooted in the anatomical network, and a coordinate point (X,Y,Z) can be clearly interpreted as "the ventral direction near the first-order anterior bifurcation point." This is a characteristic that the two comparative examples do not possess at all, and it is crucial for subsequent biological data analysis.

[0138] In summary, this embodiment demonstrates in detail the complete process of the method of the present invention from data acquisition to result output, and through quantitative comparison with comparative examples, confirms its significant technical progress in improving the robustness, anatomical significance and traceability of spatial measurement benchmarks.

[0139] This invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of this invention. To provide the public with a thorough understanding of this invention, specific details are described in detail in the following preferred embodiments; however, those skilled in the art will fully understand the invention even without these details. Furthermore, to avoid unnecessary misunderstanding of the essence of this invention, well-known methods, processes, procedures, components, and circuits are not described in detail.

[0140] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for constructing a spatial measurement benchmark based on a three-dimensional organ model, characterized in that, The method includes the following steps: Step 1: Collect voxel data of the target three-dimensional organ model, and identify and extract the three-dimensional coordinate data and topological connection relationship of multiple anatomical feature points inside the target three-dimensional organ model to form a target anatomical feature point set; Step 2: Based on prior anatomical knowledge, define a hierarchical reference space network that is independent of specific three-dimensional organ models. The hierarchical reference space network includes a topological layer that defines node types, a geometric constraint layer that defines the relative spatial relationships between nodes, and a coordinate system layer that defines the absolute spatial reference. Step 3: Map and adapt the target anatomical feature point set to the hierarchical reference space network, and obtain the coordinate transformation relationship from the original space of the target three-dimensional organ model to the standard coordinate system of the hierarchical reference space network through optimization solution; Step 4: Based on the coordinate transformation relationship, a three-dimensional continuous coordinate mapping field covering all voxels of the target three-dimensional organ model is constructed using a spatial interpolation algorithm. The three-dimensional continuous coordinate mapping field is used to map the original coordinates of any voxel in the target three-dimensional organ model to the standard coordinate system. Step 5: Output the parameterized organ model carried in the standard coordinate system and the coordinate mapping parameter set that records the coordinate transformation relationship and the parameters of the three-dimensional continuous coordinate mapping field.

2. The method for constructing a spatial measurement benchmark based on a three-dimensional organ model according to claim 1, characterized in that, Step 1, which involves identifying and extracting multiple anatomical feature points within the target 3D organ model, specifically includes: The anatomical feature points are selected from the inherent anatomical structural landmarks within the target three-dimensional organ model. These anatomical structural landmarks include the bifurcation points of the vascular tree, the entry points of nerve bundles, the geometric centroids of specific anatomical functional zones, and the opening points of glandular ducts. The identification and extraction process is completed by combining an automatic image segmentation algorithm with manual correction. The automatic image segmentation algorithm locates candidate regions of feature points based on the voxel intensity gradient, local texture features, and a pre-trained deep learning model of the target three-dimensional organ model. The manual correction is performed by domain experts who verify, adjust, and confirm the algorithm's localization results based on anatomical knowledge. For each identified and extracted anatomical feature point, its three-dimensional Cartesian coordinates in the original space of the target three-dimensional organ model are recorded. Based on the physiological connection relationship between the anatomical structure landmark points, an undirected graph describing the point-to-point connection relationship or a directed graph describing the branch flow relationship is constructed to formally record the topological connection relationship. The number of anatomical feature points in the target anatomical feature point set shall not be less than 8, and the anatomical feature points shall be distributed in at least three different main anatomical sub-regions of the target three-dimensional organ model to ensure the breadth and representativeness of spatial distribution.

3. The method for constructing a spatial measurement benchmark based on a three-dimensional organ model according to claim 1, characterized in that, The hierarchical reference space network defined in step 2 is constructed as follows: The topology layer consists of multiple abstract network nodes, each of which corresponds to a type of feature point with universal anatomical significance. The connection edges between the abstract network nodes are defined according to the physiological structural connectivity relationships recorded in standard anatomical atlases. The geometric constraint layer assigns a set of relative geometric constraint parameters to each connection edge in the topology layer. These parameters describe the allowable range of the azimuth angle, zenith angle, and relative distance ratio of the child node relative to its parent node in spherical coordinates. The boundary values ​​of these allowable ranges are obtained through statistical learning on a 3D organ model database containing multiple standard samples. The statistical learning calculates the mean and standard deviation of the geometric relationship between all corresponding feature point pairs in the database, and uses the mean plus or minus three times the standard deviation as the initial boundary of the allowable range. The coordinate system layer establishes the absolute origin, axis, and scale of the standard coordinate system by assigning fixed three-dimensional calibration coordinates to three pre-selected non-collinear key abstract network nodes in the topology layer. The selection of the three key abstract network nodes must meet the requirement of uniquely determining a spatial rectangular coordinate system.

4. The method for constructing a spatial measurement benchmark based on a three-dimensional organ model according to claim 1, characterized in that, Step 3, which maps and adapts the target anatomical feature point set to the hierarchical reference space network, specifically includes the following sub-steps: Step 3.1: Based on the anatomical semantic consistency, match each anatomical feature point in the target anatomical feature point set with the corresponding abstract network node in the hierarchical reference space network topology layer to establish a one-to-one mapping pair; Step 3.2: Using the geometric constraint layer parameters of the hierarchical reference space network as soft constraints, construct a nonlinear optimization objective function. The first part of the objective function minimizes the sum of Euclidean distances between the coordinates of the target anatomical feature points after global rigid body transformation and the ideal coordinates of the corresponding abstract network nodes in the standard coordinate system. The second part of the objective function applies a penalty term to cases where the relative geometric constraint parameters are violated after transformation. The weight coefficient of the penalty term is proportional to the degree of violation. Step 3.3: Solve the nonlinear optimization objective function using an iterative optimization algorithm, including the Levenberg-Marquardt algorithm, to obtain the optimal global rotation matrix, translation vector, and anisotropic scaling factor, which together constitute the initial rigid body transformation component in the coordinate transformation relationship; Step 3.4: Based on the initial rigid body transformation, a thin plate spline transformation that allows local elastic deformation is introduced as a non-rigid correction component to further eliminate the residual local registration error between the target anatomical feature point set and the hierarchical reference space network, and finally form a complete coordinate transformation relationship containing rigid and non-rigid components, and calculate its inverse transformation.

5. The method for constructing a spatial measurement benchmark based on a three-dimensional organ model according to claim 1, characterized in that, In step 4, the construction of the three-dimensional continuous coordinate mapping field adopts a thin-plate spline interpolation method based on radial basis functions. The specific process is as follows: All anatomical feature points that have been mapped and adapted in step 3 are used as control points for thin-plate spline interpolation. The coordinates of the control points in the original space of the target three-dimensional organ model constitute the source point set, and the coordinates in the standard coordinate system constitute the target point set. The thin-plate spline interpolation method solves for a mapping function that makes the mapping error of all control points zero, and at the same time minimizes the bending energy function of the mapping function over the entire space. The bending energy function is the integral of the square of the second-order partial derivative of the mapping function, which is used to ensure the smoothness and physical rationality of the mapping. The coefficients of the thin plate spline interpolation function are obtained by solving a system of linear equations, the construction of which combines the correspondence of the control points with the condition for minimizing bending energy. For any non-control point voxel in the target three-dimensional organ model, its original coordinates are input into the solved thin plate spline interpolation function. By calculating the radial distance between the voxel and all control point source points and performing a weighted summation, the coordinates of the voxel in the standard coordinate system are directly output, thereby realizing continuous coordinate mapping of the entire model space.

6. The method for constructing a spatial measurement benchmark based on a three-dimensional organ model according to claim 5, characterized in that, After constructing the three-dimensional continuous coordinate mapping field, the method further includes a global optimization step based on tissue type consistency of the mapping field: Obtain the tissue type label of each voxel in the target three-dimensional organ model. The tissue type label is obtained through image segmentation and includes cortical tissue, medullary tissue, epithelial tissue, or connective tissue. Define an organization deformation consistency constraint term, which calculates the coefficient of variation of the distance between adjacent voxels of the same organization type label in the standard coordinate system relative to their corresponding distance in the original space, and promotes the coefficient of variation to approach zero. The tissue deformation consistency constraint term is used as a regularization term and added to the objective function when constructing the thin plate spline interpolation function. Together with the bending energy function, they constitute the overall optimization objective. By resolving the constrained optimization problem, an optimized three-dimensional continuous coordinate mapping field is obtained. The optimized three-dimensional continuous coordinate mapping field ensures that the spatial continuity within the same tissue is better maintained during the mapping process while maintaining accurate mapping of anatomical feature points.

7. The method for constructing a spatial measurement benchmark based on a three-dimensional organ model according to claim 1, characterized in that, The coordinate mapping parameter set output in step 5 is a structured data file, which contains the following traceable information: The first module records the complete definition of the hierarchical reference space network, including the type list and connection matrix of all abstract network nodes in the topology layer, the specific values ​​of all relative geometric constraint parameters in the geometric constraint layer, and the calibration coordinates of the three key abstract network nodes in the coordinate system layer. The second module records the mapping correspondence table between the target anatomical feature point set and the hierarchical reference space network, as well as all parameters of the final coordinate transformation relationship obtained by optimization in step 3. All parameters include the rotation and translation matrix of the global rigid body transformation, the anisotropic scaling factor, and the coefficient matrix of the non-rigid transformation of the thin plate spline. The third module records the core interpolation parameters of the three-dimensional continuous coordinate mapping field constructed in step 4. When thin plate spline interpolation is used, the core interpolation parameters include the source coordinates and target coordinates of all control points, as well as the corresponding thin plate spline coefficient weight vector. The fourth module records the quality assessment indicators generated during the mapping process, including the average positioning error and maximum positioning error after mapping the target anatomical feature point set, as well as the statistical value of the Jacobian matrix of the deformation field of the three-dimensional continuous coordinate mapping field in the non-control point region, which are used to evaluate the local reversibility and biomechanical rationality of the mapping.

8. The method for constructing a spatial measurement benchmark based on a three-dimensional organ model according to claim 1, characterized in that, Between steps 3 and 4, the method further includes a step of fine-tuning the individualized geometric constraints of the hierarchical reference space network: After completing the initial mapping adaptation in step 3, calculate the actual relative geometric relationship of all mapping point pairs in the target anatomical feature point set under the standard coordinate system, including the actual azimuth angle, actual zenith angle, and actual relative distance ratio. The calculated actual relative geometric relationship is compared and analyzed with the preset allowable range in the hierarchical reference space network geometric constraint layer. If the statistical distribution of the actual relative geometric relationship of a certain type of connecting edge is significantly concentrated in a sub-interval of the allowable range, then the fine-tuning procedure is started. The fine-tuning program uses multiple sample data from a specific population or disease cohort to which the target 3D organ model belongs as the learning object, recalculates the geometric constraint parameters of the connection edges, and replaces the original preset parameters in the hierarchical reference space network with the updated geometric constraint parameters to form an adaptive reference space network. This network is used to guide the subsequent construction of references for the same type of 3D organ model, making the constructed references more reflective of the anatomical commonalities of a specific group.

9. The method for constructing a spatial measurement benchmark based on a three-dimensional organ model according to claim 1, characterized in that, The standard coordinate system and coordinate mapping parameter set constructed by the method are used to realize cross-sample spatial data integration and analysis. Specific application methods include: For the second three-dimensional organ model to be analyzed, repeat steps 1 to 5 to map it to the same standard coordinate system to generate the second parameterized organ model; Under the standard coordinate system, the differences in anatomical morphology, tissue density, or functional characteristics between the first and second parametric organ models at corresponding spatial locations are directly and quantitatively compared, and the corresponding spatial locations are defined by the same standard coordinate system. Alternatively, multiple three-dimensional organ model data from different imaging modalities, including computed tomography, magnetic resonance imaging, and tissue slice images, can be mapped to the standard coordinate system. Pixel-level or feature-level fusion of the multimodal data can be performed in the standard coordinate system to generate a comprehensive organ atlas containing multimodal attributes.

10. The method for constructing a spatial measurement benchmark based on a three-dimensional organ model according to claim 1, characterized in that, The method incorporates a multi-level error propagation and uncertainty quantification model throughout the entire process of defining and optimizing the coordinate transformation relationship. The uncertainty quantification model models the localization error of the anatomical feature point identification and extraction in step 1, the range error of the geometric constraint layer parameters based on statistical learning in step 2, and the residual error of the optimization solution in step 3 as a Gaussian distribution with zero mean and specific variance. In the process of constructing the coordinate mapping field in step 4, the error is transmitted through the coefficients of the linear equation system of the thin plate spline interpolation function, and finally the confidence interval of each voxel coordinate value in the standard coordinate system is calculated. The confidence interval is represented in the form of an elliptic. The three principal axes and length of the elliptic are determined by the eigenvectors and eigenvalues ​​of the covariance matrix of the voxel coordinates, and are saved as metadata along with the parameterized organ model output in step 5. When spatial distance or volume measurement is performed in the standard coordinate system, the uncertainty of the measurement result can be calculated and reported according to the coordinate confidence interval of the voxels involved, using the error propagation law, thereby realizing the full-process uncertainty quantification from raw data to final measurement result.

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