Personalized registration method for template library of anatomical morphology and mechanical properties of materials of bone ct images

A personalized registration method for a template library of anatomical morphology and mechanical properties of materials of bone CT images, comprising the following steps:

• S1:
• building a statistical model containing a shape model of anatomical morphology of bones and a gray model of mechanical properties of materials;
• S11:
• processing data;
• collating a large number of bone CT images of healthy persons as a sample set, and normalizing pixel resolutions and gray ranges of the sample set;
• and resampling the unified spatial resolution, and selecting the finest spatial resolution;
• S12:
• calibrating anatomical characteristic information;
• marking anatomical landmarks of all the sample images in the sample set, and donating as L={(x1, y1, z1), . . . , (xi, yi, zi), . . . , (xk, yk, zk)}, wherein k is the number of the anatomical landmarks, and (xi, yj, zi) represents the 3D coordinate of the ith point;
• S13:
• building an average template image;
• selecting an average image or any sample image from the sample set as the initial template, deforming all the samples into the space of the average image by means of image registration, calculating a new average image to substitute the initial template image, and repeating the registration operation until the average template image no longer changes;
• S14:
• modeling the shape;
• obtaining the position changes of corresponding pixels between images through image registration;
• the deformation field of an area where the bone is located describes the morphology changes of the bone, and the deformation field is used to build a shape model of the bone;
• S15:
• modeling the gray;
• the gray value of CT images reflects the attenuation coefficient of organs to X-ray, and the high contrast of bone CT images with surrounding soft tissues accurately describes the geometrical morphology of the bone;
• statistically modeling the gray of the bone by using the gray value of the CT images;
• and modeling the gray for all the bone CT images by PCA after down-sampling of the CT images, with the formula as follows:
• g=g+Φgbg
• wherein g∈RN represents the average gray vector of the sample set;
• Φg∈RN×M is a gray feature matrix of the gray model in the statistical model obtained by PCA of the sample set, containing M gray changing patterns learned from the sample set, and the subscript g represents the gray;
• and bg∈RM is a gray parameter, g∈RN represents the gray of the model, the value of g is under control of the gray parameter bg, and the purpose of controlling the gray change of the model is achieved by adjusting the value of the gray parameter bg;
• S2:
• building a prosthesis template library;
• S21:
• collecting and processing data;
• establishing a pre-implantation data set D1 and a post-implantation data set D2 according to the bone CT image samples before and after bone prosthesis implantation, wherein D1 contains the shape and gray information of damaged bones of the patient, and the post-implantation data set D2 contains the shape and material information of a personalized bone prosthesis;
• and normalizing pixel resolutions and gray ranges of D1 and D2, and marking the anatomical landmarks of the images in D1;
• S22:
• matching the shape model;
• registering and fitting the shape model in the statistical model to the bone CT images of the patient not implanted with a bone prosthesis, and calculating the shape parameter bs of the bone of the patient;
• S23:
• matching the gray model;
• fitting the gray model in the statistical model to the bone images of the patient not implanted with a bone prosthesis, and calculating the gray parameter bg of the bone of the patient;
• Φgbg=gp, wherein gp represents the standard deviation between the gray vector of the sampled bone of the patient and the average gray vector, and Φg represents the gray feature matrix of the gray model in the statistical model;
• S24:
• acquiring a bone prosthesis model;
• extracting the tagged image of a prosthesis implant from the CT images of the postoperative patient with a prosthesis by the threshold segmentation method, and transforming the tagged image of the prosthesis to a 3D surface model by the Marching Cubes algorithm;
• S25:
• building a prosthesis template library;
• building a prosthesis template library based on the statistical model, the CT image data of the patient, the shape parameter and gray parameter of the bone of the patient, and the prosthesis model;
• S3. carrying out personalized registration of the template library;
• obtaining the shape parameter and the gray parameter of the bone through personalized registration of the prosthesis template library and the CT images, and retrieving from the prosthesis template library a prosthesis model matching with the bone in the CT images best;
• S31:
• preprocessing data;
• acquiring the bone CT images of the patient to be implanted with a bone prosthesis, carrying out unified space and gray normalization on the CT images, and marking the anatomical landmarks of the bone CT images of the patient;
• S32:
• carrying out personalized registration and parameterized representation;
• carrying out personalized registration on the bone CT images of the patient by using the statistical model, and calculating the shape parameter b′s and the gray parameter b′g of the bone of the patient through matching of the shape model and the gray model;
• S33:
• matching data;
• retrieving the data of template images stored in the prosthesis template library and similar to those of the bone of the patient from the prosthesis template library by using a similarity calculation formula according to the shape parameter and gray parameter describing the bone of the patient obtained by registration, the similarity calculation formula is as follows:
• D
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• wherein
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• is the variance between the shape parameter of the bone of the patient and that of the template image in the prosthesis template library for measurement of the level of similarity in the shape of the bone between two images;
• Σi=0M(b′g−bg)2 is the variance between the gray parameter of the bone of the patient and that of the template image in the prosthesis template library for measurement of the level of similarity in the gray of the bone between two images;
• and λ1 and λ2 are weights of the shape similarity and the gray similarity, the sum thereof is 1, and the values of λ1 and λ2 are assigned according to different weights to realize the retrieval matching method based on the shape similarity or based on the gray similarity;
• calculating the similarity D between the data in the prosthesis template library and the data of the patient, obtaining the template CT image most similar to the bone of the patient after comparison, and acquiring a bone prosthesis model corresponding to the image as the initial reference template for the personalized bone prosthesis of the patient for subsequent analysis and design of bone prostheses.

The personalized registration method for a template library of anatomical morphology and mechanical properties of materials of bone CT images according to claim 1, wherein the steps of modeling the shape in S14 are as follows:

• S141:
• calculating shape vectors;
• calculating nonlinear spatial transformation between the sample image and the average template image by means of image registration, building a shape vector for each sample, and letting si=[pi, li]∈R3N as the shape vector of the sample i, wherein pi∈R3N is a 3D coordinate set of N pixels obtained by registering the average template to the sample i, and li∈R3K is a 3D coordinate set of K anatomical landmarks in the sample image.
• S142:
• aligning the shape vectors si of all the samples by generalized procrustes analysis;
• S143:
• modeling the shape change of the bone by principal component analysis;
• the shape model is as follows:
• s=s+Φsbs
• wherein s∈R3N represents the average shape of the sample set, Φs ∈R3(N+K)×M represents an eigenvector matrix obtained by principal component analysis of the sample set, and M feature vectors represent M bone deformation patterns learned by the shape model;
• bs∈RM is a shape parameter, and M elements in bs respectively represent weights of M deformation patterns in Φs superimposed with the average shape;
• and s∈R3(N+K) represents the shape of the model, s is under control of bs, and the purpose of controlling model deformation is achieved by adjusting the value of bs.

The personalized registration method for a template library of anatomical morphology and mechanical properties of materials of bone CT images according to claim 1, wherein the steps of matching the shape model in S22 are as follows:

• S221:
• sampling;
• carrying out equidistant sampling on the vertexes of the average shape in the shape model, and selecting a small number of sampling points for subsequent calculation;
• S222:
• carrying out personalized registration;
• obtaining the mapping relationship, i.e., deformation field, between the average template and the bone image of the patient by the nonlinear registration method of the image, and deforming the vertexes of the average shape in the shape model by using the deformation field to obtain a shape vector describing the bone of the patient;
• the gray similarity measure between images and the distance measure of the anatomical landmarks are used as the constraints for the loss function of nonlinear registration, and the objective function is as follows:
• E=ωiEi+ωlEl
• wherein E is the weighted similarity measure between the template and the image of the patient, Ei is the gray similarity measure between the template and the image of the patient, and El is the distance measure of the anatomical landmarks;
• and ωi and ωl are weights of the two measures, and the sum thereof is 1;
• S223:
• aligning the registered shape vector of the bone of the patient with the average shape vector, wherein similarity transformation is composed of a scaling factor and a rotation matrix, the scaling factor is obtained by calculating the ratio of the distance between the vertex and the centroid of the registered shape vector of the bone to that of the average shape vector, and the rotation matrix is obtained by singular value decomposition of the vertex matrixes of the two shape vectors;
• S224:
• setting the number of the shape parameters bs;
• directly defining the number of the shape parameters bs or selecting the number of the shape parameters bs capable of retaining more than 95% of data information;
• and extracting the corresponding shape feature matrix Φs from the shape model according to the number of the shape parameters bs;
• S225:
• calculating the shape parameter bs of the bone of the patient;
• carrying out linear regression fitting by least squares according to the shape feature matrix Φs extracted from the shape model and the registered shape vector of the bone of the patient, and solving the system of linear equations Φsbs=sp to obtain the shape parameter bs of the bone of the patient, wherein sp represents the displacement deviation between the shape vector of the bone of the patient and the average shape vector, and Φs represents the shape feature matrix contained in the shape model in the statistical model.