A 2D/3D correspondence building method for reconstruction of a 3D bone surface model Longwei Fang

Contents Introduction Principle Experiments and Results Conclusions 2

Introduction The application of X-ray imaging in orthopedic surgery are pervasive Limited field of view, distorted image, high radiation Build a statistical shape model and adapt it to the patient’ individual anatomy on a limited number of x-ray image. 3

Principle 4

Statistical model construction Using a Point Distribution Model (PDM) Achieved using principle component analysis(PCA) Parameter setdescribes an instance Shape coefficients obey the normal distribution 5

Principle 6

2D/3D correspondence building Bone edge extraction Apparent contour extraction Iterative non-rigid 2D matching process 3D point pair building 7

Bone edge extraction Bayesian inference method to extract the bone contours Silhouette of the projected 3D statistical model Candidate contour Define Potential function Bayesian Maximal Likelihood 8

Apparent contour extraction 9 The silhouette set for the smooth surface is the set of points p of the surface such that: Algorithm based on dual surfaces

Iterative non-rigid 2D matching process Matching uses the Symmetric injective Nearest-neighbor(SIN) Mapping operator Algorithm: the implantation of the SIN-MO 10

Iterative non-rigid 2D matching process Using the Thin-plate splines method to enlarge the number of paired points Bending energy function: Cost function 11

3D point pair building 12

Principle 13

3D/3D Reconstruction Scaled rigid registration Statistical instantiation 14

Scaled rigid registration Using ICP find the matching points Minimize the difference between two clouds of points. One point cloud, the reference, or target, is kept fixed, while the other one, the source, is transformed to best match the reference. 15

Statistical instantiation Cost function solution 16

Principle 17

Regularized shape deformation 3D surface TPS Cost function 18

Experiments Two institutions: MEM research center(MEM-PDM) and BrainLAB AG(BrainLAB-PDM) institutionsamples segamented partdifferenceexperiments MEM 30 CT scans of hips without pathology, each 4098 vertices lesser trochanter smooth 1.experiment on 2D shapes to evaluate the performance of the iterative non-rigid 2D matching process 2.experiment on calibrated C-arm images of cadaveric femurs to evaluate: （ 1 ） convergence and robustness of the 2D/3D correspondence building method; （ 2 ） reconstruction accuracies of statistical instantiation and regularized shape deformation; （ 3 ） the effect of the number of the X-ray images on the reconstruction accuracy of the 2D/3D reconstruction scheme. 1.evaluate the performance of the present approach in clinical settings on calibrated C-arm image 2.evaluate the overall accuracy and robustness of the present approach on calibrated X-ray radiographs of twenty-two femurs with both non- pathologic and pathologic case BrainLAB 23 CT scans,one as master shape, others aligned with the master shape much larger part than MEM much noise 19

Experiment on 2D shapes Target: whether the non-rigid 2D matching process could find a fraction of points pairs Procedure: 1.Interpolation 2.Building correspondences 3.Scaled rigid registration 4. Building correspondence 5.2D TPS interpolation 6. Repeat

Experiment on 2D shapes Target: compare ICP with the proposed method Procedure: 1.Interpolation 2.Building correspondences 3.Scaled rigid registration 4. Building correspondence 5.2D TPS interpolation 6. Repeat

Experiment on 2D shapes Target: further compare ICP with the proposed method 22

Experiment on calibrated C-arm images of cadaveric femurs Convergence of the 2D/3d Correspondence building method Reconstruction accuracies instantiation of statistical and regularized shape deformation Effect of the number of x-ray images on the overall reconstruction accuracy of the 2D/3D reconstruction scheme The first and second studies: Plastic bone with CT scan, the surface segmented form CT scan as ground truth, BrainLAB The last one study: 11 cadaveric bones, surface built using tracked probe as ground truth, MEM 23

Convergence of the 2D/3d Correspondence building method Evaluation: Number of the found 3D point pairs The mean distance between the found 3D point pairs Two fluoroscopic images, angle 20° 24

Reconstruction accuracies instantiation of statistical and regularized shape deformation Target: whether the regularized shape deformation stage will further improve the reconstruction accuracy of instantiation stage or not methodmedium root mean square distancemean distancemaximum distance SI0.9mm1.4mm1.1mm5.0mm R0.7mm1.3mm1.0mm4.8mm 25

Effect of the number of x-ray images on the overall reconstruction accuracy of the 2D/3D reconstruction scheme 26

Experiment on calibrated C-arm images of three patients 27

Experiments on calibrated X-ray radiographs of cadaveric femurs G enerate a surface model of the proximal femur using two pre-operatively acquired X-ray radiographs and then to register the reconstructed surface model to the patient reference coordinate system using intra-operatively acquired sparse-point data to provide a patient-specific 3D model for surgical planning and navigation. Procedure: 1.Interactive way to identify contours(4-50 points for each contour) 2.cubic-spline interpolation Ground truthsamples Hand-held laser-scan reconstruction method 18 naked bones CT-scan reconstruction method 2 wet cadaver pelvis, other 2 dry femurs but glue together 28

Experiments on calibrated X-ray radiographs of cadaveric femurs Color-coded error distribution when the reconstructed surface model was compared to its ground truth obtained by a laser-scan reconstruction method (the maximal error distance = 3.7 mm and the mean error distance = 0.7 mm) surface model of a pathologic femur. Left and right images: the input X-ray radiographs; middle: the front (top) and the back (bottom) view of the comparison of the reconstructed surface model (color-coded) with its ground truth. Errors of reconstructing surface models of all 22 femurs, where femur 15 and 16 are parts of a wet cadaver pelvis, femur 13 and 14 are glued with their associated acetabula, and others are naked femurs. 29

Conclusions Presented a 2D/3D correspondence building method. 1.feature-based methods to extraction of bone edge. 2.Based on dual space to generate apparent contour. 3.Use a symmetric injective nearest-neighbor mapping operator and 2D thin-plate splines based deformations to find point pairs. A. one to one mapping B. symmetric to both x-ray image and 3D silhouette C. handle certain level noise/outliers D. excluding the cross matching A 2D/3D reconstruction scheme combining a statistical instantiation and regularized shape deformation regularized shape deformation can further fine the surface 30