2 X a) 3D Reconstruction of Femoral Shape Using a Two 2D Radiographs and Statistical Parametric Model Ryo KURAZUME a), Kahori NAKAMURA, Toshiyuki OKAD

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1 2 X a) 3D Reconstruction of Femoral Shape Using a Two 2D Radiographs and Statistical Parametric Model Ryo KURAZUME a), Kahori NAKAMURA, Toshiyuki OKADA, Yoshinobu SATO, Nobuhiko SUGANO, Tsuyoshi KOYAMA, Yumi IWASHITA, and Tsutomu HASEGAWA X CT MRI X X X X 51 CT X X X 1. X CT Computed Tomography MRI Magnetic Resonance Imaging X CT X Graduate School of Information Science and Electrical Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka-shi, Japan Graduate School of Information Science and Technology, Osaka University, 1 3 Machikaneyama-cho, Toyonaka-shi, Japan Graduate School of Medicine, Osaka University, 2 2 Yamadaoka, Suita-shi, Japan a) kurazume@is.kyushu-u.ac.jp CT X X X CT X CT X X ill-posed D Vol. J90 D No. 3 pp c

2 2007/3 Vol. J90 D No. 3 X 2 2 X Level Set Method Fast Marching Method X 51 CT 10 X X CT 2. 1 [1] [3] 2 [4] [7] 3 [8] [11] CT MRI X 2D-3D [23] [28] CT Digitally Reconstructed Radiographs DRRs X X [23] [25] soft tissue [12] [13] [14] quadric/superquadric [15] displacement-field-based transformation [16] [17] [18] [19] [20] [19] step step 2 step 3 step 4 step

2 X 1 Table 1 List of antomical features of femur. V Hc A P A N P Nc V Gt V Lt V Lp L R L V 2 Fig. 2 Conrtibutions of parametric model. 51 2 1 Fig. 1 (a) Front (b) Back Antomical features of femur.

3 2 X 1 Table 1 List of antomical features of femur. V Hc A P A N P Nc V Gt V Lt V Lp L R L V 2 Fig. 2 Conrtibutions of parametric model Fig. 1 (a) Front (b) Back Antomical features of femur x x s i, i =1 50 (1) x = x + s i σ i e i (1) i σ i e i i 50 CT 4. X X Level Set Method Fast Marching Method X X [8] 2 2 X x i 1 i N N 3 o j =(l, m, n) 1 l, m, n N 1 j M M s i σ i e i 947

2007/3 Vol. J90 D No. 3 x i (1) x i 8(c) 4. 1

4 X OpenGL step 5(a) step 6(a) M step 7(a) Step 3 Step 6(a) step 8(a) Step 3 Step 7(a) 4. 1.

4 2007/3 Vol. J90 D No. 3 x i (1) x i 8(c) X [8] step 1 Level Set Method [8], [21] X step 2 Level Set Method Fast Marching Method [22] X 3 step 3 X step 4 X OpenGL step 5(a) step 6(a) M step 7(a) Step 3 Step 6(a) step 8(a) Step 3 Step 7(a) Step 5(a) 7(a) M Step 4 (s, t) i D i D i = D s,t (2) D u,v (u, v) i f i 4 5 f i = D i D i D i (3) D i (s, t) M F M 3 Fig. 3 Distance map on femoral image. 4 f Fig. 4Applying force f to patches on contour line. 948

5 2 X (a) (b) 5 Fig. 5 Force and moment around the center of gravity. F = ψ(f i) (4) i M = ψ(r i f i) (5) i r i i ψ(z) X X step 4 step 5(b) E step 6(b) E step 7(b) step 8(b) Step 3 Step 7(b) E Step 5(b) 7(b) P p E(S) E(S) = D i P =p (6) i S = {s i} E(S) S P S 4. 3 OpenGL modeldata testdata X 2 X 6 A P

9 Estimation errors for various numbers of

7 Synthesized radiographs. (a) (b) (c) 8 Fig.

CT 0 10 testdata 4 8 CT 9 3.8 mm 1.5 mm 12.2 mm 0.

6 2007/3 Vol. J90 D No. 3 Fig. 6 6 Bearings of exposure axes. 9 Fig. 9 Estimation errors for various numbers of parameters. Front view Side view 7 X Fig. 7 Synthesized radiographs. (a) (b) (c) 8 Fig. 8 Femoral models for parameter estimation. CT 0 10 testdata 4 8 CT mm 1.5 mm 12.2 mm 0.5 mm Fig. 10 Estimation errors for femoral models. (number of parameters is 5)

7 2 X 2 [mm] Table 2 Average of estimation errors [mm] testdata modeldata CT mm X X 190 X Siremobil ISO-C C-Arm C-Arm X X C-Arm X C-Arm X 11 X 50 CT Light Speed Plus GE Yokogawa Medical Systems Tsai [29] X 11 X Light Speed Plus GE Yokogawa Medical Systems Fig. 11 Radiographs of calibration markers and phantom femur. 12 X Siremobil ISO-C Fig. 12 Measured radiographs. CT dpi 1.25 mm X dpi CT 2 951

8 2007/3 Vol. J90 D No X 4 24 Fig. 13 Radiographs. (No.4and No.24) Fig Process of shape and pose estimation. 14 Fig. 14Estimation errors for numbers of parameters. 16 Fig. 16 Estimated shapes of the femur. 3 [mm] Table 3 Average of estimation errors for numbers of parameters [mm] Fig. 17 Estimation errors for various pairs of radiographs X 4 C-Arm Level Set Method 1 Pentium IV 3.2 GHz C-Arm X 1.2 mm X 952

9 2 X Fast Marching Method 51 CT 10 X 1.1 mm 2 X 1.2 mm [1] I. Stamos and P.K. Allen, Integration of range and image sensing for photorealistic 3d modeling, Proc IEEE International Conference on Robotics and Automation, pp , [2] I. Stamos and P.K. Allen, Automatic registration of 2-d with 3-d imagery in urban environments, Proc. International Conference on Computer Vision, pp , [3] L. Liu and I. Stamos, Automatic 3d to 2d registration for the photorealistic rendering of urvan scenes, IEEE International Conference on Computer Vision and Pattern Recognition, pp , [4] R. Kurazume, K. Noshino, Z. Zhang, and K. Ikeuchi, Simultaneous 2d images and 3d geometric model registration for texture mapping utilizing reflectance attribute, Proc. Fifth Asian Conference on Computer Vision (ACCV), pp , [5] M.D. Wheeler, D-II vol.j85-d-ii, no.6, pp , June [6] M.D. Elstrom and P.W. Smith, Stereo-based registration of multi-sensor imagery for enhanced visualization of remote environments, Proc IEEE International Conference on Robotics and Automation, pp , [7] K. Umeda, G. Godin, and M. Rioux, Registration of range and color images using gradient constraints and range intensity images, Proc. 17th International Conference on Pattern Recognition, pp.12 15, [8] D-II vol.j88-d- II, no.9, pp , Sept [9] Q. Delamarre and O. Faugeras, 3d articulated models and multi-view tracking with silhouettes, Proc. International Conference on Computer Vision, vol.2, pp , [10] K. Matsushita and T. Kaneko, Efficient and handy texture mapping on 3d surfaces, Comput. Graphics Forum 18, pp , [11] P.J. Neugebauer and K. Klein, Texturing 3d models of real world objects from multiple unregistered photographic views, Computer Graphics Forum 18, pp , [12] C.V. Stewart, C.L. Tsai, and A. Perera, A viewbased approach to registration: Theory and application to vascular image regisrtaion, International Conference on Information Processing in Medical Imaging (IPMI), pp , [13] C.V. Stewart, C.L. Tsai, and A. Perera, Rigid and affine registration of smooth surfaces using differential properties, Proc. Third European Conference on Computer Vision (ECCV 94), pp , [14] A. Gueziec, X. Pennec, and N. Ayache, Medical image registration using geometric hashing, IEEE Computational Science and Engineering, special issue on Geometric Hashing, vol.4, no.4, pp.29 41, [15] E. Bardinet, L.D. Cohen, and N. Ayache, A parametric deformable model to fit unstructured 3d data, Computer Vision and Image Understanding, vol.71, no.1, pp.39 54, [16] P.R. Andresen and M. Nielsen, Non-rigid registration by geometry constrained diffusion, Medical Image Computing and Computer-Assisted Intervention (MICCAI 99), pp , [17] T. Masuda, Y. Hirota, K. Ikeuchi, and K. Nishino, Simultaneous determination of registration and deformation parameters among 3d range images, Proc. Fifth International Conference on 3-D Digital Imaging and Modeling, pp , [18] C.S.K. Chan, D.C. Barratt, P.J. Edwards, G.P. Penney, M. Slomczykowski, T.J. Charter, and D.J. Hawkes, Cadaver validation of the use of ultrasound for 3d model instantiation of bony anatomy in image 953

2007/3 Vol. J90 D No. 3 guided orthopaedic surgery, Lecture Notes in Computer Science, 3217 (Proc.

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11 2 X International Society for Computer Assisted Orthopaedic Surgery 2004 IEEE

proc.dvi

proc.dvi M. D. Wheler Cyra Technologies, Inc. 3 3 CAD albedo Mapping textures on 3D geometric model using reflectance image Ryo Kurazume M. D. Wheler Katsushi Ikeuchi The University oftokyo Cyra Technologies, Inc.