A Parameterization Based Correspondence Method for PDM Building
Guangxu Li, Hyoungseop Kim, Joo Kooi Tan,
and Seiji Ishikawa
Department of Mechanical and Control Engineering, Kyushu Institute of Technology, 1-1 Sensui-cho, Tobata-ku, Kitakyushu-shi, Fukuoka 804-8550, Japan
Place-march of corresponding landmarks is one of the major factors influencing 3D Points Distribution Model (PDM) quality. In this study, we propose a semi-automatic correspondence method based on surface parameterization theory. All the training sets are mapped into a spherical domain previously. The rotation transformation of training samples is regarded as spherical rotation of their maps. We solve it by comparing the density distribution of surface map of training sample with respect to the reference model. Simultaneously, the corresponding landmarks across the whole training set are marketed depending on the spherical coordinates on parameter domain. In this paper, we also compared the corresponding results with two constraint conditions of spherical conformal mapping: 3 datum points constrain and zero-mass constrain. Experimental results are given for left lung training sets of 3D shapes. The mean result with the 3 datum points constraint and the zero mass-center constraint was 21.65 mm and 20.19 mm respectively.
-  T. F. Cootes and C. J. Taylor, “Statistical Models of Appearance for Medical Image Analysis and Computer Vision,” Proc. SPIE Medical Imaging, pp. 236-248, 2001.
-  H. Park et al., “Construction of an abdominal probabilistic atlas and its application in segmentation,” IEEE Trans. on Medical Imaging, Vol.22, No.4, pp. 483-492, 2003.
-  N. Duta, A. Jain, and M. Dubuisson-Jolly, “Automatic construction of 2D shape models,” IEEE Trans. on Pattern Analysis and Machine Intell., Vol.23, No.5, pp. 433-445, 2001.
-  R. H. Davies, C. J. Twining, T. F. Cootes, and C. J. Taylor, “Building 3-D Statistical Shape Models by Direct Optimization,” IEEE Trans. on Medical Imaging, Vol.29, No.4, pp. 961-981, 2010.
-  M. A. Audette, F. P. Ferrie, and T. M. Peters, “An Algorithmic Overview of Surface Registration Techniques for Medical Imaging,” Medical Image Analysis, Vol.4, No.3, pp. 201-217, 2000.
-  H. Chui, “A new point matching algorithm for non-rigid registration,” Computer Vision and Image Understanding, Vol.89, No.2, pp. 114-141, 2003.
-  P. J. Besl, “A Method for Registration of 3-D Shapes,” IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol.14, No.2, pp. 239-256, 1992.
-  L. Thomas, W. Stefan, R. Karl, and M. S. Peter, “Landmark-Based 3D Elastic Registration of Pre- and Postoperative Liver CT Data,” Proc. SPIE Medical Imaging, pp. 107-111, 2001.
-  M. Andriy and X. Song, “Point Set Registration: Coherent Point Drift,” IEEE Trans. on Pattern analysis and Machine Intelligence, Vol.32, No.12, pp. 2262-2275, 2011.
-  J. Bing and B. C. Vemuri, “Roust Point Set Registration Using Gaussian Mixture Models,” IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol.33, No.8, pp. 1633-1645, 2011.
-  J. Qu, L. Gong, and L. Yang, “A 3D point matching algorithm for affine registration,” Int. J. of Computer Assisted Radiology and Surgery, Vol.6, No.2, pp. 229-236, 2011.
-  A. T. Heimann and H. Meinzer, “Statistical Shape Models for 3D Medical Image Segmentation: A review,” Medical Image Analysis, Vol.13, No.4, pp. 543-563, 2009.
-  D. Han and J. Bayouth et al., “Motion artifact Reduction in 4D Helical CT: Graph-based Structure Alignment,” Medical Computer Vision. Recognition Techniques and Applications inMedical Imaging, Lecture Notes in Computer Science, Vol.6533, pp. 63-73, 2011.
-  D. Han and J. Bayouth et al., “Feature Guided Motion Artifact Reduction with Structure-Awareness in 4D CT Images,” IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), pp. 1057-1064, 2011.
-  A. Sheffer, E. Praun, and K. Rose, “Mesh Parameterization Methods and their Applications,” Foundations and Trends in Computer Graphics and Vision, Vol.2, No.2, pp. 105-171, 2006.
-  A. Baumberg and D. Hogg, “Learning flexible models from image sequences,” Proc. of European Conf. on Computer Vision (ECCV), pp. 299-308, 1994.
-  Y. Wang, B. S. Peterson, and L. H. Staib, “Shape-based 3D surface correspondence using geodesics and local geometry,” Proc. of IEEE Conf. on Computer Vision and Pattern Recognition, pp. 644-651, 2000.
-  S. Belongie, J. Malik, and J. Puzicha, “Shape matching and object recognition using shape contexts,” IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol.42, No.4, pp. 509-522, 2002.
-  G. L. Scott and H. C. Longuet-Higgins, “An algorithm for associating the features of two images,” Proc. of the Royal Society of London, Vol.244, No.1309, pp. 21-26, 1991.
-  A. Kelemen, G. Szekely, and G. Gerig, “Elastic model-based segmentation of 3-D neuroradiological data sets,” IEEE Trans. on Medical Imaging, Vol.18, No.10, pp. 828-839, 1999.
-  D. Meier and E. Fisher, “Parameter space warping: shape-based correspondence between morphologically different objects,” IEEE Trans. on Medical Imaging, Vol.21, No.1, pp. 31-47, 2002.
-  X. Gu, Y. Wang, T. F. Chan, P. M. Thompson, and S. Yau, “Genus Zero Surface Conformal Mapping and Its Application to Brain Surface Mapping,” IEEE Trans. on Medical Imaging, Vol.23, No.8, pp. 949-958, 2004.
-  X. Gu, Y. Wang, and S. T. Yau, “Geometric Compression Using Riemann Surface Structure,” Communications in Information and Systems, Vol.3, No.3, pp. 171-182, 2004.
-  M. S. Floater and K. Hormann, “Surface Parameterization: a Tutorial and Survey,” Advances in Multiresolution for Geometric Modelling Mathematics and Visualization, pp. 157-186, 2005.
-  M. Mark, D. Mathieu, S. Peter, and H. B. Alan, “Discrete Differential-Geometry Operators for Triangulated 2-Manifolds,” Proc. of Visualization and Mathematics (VisMath), 2002.
-  J. Arvo, “Fast Random Rotation Matrices,” Graphics Gems III, Academic Press, 1992.
-  W. E. Lorensen and H. E. Cline, “Marching Cubes: A High Resolution 3D Surface Construction Algorithm,” ACM SIGGRAPH computer Graphics, Vol.21, No.4, pp. 163-169, 1987.
-  C. J. Twining, T. F. Cootes et al., “A unified information-theoretic approach to groupwise non-rigid registration and model building,” Information Proc. in Medical Imaging (IPMI), pp. 167-198, 2005.
-  Y. Wang, “Brain Surface Conformal Parameterization With the Ricci Flow,” IEEE Trans. on Medical Imaging, Vol.31, No.2, pp. 251-264, 2012.