cvpr cvpr2013 cvpr2013-44 cvpr2013-44-reference knowledge-graph by maker-knowledge-mining
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Author: Zhengyu Su, Wei Zeng, Rui Shi, Yalin Wang, Jian Sun, Xianfeng Gu
Abstract: Brain mapping transforms the brain cortical surface to canonical planar domains, which plays a fundamental role in morphological study. Most existing brain mapping methods are based on angle preserving maps, which may introduce large area distortions. This work proposes an area preserving brain mapping method based on MongeBrenier theory. The brain mapping is intrinsic to the Riemannian metric, unique, and diffeomorphic. The computation is equivalent to convex energy minimization and power Voronoi diagram construction. Comparing to the existing approaches based on Monge-Kantorovich theory, the proposed one greatly reduces the complexity (from n2 unknowns to n ), and improves the simplicity and efficiency. Experimental results on caudate nucleus surface mapping and cortical surface mapping demonstrate the efficacy and efficiency of the proposed method. Conventional methods for caudate nucleus surface mapping may suffer from numerical instability; in contrast, current method produces diffeomorpic mappings stably. In the study of cortical sur- face classification for recognition of Alzheimer’s Disease, the proposed method outperforms some other morphometry features.
[1] http://www.csie.ntu.edu.tw/ cjlin/libsvm/.
[2] A. D. Alexandrov. Convex Polyhedra. Springer, 2005.
[3] S. Angenent, S. Haker, A. Tannenbaum, and R. Kikinis. Conformal geometry and brain flattening. In Med. Image Comput. Comput.Assist. Intervention, pages 271–278, 1999.
[4] L. G. Apostolova, M. Beyer, A. E. Green, K. S. Hwang, J. H. Morra, Y. Y. Chou, C. Avedissian, D. Aarsland, C. C. Janvin, J. L. Cummings, and P. M. Thompson. Hippocampal, caudate, and ventricular changes in Parkinson’s disease with and without dementia. Mov. Disord., pages 687–695, 2010.
[5] J. Ashburner, C. Hutton, R. Frackowiak, I. Johnsrude, C. Price, and K. Friston. Identifying global anatomical differences: deformation-based morphometry. Human Brain Mapping, 6(5-6):348–357, 1998. 222222334199
[6] M. Balasubramanian, J. Polimeni, and E. Schwartz. Exact geodesics and shortest paths on polyhedral surfaces. IEEE Trans. Patt. Anal. Mach. Intell. , pages 1006–1016, 2009.
[7] D. M. Boyer, Y. Lipman, E. St Clair, J. Puente, B. A. Patel, T. Funkhouser, J. Jernvall, and I. Daubechies. Algorithms to automatically quantify the geometric similarity of anatomical surfaces. Proc. Natl. Acad. Sci., 108: 18221–18226, 2011.
[8] Y. Brenier. Polar factorization and monotone rearrangement of vector-valued functions. Com. Pure Appl. Math., 64:375– 417, 1991.
[9] A. M. Bronstein, M. M. Bronstein, and R. Kimmel. Generalized multidimensional scaling: a framework for isometryinvariant partial surface matching. Proc. Natl. Acad. Sci., 103:1 168–1 172, 2006.
[10] R. Cuingnet, E. Gerardin, J. Tessieras, G. Auzias, S. Lehericy, M. Habert, M. Chupin, H. Benali, , and O. Colliot. Automatic classification of patients with Alzheimer’s disease from structural MRI: A comparison of ten methods using the ADNI database. Neuroimage, 56(2), 2011.
[11] R. S. Desikan, F. Segonne, B. Fischl, B. T. Quinn, B. C. Dickerson, D. Blacker, R. L. Buckner, A. M. Dale, R. P. Maguire, B. T. Hy-man, M. S. Albert, and R. J. Killiany. An automated labelingsystem for subdividing the human cerebral cortex on MRI scans into gyral based regions of interest. Neuroimage, 31:968–980, 2006.
[12] H. A. Drury, D. C. Van Essen, C. H. Anderson, C. W. Lee, T. A. Coogan, and J. W. Lewis. Computerized mappings of the cerebral cortex: A multiresolution flattening method and a surface-based coordinate system. J. Cognitive Neurosciences, 8: 1–28, 1996.
[13] B. Fischl, M. I. Sereno, and A. M. Dale. Cortical surfacebased analysis II: Inflation, flattening, and a surface-based coordinate system. NeuroImage, 9(2): 195 – 207, 1999.
[14] N. C. Fox, R. I. Scahill, W. R. Crum, and M. N. Rossor. Correlation between rates of brain atrophy and cognitive decline in AD. Neurology, 52: 1687–1689, 1999.
[15] G. B. Frisoni, N. C. Fox, C. R. J. Jr, P. Scheltens, and P. M. Thompson. The clinical use of structural MRI in Alzheimer’s
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25] disease. Nature Reviews Neurology, 6(2):67–77, 2010. F. Gardiner and N. Lakic. Quasiconformal teichmuller theory. American Mathematics Society, 2000. X. Gu, Y. Wang, T. F. Chan, P. M. Thompson, and S.-T. Yau. Genus zero surface conformal mapping and its application to brain surface mapping. IEEE Trans. Med. Imag., 23:949– 958, 2004. X. Gu and S.-T. Yau. Computing conformal structures of surfaces. Communications in Information and Systems, 2: 121– 146, 2002. S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent. Optimal mass transport for registration and warping. International Journal on Computer Vision, 60(3):225–240, 2004. R. S. Hamilton. The Ricci flow on surfaces. Mathematics and general relativity, 71:237–262, 1988. M. K. Hurdal and K. Stephenson. Cortical cartography using the discrete conformal approach of circle packings. NeuroImage, 23:S1 19–S128, 2004. C. R. J. Jack, M. A. Bernstein, N. C. Fox, P. M. Thompson, G. Alexander, D. Harvey, B. Borowski, P. J. Britson, J. L. Whitwell, C. Ward, and et al. The Alzheimer’s disease neuroimaging initiative (ADNI): MRI methods. J. of Mag. Res. Ima., 27:685–691, 2007. L. Ju, M. K. Hurdal, J. Stern, K. Rehm, K. Schaper, and D. Rottenberg. Quantitative evaluation of three surface flattening methods. NeuroImage, 28:869–880, 2005. L. V. Kantorovich. On a problem of monge. Uspekhi Mat. Nauk., 3:225–226, 1948. S. K. Madsen, A. J. Ho, X. Hua, P. S. Saharan, A. W. Toga, C. R. Jack, M. W. Weiner, and P. M. Thompson. 3D maps localize caudate nucleus atrophy in 400 Alzheimer’s dis-
[26]
[27]
[28]
[29]
[30] [3 1]
[32]
[33] ease, mild cognitive impairment, and healthy elderly subjects. Neurobiol. Aging, 3 1:13 12–1325, 2010. T. Rehman, E. Haber, G. Pryor, and A. Tannenbaum. Fast optimal mass transport for 2D image registration and morphing. Elsevier Journal of Image and Vision Computing, 2008. E. Sharon and D. Mumford. 2D-shape analysis using conformal mapping. In Proc. IEEE Conf. Computer Vision and Pattern Recognition, pages 350–357, 2004. Y. Shi, R. Lai, and A. Toga. Corporate: cortical reconstruction by pruning outliers with Reeb analysis and topologypreserving evolution. Information Process Medical Imaging, 22:233–244, 2011. S. M. Smith, M. Jenkinson, M. W. Woolrich, C. F. Beckmann, T. E. Behrens, H. Johansen-Berg, P. R. Bannister, M. De Luca, I. Drobnjak, D. E. Flitney, R. K. Niazy, J. Saunders, J. Vickers, Y. Zhang, N. De Stefano, J. M. Brady, and P. M. Matthews. Advances in functional and structural MR image analysis and implementation as FSL. Neuroimage, 23 Suppl 1:S208–219, 2004. P. M. Thompson and A. W. Toga. A surface-based technique for warping 3-dimensional images of the brain. IEEE Trans. Med. Imag., 15: 1–16, 1996. B. Timsari and R. M. Leahy. Optimization method for creating semi-isometric flat maps of the cerebral cortex. Medical Imaging 2000: Image Processing, 3979:698–708, 2000. D. Tosun and J. Prince. A geometry-driven optical flow warping for spatial normalization of cortical surfaces. IEEE Trans. Med. Imag., 27: 1739 –1753, 2008. Y. Wang, X. Gu, T. F. Chan, P. M. Thompson, and S.-T. Yau. Conformal slit mapping and its applications to brain surface parameterization. In Med. Image Comp. Comput.-Assist. In- tervention, Proceedings, Part I, pages 585–593, 2008.
[34] Y. Wang, J. Shi, X. Yin, X. Gu, T. F. Chan, S. T. Yau, A. W. Toga, and P. M. Thompson. Brain surface conformal parameterization with the Ricci flow. IEEE Trans Med Imaging, 31(2):251–264, 2012.
[35] W. Zeng, X. Yin, Y. Zeng, Y. L. X. Gu, and D. Samaras. 3D face matching and registration based on hyperbolic Ricci flow. CVPR Workshop on 3D Face Processing, pages 1–8, 2008.
[36] L. Zhu, S. Haker, and A. Tannenbaum. Area-preserving mappings for the visualization of medical structures. In Medical Image Computing and Computer-Assisted Intervention, 2879:277–284, 2003. 222222444200