Geodesic Distances to Landmarks for Dense Correspondence on Ensembles of Complex Shapes

作者: Manasi Datar , Ilwoo Lyu , SunHyung Kim , Joshua Cates , Martin A. Styner

DOI: 10.1007/978-3-642-40763-5_3

关键词: Computational complexity theoryEntropy (information theory)GeodesicMathematicsPattern recognitionEikonal equationComputer visionLandmarkAmbiguityComputationA priori and a posterioriArtificial intelligence

摘要: Establishing correspondence points across a set of biomedical shapes is an important technology for variety applications that rely on statistical analysis individual subjects and populations. The inherent complexity (e.g. cortical surface shapes) variability cardiac chambers) evident in many introduce significant challenges finding useful dense correspondences. Application specific strategies, such as registration simplified inflated or smoothed) surfaces relying manually placed landmarks, provide some improvement but suffer from limitations including increased computational ambiguity landmark placement. This paper proposes method point shape ensembles using geodesic distances to priori landmarks features. A novel numerical techniques fast computation sets used extract these proposed minimizes the ensemble entropy based features, resulting isometry invariant correspondences very general, flexible framework.

参考文章(14)
Manasi Datar, Yaniv Gur, Beatriz Paniagua, Martin Styner, Ross Whitaker, Geometric Correspondence for Ensembles of Nonregular Shapes Lecture Notes in Computer Science. ,vol. 14, pp. 368- 375 ,(2011) , 10.1007/978-3-642-23629-7_45
Guido Gerig, Christian Brechbühler, Dimitrios Pantazis, James J Levitt, Martin Styner, Shun Xu, Martha E Shenton, Ipek Oguz, Framework for the Statistical Shape Analysis of Brain Structures using SPHARM-PDM Insight Journal. pp. 242- 250 ,(2006)
Peter Lorenzen, Brad C. Davis, Sarang Joshi, Unbiased Atlas Formation Via Large Deformations Metric Mapping Lecture Notes in Computer Science. ,vol. 8, pp. 411- 418 ,(2005) , 10.1007/11566489_51
Joshua Cates, P. Thomas Fletcher, Martin Styner, Martha Shenton, Ross Whitaker, Shape modeling and analysis with entropy-based particle systems information processing in medical imaging. ,vol. 20, pp. 333- 345 ,(2007) , 10.1007/978-3-540-73273-0_28
Zhisong Fu, Won-Ki Jeong, Yongsheng Pan, Robert M. Kirby, Ross T. Whitaker, A Fast Iterative Method for Solving the Eikonal Equation on Triangulated Surfaces SIAM Journal on Scientific Computing. ,vol. 33, pp. 2468- 2488 ,(2011) , 10.1137/100788951
Alexander M. Bronstein, Michael M. Bronstein, Ron Kimmel, Mona Mahmoudi, Guillermo Sapiro, A Gromov-Hausdorff Framework with Diffusion Geometry for Topologically-Robust Non-rigid Shape Matching International Journal of Computer Vision. ,vol. 89, pp. 266- 286 ,(2010) , 10.1007/S11263-009-0301-6
Facundo Mémoli, Guillermo Sapiro, A Theoretical and Computational Framework for Isometry Invariant Recognition of Point Cloud Data Foundations of Computational Mathematics. ,vol. 5, pp. 313- 347 ,(2005) , 10.1007/S10208-004-0145-Y
Oliver Lyttelton, Maxime Boucher, Steven Robbins, Alan Evans, An unbiased iterative group registration template for cortical surface analysis. NeuroImage. ,vol. 34, pp. 1535- 1544 ,(2007) , 10.1016/J.NEUROIMAGE.2006.10.041
A. M. Bronstein, M. M. Bronstein, R. Kimmel, Generalized multidimensional scaling: A framework for isometry-invariant partial surface matching Proceedings of the National Academy of Sciences of the United States of America. ,vol. 103, pp. 1168- 1172 ,(2006) , 10.1073/PNAS.0508601103