Combinatorial Ricci Curvature for Image Processing

A new Combinatorial Ricci curvature and Laplacian operators for grayscale images are introduced and tested on 2D medical images. These notions are based upon more general concepts developed by R. Forman. Further applications are also suggested.

[1]  伏信 進矢,et al.  アイオワで computational な夏 , 2007 .

[2]  B. Chow,et al.  COMBINATORIAL RICCI FLOWS ON SURFACES , 2002, math/0211256.

[3]  N. Hitchin A panoramic view of riemannian geometry , 2006 .

[4]  Xianfeng Gu,et al.  Discrete Surface Ricci Flow: Theory and Applications , 2007, IMA Conference on the Mathematics of Surfaces.

[5]  C. Rourke,et al.  Introduction to Piecewise-Linear Topology , 1972 .

[6]  David Glickenstein A combinatorial Yamabe flow in three dimensions , 2005 .

[7]  Naokazu Yokoya,et al.  Range Image Segmentation Based on Differential Geometry: A Hybrid Approach , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[8]  Gabor T. Herman,et al.  Geometry of digital spaces , 1998, Optics & Photonics.

[9]  Feng Luo,et al.  A combinatorial curvature flow for compact 3-manifolds with boundary , 2004 .

[10]  Siddhartha Gadgil,et al.  Ricci Flow and the Poincaré Conjecture , 2007 .

[11]  Robin Forman,et al.  Bochner's Method for Cell Complexes and Combinatorial Ricci Curvature , 2003, Discret. Comput. Geom..

[12]  J. Morgan,et al.  Ricci Flow and the Poincare Conjecture , 2006, math/0607607.

[13]  Yehoshua Y. Zeevi,et al.  Sampling and Reconstruction of Surfaces and Higher Dimensional Manifolds , 2007, Journal of Mathematical Imaging and Vision.

[14]  Yehoshua Y. Zeevi,et al.  Combinatorial Ricci Curvature and Laplacians for Image Processing , 2009, 2009 2nd International Congress on Image and Signal Processing.

[15]  Preface A Panoramic View of Riemannian Geometry , 2003 .