Persistence-based segmentation of deformable shapes

In this paper, we combine two ideas: persistence-based clustering and the Heat Kernel Signature (HKS) function to obtain a multi-scale isometry invariant mesh segmentation algorithm. The key advantages of this approach is that it is tunable through a few intuitive parameters and is stable under near-isometric deformations. Indeed the method comes with feedback on the stability of the number of segments in the form of a persistence diagram. There are also spatial guarantees on part of the segments. Finally, we present an extension to the method which first detects regions which are inherently unstable and segments them separately. Both approaches are reasonably scalable and come with strong guarantees. We show numerous examples and a comparison with the segmentation benchmark and the curvature function.

[1]  Anshuman Razdan,et al.  A hybrid approach to feature segmentation of triangle meshes , 2003, Comput. Aided Des..

[2]  Marco Attene,et al.  Mesh Segmentation - A Comparative Study , 2006, IEEE International Conference on Shape Modeling and Applications 2006 (SMI'06).

[3]  Ioannis Pratikakis,et al.  Protrusion-oriented 3D mesh segmentation , 2009, The Visual Computer.

[4]  Ross T. Whitaker,et al.  Partitioning 3D Surface Meshes Using Watershed Segmentation , 1999, IEEE Trans. Vis. Comput. Graph..

[5]  Andrea Fusiello,et al.  Visual Vocabulary Signature for 3D Object Retrieval and Partial Matching , 2009, 3DOR@Eurographics.

[6]  Luiz Velho,et al.  A Hierarchical Segmentation of Articulated Bodies , 2008, Comput. Graph. Forum.

[7]  Raif M. Rustamov,et al.  Laplace-Beltrami eigenfunctions for deformation invariant shape representation , 2007 .

[8]  Thomas A. Funkhouser,et al.  A benchmark for 3D mesh segmentation , 2009, ACM Trans. Graph..

[9]  Martin Reuter,et al.  Hierarchical Shape Segmentation and Registration via Topological Features of Laplace-Beltrami Eigenfunctions , 2010, International Journal of Computer Vision.

[10]  Ayellet Tal,et al.  Polyhedral surface decomposition with applications , 2002, Comput. Graph..

[11]  Ariel Shamir,et al.  A survey on Mesh Segmentation Techniques , 2008, Comput. Graph. Forum.

[12]  Herbert Edelsbrunner,et al.  Topological persistence and simplification , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[13]  Leonidas J. Guibas,et al.  Persistence-based clustering in riemannian manifolds , 2011, SoCG '11.

[14]  Gunnar E. Carlsson,et al.  Topology and data , 2009 .

[15]  E. Davies,et al.  Non‐Gaussian Aspects of Heat Kernel Behaviour , 1997 .

[16]  Ioannis Pratikakis,et al.  3D Mesh Segmentation Methodologies for CAD applications , 2007 .

[17]  Alexander M. Bronstein,et al.  Numerical Geometry of Non-Rigid Shapes , 2009, Monographs in Computer Science.

[18]  Rasmus Larsen,et al.  Shape Analysis Using the Auto Diffusion Function , 2009 .

[19]  Ioannis Pratikakis,et al.  Retrieval of 3D Articulated Objects Using a Graph-based Representation , 2009, 3DOR@Eurographics.

[20]  Leonidas J. Guibas,et al.  Proximity of persistence modules and their diagrams , 2009, SCG '09.

[21]  Mikhail Belkin,et al.  Discrete laplace operator on meshed surfaces , 2008, SCG '08.

[22]  Ayellet Tal,et al.  Mesh segmentation using feature point and core extraction , 2005, The Visual Computer.

[23]  David Cohen-Steiner,et al.  Stability of Persistence Diagrams , 2005, Discret. Comput. Geom..

[24]  Afra Zomorodian,et al.  Computing Persistent Homology , 2004, SCG '04.

[25]  Leonidas J. Guibas,et al.  A concise and provably informative multi-scale signature based on heat diffusion , 2009 .