Perceptual organization and the representation of natural form
Artificial Intelligence
Surface Coding Based on Morse Theory
IEEE Computer Graphics and Applications
Constructing a Reeb graph automatically from cross sections
IEEE Computer Graphics and Applications
Invited Lecture: A Shape Abstraction Paradigm for Modeling Geometry and Semantics
CGI '98 Proceedings of the Computer Graphics International 1998
Computational Topology for Shape Modeling
SMI '99 Proceedings of the International Conference on Shape Modeling and Applications
Re-Meshing Techniques for Topological Analysis
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
A robust technique for surface reconstruction from orthogonal slices
Machine Graphics & Vision International Journal
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
Harmonic 1-form based skeleton extraction from examples
Graphical Models
Abstraction of man-made shapes
ACM SIGGRAPH Asia 2009 papers
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This paper investigates the possible role of the new field of computational topology for incorporating abstraction mechanisms in shape modelling. The effectiveness of computational topology techniques is exemplified with an application of discrete differential topology. In particular, a method is proposed for the extraction of a critical point configuration graph from a triangulated surface. Starting from the definition of the Reeb graph in the smooth domain, the concept of critical point is extended to critical areas, which may represent isolated as well as degenerated critical points in the discrete domain. The resulting graph effectively represents the surface shape and has been successfully used as a basis for model compression and restoring purposes.