A survey of moment-based techniques for unoccluded object representation and recognition
CVGIP: Graphical Models and Image Processing
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
Computing homology: a global reduction approach
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Invariant representative cocycles of cohomology generators using irregular graph pyramids
Computer Vision and Image Understanding
Homological spanning forest framework for 2D image analysis
Annals of Mathematics and Artificial Intelligence
Suspension models for testing shape similarity methods
Computer Vision and Image Understanding
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In this paper, we propose a novel method for shape analysis that is suitable for any multi-dimensional data set that can be modelled as a manifold. The descriptor is obtained for any pair (M,@f), where M is a closed smooth manifold and @f is a Morse function defined on M. More precisely, we characterize the topology of all pairs of sub-level sets (M"y,M"x) of @f, where M"a=@f^-^1((-~,a]), for all a@?R. Classical Morse theory is used to establish a link between the topology of a pair of sub-level sets of @f and its critical points lying between the two levels.