IEEE Trans Pattern Anal Mach Intell - Theory and Algorithms for Constructing Discrete Morse Complexes from Grayscale Digital Images.

Tópicos

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Resumo

We present an algorithm for determining the Morse complex of a two or three-dimensional grayscale digital image. Each cell in the Morse complex corresponds to a topological change in the level sets (i.e., a critical point) of the grayscale image. Since more than one critical point may be associated with a single image voxel, we model digital images by cubical complexes. A new homotopic algorithm is used to construct a discrete Morse function on the cubical complex that agrees with the digital image and has exactly the number and type of critical cells necessary to characterize the topological changes in the level sets. We make use of discrete Morse theory and simple homotopy theory to prove correctness of this algorithm. The resulting Morse complex is considerably simpler than the cubical complex originally used to represent the image and may be used to compute persistent homology.

Resumo Limpo

present algorithm determin mors complex two threedimension grayscal digit imag cell mors complex correspond topolog chang level set ie critic point grayscal imag sinc one critic point may associ singl imag voxel model digit imag cubic complex new homotop algorithm use construct discret mors function cubic complex agre digit imag exact number type critic cell necessari character topolog chang level set make use discret mors theori simpl homotopi theori prove correct algorithm result mors complex consider simpler cubic complex origin use repres imag may use comput persist homolog

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