Rank-based decompositions of morphological templates
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Updated: Jul 7, 2026

Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations
Published on: February 15, 2017
1Institute of Mathematics, Statistics, and Scientific Computation, State University of Campinas, 13083 Campinas, S.P., Brazil. sussner@ime.unicamp.br
Abstract:
Methods for matrix decomposition have found numerous applications in image processing, in particular for the problem of template decomposition. Since existing matrix decomposition techniques are mainly concerned with the linear domain, we consider it timely to investigate matrix decomposition techniques in the nonlinear domain with applications in image processing. The mathematical basis for these investigations is the new theory of rank within minimax algebra. Thus far, only minimax decompositions of rank 1 and rank 2 matrices into outer product expansions are known to the image processing community. We derive a heuristic algorithm for the decomposition of matrices having arbitrary rank.
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