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2014 (v1)PublicationUploaded on: December 5, 2022
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2012 (v1)Publication
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2012 (v1)Publication
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2015 (v1)Publication
Morse theory offers a natural and mathematically-sound tool for shape analysis and understanding. It allows studying the behavior of a scalar function defined on a manifold. Starting from a Morse function, we can decompose the domain of the function into meaningful regions associated with the critical points of the function. Such...
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2016 (v1)Publication
We consider the problem of segmenting triangle meshes endowed with a discrete scalar function f based on the critical points of f . The watershed transform induces a decomposition of the domain of function f into regions of influence of its minima, called catchment basins. The discrete Morse gradient induced by f allows recovering not only...
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2014 (v1)Publication
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Uploaded on: March 27, 2023 -
2013 (v1)Publication
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Uploaded on: March 27, 2023 -
2013 (v1)Publication
With improvements in sensor technology and simulation methods, datasets are growing in size, calling for the investigation of efficient and scalable tools for their analysis. Topological methods, able to extract essential features from data, are a prime candidate for the development of such tools. Here, we examine an approach based on discrete...
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2013 (v1)Publication
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2013 (v1)Publication
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2011 (v1)Publication
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2012 (v1)Publication
We investigate a morphological approach to the analysis and understanding of three-dimensional scalar fields, and we consider applications to 3D medical and molecular images as examples.We consider a discrete model of the scalar field obtained by discretizing its 3D domain into a tetrahedral mesh. In particular, our meshes correspond to...
Uploaded on: April 14, 2023