Singularity theory and heat equation
Jean Petitot
TL;DR
This paper illustrates how singularity theory can be applied to the heat equation, demonstrating a 1D unfolding of an elliptic umbilic catastrophe within multiscale image analysis models.
Contribution
It adapts Thom-Mather's singularity theory to multiscale models in image processing, providing graphical examples of solutions to the heat equation.
Findings
Graphical example of heat equation solution as elliptic umbilic unfolding
Application of singularity theory to multiscale image analysis
Integration of Thom-Mather's theory into heat equation models
Abstract
The paper (in French) exemplifies graphically a solution of the heat equation which is a 1-dimensional unfolding of an elliptic umbilic catastrophe. The example is due to James Damon and adapts Thom-Mather's singularity theory to multiscale models of scale-space analysis in image processing.
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Taxonomy
TopicsMedical Image Segmentation Techniques · Image Retrieval and Classification Techniques · Cell Image Analysis Techniques