2008/06/04 by Darryl D. Holm, Holm, Darryl D., Alain Trouve +5 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Chaotic Dynamics (nlin.CD) #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Physical sciences #Geometric and Algebraic Topology #Nonlinear Waves and Solitons #cs.CV #nlin.CD
paper · pdf · doi:10.48550/arxiv.0806.0870
arxiv created 2008/06/04 · openalex publication_date 2008/06/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the pattern matching approach to imaging science, the process of ``metamorphosis'' is template matching with dynamical templates. Here, we recast the metamorphosis equations of into the Euler-Poincare variational framework of and show that the metamorphosis equations contain the equations for a perfect complex fluid \citeHo2002. This result connects the ideas underlying the process of metamorphosis in image matching to the physical concept of order parameter in the theory of complex fluids. After developing the general theory, we reinterpret various examples, including point set, image and density metamorphosis. We finally discuss the issue of matching measures with metamorphosis, for which we provide existence theorems for the initial and boundary value problems.