Math @ Duke

Publications [#264925] of Guillermo Sapiro
Papers Published
 Caselles, V; Sapiro, G; Chung, DH, Vector median filters, infsup operations, and coupled PDE's: Theoretical connections,
Journal of Mathematical Imaging and Vision, vol. 12 no. 2
(2000),
pp. 109119 [doi]
(last updated on 2018/09/24)
Abstract: In this paper, we formally connect between vector median filters, infsup morphological operations, and geometric partial differential equations. Considering a lexicographic order, which permits to define an order between vectors in IRN, we first show that the vector median filter of a vectorvalued image is equivalent to a collection of infimumsupremum morphological operations. We then proceed and study the asymptotic behavior of this filter. We also provide an interpretation of the infinitesimal iteration of this vectorial median filter in terms of systems of coupled geometric partial differential equations. The main component of the vector evolves according to curvature motion, while, intuitively, the others regularly deform their levelsets toward those of this main component. These results extend to the vector case classical connections between scalar median filters, mathematical morphology, and mean curvature motion.


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