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Vector median filters, morphology, and PDE's: Theoretical connections

Publication ,  Journal Article
Caselles, V; Sapiro, G; Chung, DH
Published in: IEEE International Conference on Image Processing
December 1, 1999

In this paper, we formally connect between vector median filters, morphological operators, 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 vector-valued image is equivalent to a collection of infimum-supremum 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 level-sets toward those of this main component. These results extend to the vector case classical connections between scalar median filters, mathematical morphology, and mean curvature motions.

Duke Scholars

Published In

IEEE International Conference on Image Processing

Publication Date

December 1, 1999

Volume

4

Start / End Page

177 / 181
 

Citation

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Caselles, V., Sapiro, G., & Chung, D. H. (1999). Vector median filters, morphology, and PDE's: Theoretical connections. IEEE International Conference on Image Processing, 4, 177–181.
Caselles, V., G. Sapiro, and D. H. Chung. “Vector median filters, morphology, and PDE's: Theoretical connections.” IEEE International Conference on Image Processing 4 (December 1, 1999): 177–81.
Caselles V, Sapiro G, Chung DH. Vector median filters, morphology, and PDE's: Theoretical connections. IEEE International Conference on Image Processing. 1999 Dec 1;4:177–81.
Caselles, V., et al. “Vector median filters, morphology, and PDE's: Theoretical connections.” IEEE International Conference on Image Processing, vol. 4, Dec. 1999, pp. 177–81.
Caselles V, Sapiro G, Chung DH. Vector median filters, morphology, and PDE's: Theoretical connections. IEEE International Conference on Image Processing. 1999 Dec 1;4:177–181.

Published In

IEEE International Conference on Image Processing

Publication Date

December 1, 1999

Volume

4

Start / End Page

177 / 181