New concepts in mathematical morphology: the topographical and differential distance functions

Francoise J. Preteux; Nicolas Merlet

doi:10.1117/12.49884

1 July 1991 New concepts in mathematical morphology: the topographical and differential distance functions

Francoise J. Preteux, Nicolas Merlet

Proceedings Volume 1568, Image Algebra and Morphological Image Processing II; (1991) https://doi.org/10.1117/12.49884
Event: San Diego, '91, 1991, San Diego, CA, United States

Abstract

If the concept of Euclidean and geodesic distance is of great importance in binary mathematical morphology (MM), the grey-level MM deals mainly with neighborhood configuration analysis. This paper presents a novel approach to grey-level MM based on the concept of the distance function relative to topographical surfaces. By introducing the notions of connection cost and deviation cost, we define the topographical and differential distances and develop a powerful theoretical framework for establishing the equivalence between the two fundamental notions of skeleton by influence zones and watershed: the SKIZ of the set of the minima of a grey-level image f with respect to the differential distance function is exactly the watershed of f. This leads to a duality between binary and grey-level images as well as new fast algorithms for computing the SKIZ and the watershed.

Citation Download Citation

Francoise J. Preteux and Nicolas Merlet "New concepts in mathematical morphology: the topographical and differential distance functions", Proc. SPIE 1568, Image Algebra and Morphological Image Processing II, (1 July 1991); https://doi.org/10.1117/12.49884

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