Topographic Maps and Local Contrast Changes in Natural Images

Authors:
Vicent Caselles;Bartomeu Coll;Jean-Michel Morel
Affiliations:
Department of Mathematics and Informatics, University of Illes Balears, 07071 Palma de Mallorca, Spain. dmivca0@ps.uib.es;Department of Mathematics and Informatics, University of Illes Balears, 07071 Palma de Mallorca, Spain. dmitcv0@ps.uib.es;CMLA, ENS. Cachan, 61 Av. du Président Wilson, Cachan, France. Jean-Michel.Morel@cmla.ens-cachan.fr
Venue:
International Journal of Computer Vision
Year:
1999

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Abstract

We call “natural” image any photograph of an outdoor orindoor scene taken by a standard camera. We discuss the physicalgeneration process of natural images as a combination ofocclusions, transparencies and contrast changes.This description fits to the phenomenological description ofGaetano Kanizsa according to which visualperception tends to remain stable withrespect to these basic operations. We define a contrastinvariant presentation ofthe digital image, the topographic map, where thesubjacent occlusion-transparency structureis put into evidence by theinterplay of level lines.We prove that each topographic map represents a classof images invariant with respect to local contrast changes.Several visualizationstrategies of the topographic map areproposed and implemented andmathematical arguments aredeveloped to establishstability properties of the topographic mapunder digitization.