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A blind definition of shape

Published online by Cambridge University Press:  15 August 2002

J. L. Lisani ,
J. M. Morel  and
L. Rudin
J. L. Lisani
Affiliation:
Univ. de les Illes Balears, Cra. de Valldemossa, km 7.5, 07071 Palma, Spain; vdmijlr0@clust.uib.es.
J. M. Morel
Affiliation:
CMLA, ENS Cachan, 61 avenue du Président Wilson, 94235 Cachan, France; morel@cmla.ens-cachan.fr.
L. Rudin
Affiliation:
Cognitech Inc., 225 S. Lake Avenue, CA-91101 Pasadena, U.S.A.; lenny@cognitech.com.
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Abstract

In this note, we propose a general definition of shape which isboth compatible with the one proposed in phenomenology(gestaltism) and with a computer vision implementation. We reversethe usual order in Computer Vision. We do not define “shaperecognition" as a task which requires a “model" pattern which issearched in all images of a certain kind. We give instead a“blind" definition of shapes relying only on invariance and repetition arguments.Given a set of images $\cal I$ , we call shape of this set anyspatial pattern which can be found at several locations of someimage, or in several different images of $\cal I$ . (This meansthat the shapes of a set of images are defined without any a priori assumption or knowledge.) The definition is powerful whenit is invariant and we prove that the following invariancerequirements can be matched in theory and in practice: localcontrast invariance, robustness to blur, noise and sampling,affine deformations. We display experiments with single images and image pairs. In eachcase,we display the detected shapes. Surprisingly enough, but in accordancewith Gestalt theory,the repetition of shapes is so frequent in human environment, that manyshapes can even be learnedfrom single images.

Keywords

Image analysisbasic shape elementscontrast invariancelevel linesscale space.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 8: A tribute to JL Lions , 2002 , pp. 863 - 872
Copyright
© EDP Sciences, SMAI, 2002

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