A blind definition of shape

J. L. Lisani; J. M. Morel; L. Rudin

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 8, page 863-872
  • ISSN: 1292-8119

Abstract

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In this note, we propose a general definition of shape which is both compatible with the one proposed in phenomenology (gestaltism) and with a computer vision implementation. We reverse the usual order in Computer Vision. We do not define “shape recognition" as a task which requires a “model" pattern which is searched 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 ℐ , we call shape of this set any spatial pattern which can be found at several locations of some image, or in several different images of ℐ . (This means that the shapes of a set of images are defined without any a priori assumption or knowledge.) The definition is powerful when it is invariant and we prove that the following invariance requirements can be matched in theory and in practice: local contrast invariance, robustness to blur, noise and sampling, affine deformations. We display experiments with single images and image pairs. In each case, we display the detected shapes. Surprisingly enough, but in accordance with Gestalt theory, the repetition of shapes is so frequent in human environment, that many shapes can even be learned from single images.

How to cite

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Lisani, J. L., Morel, J. M., and Rudin, L.. "A blind definition of shape." ESAIM: Control, Optimisation and Calculus of Variations 8 (2010): 863-872. <http://eudml.org/doc/90674>.

@article{Lisani2010,
abstract = { In this note, we propose a general definition of shape which is both compatible with the one proposed in phenomenology (gestaltism) and with a computer vision implementation. We reverse the usual order in Computer Vision. We do not define “shape recognition" as a task which requires a “model" pattern which is searched 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 any spatial pattern which can be found at several locations of some image, or in several different images of $\cal I$. (This means that the shapes of a set of images are defined without any a priori assumption or knowledge.) The definition is powerful when it is invariant and we prove that the following invariance requirements can be matched in theory and in practice: local contrast invariance, robustness to blur, noise and sampling, affine deformations. We display experiments with single images and image pairs. In each case, we display the detected shapes. Surprisingly enough, but in accordance with Gestalt theory, the repetition of shapes is so frequent in human environment, that many shapes can even be learned from single images. },
author = {Lisani, J. L., Morel, J. M., Rudin, L.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Image analysis; basic shape elements; contrast invariance; level lines; scale space.; image analysis; scale space},
language = {eng},
month = {3},
pages = {863-872},
publisher = {EDP Sciences},
title = {A blind definition of shape},
url = {http://eudml.org/doc/90674},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Lisani, J. L.
AU - Morel, J. M.
AU - Rudin, L.
TI - A blind definition of shape
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 8
SP - 863
EP - 872
AB - In this note, we propose a general definition of shape which is both compatible with the one proposed in phenomenology (gestaltism) and with a computer vision implementation. We reverse the usual order in Computer Vision. We do not define “shape recognition" as a task which requires a “model" pattern which is searched 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 any spatial pattern which can be found at several locations of some image, or in several different images of $\cal I$. (This means that the shapes of a set of images are defined without any a priori assumption or knowledge.) The definition is powerful when it is invariant and we prove that the following invariance requirements can be matched in theory and in practice: local contrast invariance, robustness to blur, noise and sampling, affine deformations. We display experiments with single images and image pairs. In each case, we display the detected shapes. Surprisingly enough, but in accordance with Gestalt theory, the repetition of shapes is so frequent in human environment, that many shapes can even be learned from single images.
LA - eng
KW - Image analysis; basic shape elements; contrast invariance; level lines; scale space.; image analysis; scale space
UR - http://eudml.org/doc/90674
ER -

References

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