# 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

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topLisani, 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 -

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