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Formalization and computational aspects of image analysis

Published online by Cambridge University Press:  07 November 2008

Luis Alvarez  and
Jean Michel Morel
Luis Alvarez
Affiliation:
Departamento de Informatica y Sistemas, Universidad de Las Palmas, Campus de Tafira, 35017 Las Palmas, Spain
Jean Michel Morel
Affiliation:
C.E.R.E.M.A.D.E.Université Paris IX Dauphine, 75775 Paris cedex 16, France
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Abstract

In this article we shall present a unified and axiomatized view of several theories and algorithms of image multiscale analysis (and low level vision) which have been developed in the past twenty years. We shall show that under reasonable invariance and assumptions, all image (and shape) analyses can be reduced to a single partial differential equation. In the same way, movie analysis leads to a single parabolic differential equation. We discuss some applications to image segmentation and movie restoration. The experiments show how accurate and invariant the numerical schemes must be and we compare several (old and new) algorithms by discussing how well they match the axiomatic invariance requirements.

Type
Research Article
Information
Acta Numerica , Volume 3 , January 1994 , pp. 1 - 59
Copyright
Copyright © Cambridge University Press 1994

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