Please use this identifier to cite or link to this item: http://hdl.handle.net/10553/52823
Title: Axioms and fundamental equations of image processing
Authors: Alvarez, Luis 
Guichard, Frédéric
Lions, Pierre Louis
Morel, Jean Michel
UNESCO Clasification: 120601 Construcción de algoritmos
120602 Ecuaciones diferenciales
220990 Tratamiento digital. Imágenes
Keywords: Classical Model
Electromagnetism
Scale Invariance
Invariance Property
Scale Space
Issue Date: 1993
Journal: Archive for rational mechanics and analysis (Print) 
Abstract: Image-processing transforms must satisfy a list of formal requirements. We discuss these requirements and classify them into three categories: “architectural requirements” like locality, recursivity and causality in the scale space, “stability requirements” like the comparison principle and “morphological requirements”, which correspond to shape-preserving properties (rotation invariance, scale invariance, etc.). A complete classification is given of all image multiscale transforms satisfying these requirements. This classification yields a characterization of all classical models and includes new ones, which all are partial differential equations. The new models we introduce have more invariance properties than all the previously known models and in particular have a projection invariance essential for shape recognition. Numerical experiments are presented and compared. The same method is applied to the multiscale analysis of movies. By introducing a property of Galilean invariance, we find a single multiscale morphological model for movie analysis.
URI: http://hdl.handle.net/10553/52823
ISSN: 0003-9527
DOI: 10.1007/BF00375127
Source: Archive for Rational Mechanics and Analysis [ISSN 0003-9527], v. 123 (3), p. 199-257
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