# Axioms and fundamental equations of image processing

@article{lvarez1993AxiomsAF, title={Axioms and fundamental equations of image processing}, author={Luis {\'A}lvarez and F. Guichard and Pierre-Louis Lions and Jean-Michel Morel}, journal={Archive for Rational Mechanics and Analysis}, year={1993}, volume={123}, pages={199-257} }

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…

## 1,162 Citations

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