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… Expand
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