Regularization, scale-space, and edge detection filters

  • Mads Nielsen
  • Luc Florack
  • Rachid Deriche
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1065)


Computational vision often needs to deal with derivatives of digital images. Such derivatives are not intrinsic properties of digital data; a paradigm is required to make them well-defined. Normally, a linear filtering is applied. This can be formulated in terms of scale-space, functional minimization, or edge detection filters. The main emphasis of this paper is to connect these theories in order to gain insight in their similarities and differences. We take regularization (or functional minimization) as a starting point, and show that it boils down to Gaussian scale-space if we require scale invariance and a semi-group constraint to be satisfied. This regularization implies the minimization of a functional containing terms up to infinite order of differentiation. If the functional is truncated at second order, the Canny-Deriche filter arises.


Tikhonov Regularization Step Edge Optimal Filter Infinite Order Functional Minimization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Mads Nielsen
    • 1
  • Luc Florack
    • 1
  • Rachid Deriche
    • 2
  1. 1.DIKUCopenhagenDenmark
  2. 2.INRIASophia AntipolisFrance

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