Abstract
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.
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© 1996 Springer-Verlag Berlin Heidelberg
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Nielsen, M., Florack, L., Deriche, R. (1996). Regularization, scale-space, and edge detection filters. In: Buxton, B., Cipolla, R. (eds) Computer Vision — ECCV '96. ECCV 1996. Lecture Notes in Computer Science, vol 1065. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61123-1_128
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DOI: https://doi.org/10.1007/3-540-61123-1_128
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