Abstract
In the literature an image scale-space is usually defined as the solution of an initial value problem described by a PDE, such as a linear or nonlinear diffusion equation. Alternatively, scale-spaces can be defined in an axiomatic way starting from a fixed-scale image operator (e.g. a linear convolution or a morphological erosion) and a group of scalings. The goal of this paper is to explain the relation between these two, seemingly very different, approaches.
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Heijmans, H.J.A.M. (2001). Scale-Spaces, PDE’s, and Scale-Invariance. In: Kerckhove, M. (eds) Scale-Space and Morphology in Computer Vision. Scale-Space 2001. Lecture Notes in Computer Science 2106, vol 2106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47778-0_18
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DOI: https://doi.org/10.1007/3-540-47778-0_18
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