Scale-space for N-D discrete signals
Imagine a two-dimensional image function consisting of two hills, one of them somewhat higher than the other one (see figure 4.1). Assume that they are smooth, wide, rather bell-shaped surfaces situated some distance apart, clearly separated by a deep valley running between them. Connect the two tops by a narrow sloping ridge without any local extrema, so that the top point of the lower hill no longer is a local maximum. Let this configuration be the input image. When the operator corresponding to the diffusion equation is applied to the geometry, the ridge will erode much faster than the hills. After a while it has eroded so much that the lower hill appears as a local maximum again. Thus, a new local extremum has been created.
KeywordsDiffusion Equation Local Extremum Coarse Scale Discrete Signal Local Minimum Point
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