Maximal Scale Ridge
The following definition can be traced to Fritsch who was interested in extracting geometric information about figures in two dimensional greyscale images. Fritsch filtered his image with a "medialness" filter that gave him information analogous to "distant to the boundary" data in scale-space. Ridges of this image, once projected to the original image, were to be analogous to a shape skeleton (e.g., the Blum Medial Axis) of the original image.
What follows is a definition for the maximal scale ridge of a function of three variables, one of which is a "scale" parameter. One thing that we want to be true in this definition is, if is a point on this ridge, then the value of the function at the point is maximal in the scale dimension. Let be a smooth differentiable function on . The is a point on the maximal scale ridge if and only if
- and, and
- and .
Read more about this topic: Ridge Detection
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