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Ridge detection.

A ridge detector can be expressed in a conceptually similar way as follows: Introduce at any image point a local (p, q)-system aligned to the principal curvature directions such that the mixed second-order derivative is zero, i.e., tex2html_wrap_inline975. Then, we can define a bright (dark) ridge point as a point for which the intensity assumes a local maximum in the main principal curvature direction. In terms of the (p, q)-coordinates, this definition can be written
depending on whether the p- or the q-direction corresponds to the maximum absolute value of the principal curvatures. At points where the gradient does not vanish, this condition can equivalently be expressed as follows in the (u, v)-system and in terms of Cartesian partial derivatives
Figure 5(b) shows the result of applying this ridge detector to an image of an arm. As can be seen, the types of ridge curves that are obtained are strongly strongly scale dependent. At very fine scales, the ridge detector responds mainly to noise and spurious fine-scale textures. Then, the fingers give rise to ridge curves at scale level t = 16.0, and the arm as a whole is extracted as a long ridge curve at t = 256.0. Notably, these ridge descriptors are much more sensitive to the choice of scale levels than the edge features in figure 5(a). In particular, no single scale level is appropriate for describing the dominant ridge structures in this image.

Tony Lindeberg
Tue Jul 1 14:57:47 MET DST 1997