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Generic properties of edges and “corners” on smooth greyvalue surfaces

✍ Scribed by J. H. Rieger

Publisher
Springer-Verlag
Year
1992
Tongue
English
Weight
581 KB
Volume
66
Category
Article
ISSN
0340-1200

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✦ Synopsis

The edge line on a smooth greyvalue surface, defined as locus of maximal slope, is a curve embedded in the negatively curved part of the greyvalue surface. For an open and dense set of greyvalue functions the edge line has transverse double points as its only singular points, meets the parabolic curve tangentially at isolated points, and intersects the zero crossings of the Laplacean of the greyvalue function transversely. Defining a greyvalue corner as a curvature extremum of the edge line one can show that, again for an open and dense set of greyvalue functions, these corners are isolated points in the image corresponding to ordinary curvature extrema of the edge. Detecting such comers in greyvalue images requires differential operators containing partial derivatives of order five, which raises some doubts about the existence of numerically robust algorithms for detecting these features in digital images.

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