Local features of smooth shapes: ridges and courses

Jan J. Koenderink; Andrea J. van Doorn

doi:10.1117/12.146617

23 June 1993 Local features of smooth shapes: ridges and courses

Jan J. Koenderink, Andrea J. van Doorn

Proceedings Volume 2031, Geometric Methods in Computer Vision II; (1993) https://doi.org/10.1117/12.146617
Event: SPIE's 1993 International Symposium on Optics, Imaging, and Instrumentation, 1993, San Diego, CA, United States

Abstract

If one direction of (three-dimensional) space is singled out, it makes sense to formulate the description of embedded curves and surfaces in a frame that is adapted both to the embedded manifold and to the special direction, rather than a frame based upon the curvature landscape. Such a case occurs often in computer vision, where the image plane plays a role that differs essentially from the direction of view. The classical case is that of geomorphology, where the vertical is the singled out dimension. In computer vision the `ridges' and `(water-)courses' are recognized as important entities and attempts have been made to make the intuitive notions precise. These attempts repeat the unfortunate misunderstandings that marked the course of the late 19th century struggle to define the `Talweg' (equals `valley path' or `(water-)course'). We elucidate the problems and their solution via novel examples.

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Jan J. Koenderink and Andrea J. van Doorn "Local features of smooth shapes: ridges and courses", Proc. SPIE 2031, Geometric Methods in Computer Vision II, (23 June 1993); https://doi.org/10.1117/12.146617

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