Smoothing images creates corners

摘要

The isophote curvature times the gradient magnitude to some power has been studied in the literature as a measure of cornerness in images. Stability in terms of sampling noise has been proposed by selecting corners at high scale and locating them at fine scale. We will examine the problem of tracking extrema of these measures in the Linear Scale-Space using catastrophe theory. This enables us to explain potential dangers of commonly used corner detectors. We conclude that creations and annihilations generically occur, implying that corners in general cannot be tracked to arbitrary fine (or coarse) scale. Experiments on real-world images confirm the practical relevance of our investigations.