On Scale Selection for Di erential Operators

Although traditional scale-space theory provides a well-founded framework for dealing with image structures at di erent scales, it does not directly address the problem of how to select appropriate scales for further analysis. This paper introduces a new tool for dealing with this problem. A heuristic principle is proposed stating that local extrema over scales of di erent combinations of normalized scale invariant derivatives are likely candidates to correspond to interesting structures. Support is given by theoretical considerations and experiments on real and synthetic data. The resulting methodology lends itself naturally to two-stage algorithms; feature detection at coarse scales followed by feature localization at ner scales. Experiments on blob detection, junction detection and edge detection demonstrate that the proposed method gives intuitively reasonable results.