On scale selection for differential operators

Although traditional scale-space theory provides a well-founded framework for dealing with image structures at different scales, it does not directly address the problem of how to selectappropriate scales for further analysis. This paper describes a systematic approach for dealing with this problem---a heuristic principle stating that local extrema over scales of different 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 finer scales. Experiments on blob detection, junction detection and edge detection demonstrate that the proposed method gives intuitively reasonable results.QC 20130423