The fact that objects in the world appear in different ways depending on the scale of observation has important implications if one aims at describing them. It shows that the notion of scale is of utmost importance when processing unknown measurement data by automatic methods. Whereas scale-space representation provides a well-founded framework for dealing with this issue by representing image structures at different scales, traditional scale-space theory does not address the problem of how to selectlocal appropriate scales for further analysis.

This article proposes a systematic approach for dealing with this problem---a heuristic principle is presented stating that local extrema over scales of different combinations of gamma-normalized derivatives are likely candidates to correspond to interesting structures. Specifically, it is proposed that this idea can be used as a major mechanism in algorithms for automatic scale selection, which adapt the local scales of processing to the local image structure.

Support is given in terms of a general theoretical investigation of the behaviour of the scale selection method under rescalings of the input pattern and by experiments on real-world and synthetic data. Support is also given by a detailed analysis of how different types of feature detectors perform when integrated with a scale selection mechanism and then applied to characteristic model patterns. Specifically, it is described in detail how the proposed methodology applies to the problems of blob detection, junction detection, edge detection, ridge detection and local frequency estimation.