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Automatic scale selection

Although the scale-space theory presented so far provides a well-founded framework for representing and detecting image structures at multiple scales, it does not address the problem of how to select locally appropriate scales for further analysis. Whereas the problem of finding ``the best scales'' for handling a given real-world data set may be regarded as intractable unless further information is available, there are many situations in which a mechanism is required for generating hypotheses about interesting scales. A general methodology for feature detection with automatic scale selection has been proposed in [, ]. The approach is based on the evolution over scales of (possibly non-linear) combinations of normalized derivatives defined by
 
where is a free parameter to be tuned to the task at hand. The basic idea proposed in the abovementioned sources is to apply the feature detector at all scales, and then select scale levels from the scales at which normalized measures of feature strength assume local maxima with respect to scale. Intuitively, this approach corresponds to the selection of the scales at which the operator response is as strongest. Moreover, it can be shown that the specific form of derivative normalization in (19) spans a large class of normalization approaches for which the scale selection mechanism has a desirable behaviour under size variations of the input pattern.

 
Table 1: Measures of feature strength used for feature detection with automatic scale selection.

Figures 6-15 show a few examples of integrating this scale selection mechanism with the differential geometric feature detectors considered in section 4. Here, the extracted features have been illustrated graphically in two ways; (i) as two-dimensional spatial projections onto the image plane, and (ii) as three-dimensional entities in scale-space, with the height over the image plane representing the selected scales.

 
• Edge detection.
• Ridge detection.
• Corner detection.
• Blob detection.