A signal can be described quantitatively by its extrema and those of its first few derivatives. However, this description depends not only on the signal but on the scale of measurement. Scale-space filtering has been developed to describe a signal in terms of zero-crossings of its second derivative, without the ambiguity of scale.The straight forward way to construct the scale-space image is to use exhaustive smoothing over a continuum of scales which is expensive. We have developed an adaptive procedure for construction of the scale-space image, which would eliminate the need for exhaustive smoothing. This is achieved by relating the zero-crossings of the smoothed signal at different scales using a similarity measure. This allows the construction of the zero-crossing contours with coarser and fewer levels of smoothing. A binary search method is used to adaptively minimize the number and maximize the spacing of the smoothing levels, and hence reduce the computation time.
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