Segmentation in Scale Space

Rolf D. Henkel

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Global Analysis as Clustering Process.

Ignoring the spatial coordinates of the feature data, we are left with a set of feature values f approximating a global probability distribution P(f). Analysis of P(f) can be done via a variety of cluster algorithms. These algorithms search prominent clusters in the data set and compute some prototypical representation tex2html_wrap_inline337 for each cluster. In a second processing step, all data is grouped into one of the found clusters by associating each f(x) to the nearest prototype tex2html_wrap_inline337 .

Since in image analysis tasks the available data base for building the prototypical feature vectors tex2html_wrap_inline337 is large, the central limit theorem assures stable performance of these types of algorithms. The intrinsic properties of the physical world -- which created the data in first place -- assure normally connectedness of the detected segments in input space (despite the fact that the spatial information was not used in the grouping operation). However, strong noise will cause algorithms based on global analysis to fail (figure 1.b). If the distributions of feature values corresponding to different objects overlap, detected regions will have many holes or they may even consist of several disconnected patches. In addition, regions far apart from each other, but possessing approximately equal feature values, will be grouped into a single object. Both types of errors can be attributed to the neglect of spatial information in a global analysis.

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