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Chapter 6CONCLUSIONSThis dissertation presents an automatic and unsupervised method for segmentingimages which attempts to be quite general and computationally fast. Theautomatic choice of the number of segments based on the BIC P L is an advanceover most other automatic segmentation methods. This procedure is supportedby a theoretical consistency result. Another contribution of this dissertation is thepresentation of a clustering procedure for spatial point processes with nonlinearfeatures.Clustering with open principal curves can be extended by considering otherdistributions for both the background noise and the distribution of feature pointsalong and about the curve. Although the BIC is used with some success for modelselection with principal curve clustering, theoretical results would provide a moresolid basis for its use. The principal curve clustering examples presented are all2-dimensional; the method can be extended to higher dimensions, though biasproblems in fitting the principal curves might increase in higher dimensions. Forinstance, a bias correction step was considered in two dimensions, which involvedsmoothing the residuals from the principal curve fit; however, this requires determinationof which side of the curve the residuals are on, which is not defined inhigher dimensions. Note that this bias problem is due to principal curves in general,and is separate from the clustering method. Another way of characterizingprincipal curves is given by Delicado (1998); his approach generalizes more easilyto higher dimensions.