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30transform type of approach. The examples in (Steger, 1998) show that the curvesfit the data quite well, but it is still up to the user to interactively choose thesensitivity parameter. The method does not include a formal way to choose thenumber of features.Spatial point process data arise in visual defect metrology, and the Hough transformhas been used previously to detect linear features in these data (Cunninghamand MacKinnon, 1998). In this application of the Hough transform, several parametersand thresholds must be specified in advance by the user. Although usersexperienced with this technique may well be able to find reasonable values for allof the needed parameters, it seems more satisfactory to estimate parameters fromthe data. Principal curve clustering allows automatic detection of both linear andnonlinear features without the need for ad hoc parameter specification.The Kohonen self-organizing feature map (SOFM) is another data-drivenapproach to feature detection (Kohonen, 1982; Ambroise and Govaert, 1996;Murtagh, 1995). Neither principal curve clustering nor the SOFM approach requiresprior specification of feature shape, and both algorithms are hierarchical innature. Like principal curves, the SOFM can be combined with further clusteringmethods to produce a more powerful clustering algorithm (Murtagh, 1995). However,unlike our method, the SOFM approach does not provide an explicit estimateof feature shape.Tibshirani (1992) proposes an alternate definition of principal curves based onmixture models and a new algorithm for fitting principal curves based on the EMalgorithm. It is argued that this definition avoids the bias problems inherent in theapproach of Hastie and Stuetzle (1989), and an example is presented showing thatthese principal curves can be different in practice from curves of the Hastie andStuetzle type. It would be of interest to see what effect this alternate definitionwould have on our results.