A survey of the Hough transform
Computer Vision, Graphics, and Image Processing
A Classification EM algorithm for clustering and two stochastic versions
Computational Statistics & Data Analysis - Special issue on optimization techniques in statistics
Interpreting the Kohonen self-organizing feature map using contiguity-constrained clustering
Pattern Recognition Letters
Existence of EMS Solutions and a Priori Estimates
SIAM Journal on Matrix Analysis and Applications
Self-organizing maps
An Unbiased Detector of Curvilinear Structures
IEEE Transactions on Pattern Analysis and Machine Intelligence
A polygonal line algorithm for constructing principal curves
Proceedings of the 1998 conference on Advances in neural information processing systems II
Fast curve estimation using preconditioned generalized Radon transform
IEEE Transactions on Image Processing
Approximate Bayes Factors for Image Segmentation: The Pseudolikelihood Information Criterion (PLIC)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast multiscale clustering and manifold identification
Pattern Recognition
Computational Statistics & Data Analysis
Clustering data with measurement errors
Computational Statistics & Data Analysis
Nonlinear Coordinate Unfolding Via Principal Curve Projections with Application to Nonlinear BSS
Neural Information Processing
Extraction of curvilinear features from noisy point patterns using principal curves
Pattern Recognition Letters
IEEE Transactions on Signal Processing
Community self-organizing map and its application to data extraction
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Locally Defined Principal Curves and Surfaces
The Journal of Machine Learning Research
Hybrid microdata via model-based clustering
PSD'12 Proceedings of the 2012 international conference on Privacy in Statistical Databases
A generative model and a generalized trust region Newton method for noise reduction
Computational Optimization and Applications
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Clustering about principal curves combines parametric modeling of noise with nonparametric modeling of feature shape. This is useful for detecting curvilinear features in spatial point patterns, with or without background noise. Applications include the detection of curvilinear minefields from reconnaissance images, some of the points in which represent false detections, and the detection of seismic faults from earthquake catalogs. Our algorithm for principal curve clustering is in two steps: The first is hierarchical and agglomerative (HPCC) and the second consists of iterative relocation based on the Classification EM algorithm (CEM-PCC). HPCC is used to combine potential feature clusters, while CEM-PCC refines the results and deals with background noise. It is important to have a good starting point for the algorithm: This can be found manually or automatically using, for example, nearest neighbor clutter removal or model-based clustering. We choose the number of features and the amount of smoothing simultaneously, using approximate Bayes factors.