GTM: the generative topographic mapping
Neural Computation
Learning and Design of Principal Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
Finding Curvilinear Features in Spatial Point Patterns: Principal Curve Clustering with Noise
IEEE Transactions on Pattern Analysis and Machine Intelligence
Piecewise Linear Skeletonization Using Principal Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
Stochastic Complexity in Statistical Inquiry Theory
Stochastic Complexity in Statistical Inquiry Theory
A k-segments algorithm for finding principal curves
Pattern Recognition Letters
A robust algorithm for image principal curve detection
Pattern Recognition Letters
Automatic parameter selection for a k-segments algorithm for computing principal curves
Pattern Recognition Letters
Contour-based shape representation using principal curves
Pattern Recognition
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A frequently encountered task in many recognition problems is the detection of multiple curvilinear features hidden in noisy spatial point patterns. This paper investigates the use of principal curves to fulfill this task. First a stochastic model is adopted for modeling the real curvilinear features, the background noise, and the relationships amongst them. In particular the real features are modeled by principal curves. Then the minimum description length principle is applied to determine simultaneously the number and the smoothness of such principal curves that are required to represent the real features. This is achieved via the use of autoregressive representation for principal curves. Practical performance of the proposed approach is demonstrated via numerical experiments.