Extraction of curvilinear features from noisy point patterns using principal curves

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.