Linear and Nonlinear Generative Probabilistic Class Models for Shape Contours

Abstract

We introduce a robust probabilistic approach to modeling shape contours based on a low- dimensional, nonlinear latent variable model. In contrast to existing techniques that use objective functions in data space without ex- plicit noise models, we are able to extract complex shape variation from noisy data. Most approaches to learning shape models slide observed data points around fixed con- tours and hence, require a correctly labeled ‘reference shape’ to prevent degenerate so- lutions. In our method, unobserved curves are reparameterized to explain the fixed data points, so this problem does not arise. The proposed algorithms are suitable for use with arbitrary basis functions and are applicable to both open and closed shapes; their effec- tiveness is demonstrated through illustrative examples, quantitative assessment on bench- mark data sets and a visualization task.