Linear and Nonlinear Generative Probabilistic Class Models for Shape Contours

摘要

We introduce a robust probabilistic approachudto modeling shape contours based on a low-uddimensional, nonlinear latent variable model.udIn contrast to existing techniques that useudobjective functions in data space without ex-udplicit noise models, we are able to extractudcomplex shape variation from noisy data.udMost approaches to learning shape modelsudslide observed data points around fixed con-udtours and hence, require a correctly labeledud‘reference shape’ to prevent degenerate so-udlutions. In our method, unobserved curvesudare reparameterized to explain the fixed dataudpoints, so this problem does not arise. Theudproposed algorithms are suitable for use withudarbitrary basis functions and are applicableudto both open and closed shapes; their effec-udtiveness is demonstrated through illustrativeudexamples, quantitative assessment on bench-udmark data sets and a visualization task.