A New Distance Measure for Probabilistic Shape Modeling

The contour of a planar shape is essentially one-dimensional signal embedded in 2-D space; thus the orthogonal distance, which only considers 1-D (norm) deviation from suggested models, is not rich enough to characterize the description quality of arbitrary model/shape pairs. This paper suggests a generalized distance measure, called Transport Distance, for probabilistic shape modeling. B-Spline primitives are used to represent models. The probability of a hypothetical model for a shape is determined on the basis of the new distance measure. Experiments show that an optimization procedure, which maximize the model probability, generates robust and visually pleasing geometric models for data.