ShapeOdds: Variational Bayesian Learning of Generative Shape Models

Shape models provide a compact parameterization of a class of shapes, and have been shown to be important to a variety of vision problems, including object detection, tracking, and image segmentation. Learning generative shape models from grid-structured representations, aka silhouettes, is usually hindered by (1) data likelihoods with intractable marginals and posteriors, (2) high-dimensional shape spaces with limited training samples (and the associated risk of overfitting), and (3) estimation of hyperparameters relating to model complexity that often entails computationally expensive grid searches. In this paper, we propose a Bayesian treatment that relies on direct probabilistic formulation for learning generative shape models in the silhouettes space. We propose a variational approach for learning a latent variable model in which we make use of, and extend, recent works on variational bounds of logistic-Gaussian integrals to circumvent intractable marginals and posteriors. Spatial coherency and sparsity priors are also incorporated to lend stability to the optimization problem by regularizing the solution space while avoiding overfitting in this high-dimensional, low-sample-size scenario. We deploy a type-II maximum likelihood estimate of the model hyperparameters to avoid grid searches. We demonstrate that the proposed model generates realistic samples, generalizes to unseen examples, and is able to handle missing regions and/or background clutter, while comparing favorably with recent, neural-network-based approaches.