The shape of an object is an important characteristic for many vision problems such as segmentation, detection and tracking. Being independent of appearance, it is possible to generalize to a large range of objects from only small amounts of data. However, shapes represented as silhouette images are challenging to model due to complicated likelihood functions leading to intractable posteriors. In this paper we present a generative model of shapes which provides a low dimensional latent encoding which importantly resides on a smooth manifold with respect to the silhouette images. The proposed model propagates uncertainty in a principled manner allowing it to learn from small amounts of data and providing predictions with associated uncertainty. We provide experiments that show how our proposed model provides favorable quantitative results compared with the state-of-the-art while simultaneously providing a representation that resides on a low-dimensional interpretable manifold.
ShapeOdds The recent ShapeOdds work of Elhabian and Whitaker @cite_14 confers state-of-the-art performance and captures many of the desired properties including a generative probabilistic model that propagates uncertainty. The approach taken is quite different to ours as they specify a detailed probabilistic model including a Gaussian Markov Random Field (MRF) with individual Bernoulli random variables for the pixel lattice. In contrast, our model is more flexible, we allow the network to learn the structure from the data directly but ensure that we still maintain uncertainty quantification throughout. We would also argue that the specific form of the low dimensional manifold we generate is desirable with its guaranteed smoothness that makes the latent space readily interpretable. This provides the tradeoff between the two models. We expect the ShapeOdds model to perform very well at generalisation due to the inclusion of the MRF prior. In contrast, our model will be more data dependent in this respect (weaker prior assumptions on the nature of images), however, it provides a generative space that is highly interpretable and easy to work with. We identify that a topic for further work would be to combine our smooth priors with the likelihood model of ShapeOdds.
@cite_14
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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.