# Gaussian Process Deep Belief Networks: A Smooth Generative Model of Shape with Uncertainty Propagation

## TL;DR

This paper introduces a generative shape model using Gaussian Process Deep Belief Networks that captures shape variations on a smooth manifold, enabling uncertainty propagation and effective learning from limited data.

## Contribution

The paper presents a novel shape modeling approach that combines Gaussian Processes with Deep Belief Networks to produce a low-dimensional, smooth, and interpretable shape manifold with uncertainty estimation.

## Key findings

- Outperforms state-of-the-art in shape modeling tasks
- Provides low-dimensional, interpretable shape representations
- Effectively propagates uncertainty in shape predictions

## Abstract

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.