A Belief-Theoretical Approach to Example-Based Pose Estimation

Abstract

In example-based human pose estimation, the configuration of an evolving object is sought given visual evidence, having to rely uniquely on a set of sample images. We assume here that, at each time instant of a training session, a number of feature measurements is extracted from the available images, while ground truth is provided in the form of the true object pose. In this scenario, a sensible approach consists in learning maps from features to poses, using the information provided by the training set. In particular, multi-valued mappings linking feature values to set of training poses can be constructed. To this purpose we propose a Belief Modeling Regression (BMR) approach in which a probability measure on any individual feature space maps to a convex set of probabilities on the set of training poses, in a form of a belief function. Given a test image, its feature measurements translate into a collection of belief functions on the set of training poses which, when combined, yield there an entire family of probability distributions. From the latter either a single central pose estimate or a set of extremal ones can be computed, together with a measure of how reliable the estimate is. Contrarily to other competing models, in BMR the sparsity of the training samples can be taken into account to model the level of uncertainty associated with these estimates. We illustrate BMR's performance in an application to human pose recovery, showing how it outperforms our implementation of both Relevant Vector Machine and Gaussian Process Regression. Finally, we discuss motivation and advantages of the proposed approach with respect to its most direct competitors.

An agenda for the future

“…As we argued in [50], geometry may be a unifying language, not only for random set and evidential theory, but for uncertainty measures more generally [49,60,61,62,65,95,99,10,120,104,194], possibly in conjunction with an algebraic perspective [58,26,35,64,30,32,46].…”

The intersection probability: betting with probability intervals

“…Geometry has been proposed by this author and others as a unifying language for the field [42,53,54,55,58,76,77,5,85,78,116], possibly in conjunction with an algebraic view [51,12,23,57,16,18,38].…”

Visions of a generalized probability theory

“…Scope of the Chapter. In this Chapter we describe a Belief Modeling Regression (BMR) [560,629] framework for example-based pose estimation based on the theory of evidence. Our framework uses the finite amount of evidence provided in a training session to build, given a new feature value, a belief function on the set of training poses.…”