Harmonic Exponential Families on Manifolds

In a range of fields including the geosciences, molecular biology, robotics and computer vision, one encounters problems that involve random variables on manifolds. Currently, there is a lack of flexible probabilistic models on manifolds that are fast and easy to train. We define an extremely flexible class of exponential family distributions on manifolds such as the torus, sphere, and rotation groups, and show that for these distributions the gradient of the log-likelihood can be computed efficiently using a non-commutative generalization of the Fast Fourier Transform (FFT). We discuss applications to Bayesian camera motion estimation (where harmonic exponential families serve as conjugate priors), and modelling of the spatial distribution of earthquakes on the surface of the earth. Our experimental results show that harmonic densities yield a significantly higher likelihood than the best competing method, while being orders of magnitude faster to train.Comment: fixed typ

Motion estimation with object based regularisation

A dynamic programming based matching method for motion estimation, that optimises a Bayesian maximum likelihood function in a 3-D optimisation space, is presented. The Bayesian function consists of a matching cost and an object based 2-D regularisation cost. The method gives results more accurate than block-based matching since the motion boundaries are close to the actual object boundaries

A sparsity-driven approach to multi-camera tracking in visual sensor networks

In this paper, a sparsity-driven approach is presented for multi-camera tracking in visual sensor networks (VSNs). VSNs consist of image sensors, embedded processors and wireless transceivers which are powered by batteries. Since the energy and bandwidth resources are limited, setting up a tracking system in VSNs is a challenging problem. Motivated by the goal of tracking in a bandwidth-constrained environment, we present a sparsity-driven method to compress the features extracted by the camera nodes, which are then transmitted across the network for distributed inference. We have designed special overcomplete dictionaries that match the structure of the features, leading to very parsimonious yet accurate representations. We have tested our method in indoor and outdoor people tracking scenarios. Our experimental results demonstrate how our approach leads to communication savings without significant loss in tracking performance

Local Visual Microphones: Improved Sound Extraction from Silent Video

Sound waves cause small vibrations in nearby objects. A few techniques exist in the literature that can extract sound from video. In this paper we study local vibration patterns at different image locations. We show that different locations in the image vibrate differently. We carefully aggregate local vibrations and produce a sound quality that improves state-of-the-art. We show that local vibrations could have a time delay because sound waves take time to travel through the air. We use this phenomenon to estimate sound direction. We also present a novel algorithm that speeds up sound extraction by two to three orders of magnitude and reaches real-time performance in a 20KHz video.Comment: Accepted to BMVC 201