Dense versus Sparse Approaches for Estimating the Fundamental Matrix

There are two main strategies for solving correspondence problems in computer vision: sparse local feature based approaches and dense global energy based methods. While sparse feature based methods are often used for estimating the fundamental matrix by matching a small set of sophistically optimised interest points, dense energy based methods mark the state of the art in optical flow computation. The goal of our paper is to show that this separation into different application domains is unnecessary and can be bridged in a natural way. As a first contribution we present a new application of dense optical flow for estimating the fundamental matrix. Comparing our results with those obtained by feature based techniques we identify cases in which dense methods have advantages over sparse approaches. Motivated by these promising results we propose, as a second contribution, a new variational model that recovers the fundamental matrix and the optical flow simultaneously as the minimisers of a single energy functional. In experiments we show that our coupled approach is able to further improve the estimates of both the fundamental matrix and the optical flow. Our results prove that dense variational methods can be a serious alternative even in classical application domains of sparse feature based approaches.