Multiview Depth Parameterisation with Second Order Regularisation

In this paper we consider the problem of estimating depth maps from multiple views within a variational framework. Previous work has demonstrated that multiple views improve the depth reconstruction, and that higher order regularisers model a good prior for typical realworld 3D scenes. We build on these findings and stress an important aspect that has not been considered in variational multiview depth estimation so far: We investigate several parameterisations of the unknown depth. This allows us to show, both analytically and experimentally, that directly work with depth values introduces an undesirable bias. As a remedy, we reveal that an inverse depth parameterisation is generally preferable. Our analysis clearly points out its benefits w.r.t. the data and the smoothness term. We verify these theoretical findings by means of experiments.