Efficient Exact Inference for 3D Indoor Scene Understanding

Abstract

In this paper we propose the first exact solution to the problem of estimating the 3D room layout from a single image. This problem is typically formulated as inference in a Markov random field, where potentials count image features ( e . g ., geometric context, orientation maps, lines in accordance with vanishing points) in each face of the layout. We present a novel branch and bound approach which splits the label space in terms of candidate sets of 3D layouts, and efficiently bounds the potentials in these sets by restricting the contribution of each individual face. We employ integral geometry in order to evaluate these bounds in constant time, and as a consequence, we not only obtain the exact solution, but also in less time than approximate inference tools such as message-passing. We demonstrate the effectiveness of our approach in two benchmarks and show that our bounds are tight, and only a few evaluations are necessary.