Abstract

In this paper we propose the first exact solution to the prob- lem of estimating the 3D room layout from a single image. This problem is typically formulated as inference in a Markov random field, where po- tentials 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 po- tentials 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.