Learning Ordinal Relationships for Mid-Level Vision

We propose a framework that infers mid-level visual properties of an image by learning about ordinal relationships. Instead of estimating metric quantities directly, the system proposes pairwise relationship estimates for points in the input image. These sparse probabilistic ordinal measurements are globalized to create a dense output map of continuous metric measurements. Estimating order relationships between pairs of points has several advantages over metric estimation: it solves a simpler problem than metric regression, humans are better at relative judgements, so data collection is easier, ordinal relationships are invariant to monotonic transformations of the data, thereby increasing the robustness of the system and providing qualitatively different information. We demonstrate that this frame-work works well on two important mid-level vision tasks: intrinsic image decomposition and depth from an RGB image. We train two systems with the same architecture on data from these two modalities. We provide an analysis of the resulting models, showing that they learn a number of simple rules to make ordinal decisions. We apply our algorithm to depth estimation, with good results, and intrinsic image decomposition, with state-of-the-art results.