Edges in an image arise from discontinuities in scene variables, namely reflectance (R), illumination (I), depth (D) and surface orientation (O). Prior studies on edge classification have viewed it as a binary classification problem: each edge is assumed to arise from one of two disjoint categories (e.g., depth or not depth, shadow or not shadow). Here we suggest an alternate view in which an edge may signal discontinuities in any combination of the scene variables (RIDO). To explore this model, we had 4 trained observers label one randomly selected edge in each of 1,000 randomly selected images drawn from the McGill Calibrated Colour Image Database and from Flickr; the averaged data provide an estimate of the joint distribution over the 4 binary variables RIDO.
To model the distribution, we consider an exhaustive set of 42 undirected and 72 directed graphical models of low-order (parameters). The models first link the RI variables, capturing the constraint but also the fact that the two variables change together less often than would be predicted by independence – it’s usually one or the other. The IO variables are then linked, which captures the fact that illumination is more likely to be changing if surface orientation is changing. More subtle relations are most efficiently captured by directed models. For example, conditioning R on D captures the increased likelihood of reflectance change at occlusion boundaries.

]]>