Scale-invariant contour completion using conditional random fields

We present a model of curvilinear grouping using piece-wise linear representations of contours and a conditional random field to capture continuity and the frequency of different junction types. Potential completions are generated by building a constrained Delaunay triangulation (CDT) over the set of contours found by a local edge detector. Maximum likelihood parameters for the model are learned from human labeled ground truth. Using held out test data, we measure how the model, by incorporating continuity structure, improves boundary detection over the local edge detector. We also compare performance with a baseline local classifier that operates on pairs of edgels. Both algorithms consistently dominate the low-level boundary detector at all thresholds. To our knowledge, this is the first time that curvilinear continuity has been shown quantitatively useful for a large variety of natural images. Better boundary detection has immediate application in the problem of object detection and recognition.