No Grouping Left Behind: From Edges to Curve Fragments

We present a framework for extracting image contours based on geometric and structural consistency among edge element locations and orientations. The paper presents two contributions. First, we observe that while the traditional edge orientation operators are based on first-order derivatives, orientation as tangent of a localized curve requires third-order derivatives. We derive a numerically stable third-order edge operator and show that it outperforms current techniques. Second, we consider all discrete n-tuples of edges in a local neighborhood (7times7) and retain those that are geometrically consistent with a third-order local curve model. This results in a number of ordered discrete combinations of edges, each represented by a bundle of curves. The resulting curve bundle map is a representation of all possible local groupings from which longer contour fragments are constructed. We validate our results and show that our framework outperforms traditional approaches to contour extraction.