The 2.1-D sketch

A model is described for image segmentation that tries to capture the low-level depth reconstruction exhibited in early human vision, giving an important role to edge terminations. The problem is to find a decomposition of the domain D of an image that has a minimum of disrupted edges-junctions of edges, crack tips, corners, and cusps-by creating suitable continuations for the disrupted edges behind occluding regions. The result is a decomposition of D into overlapping regions R₁∪. . .∪R_n ordered by occlusion, which is called the 2.1-D sketch. Expressed as a minimization problem, the model gives rise to a family of optimal contours, called nonlinear splines, that minimize length and the square of curvature. These are essential in the construction of the 2.1-D sketch of an image, as the continuations of disrupted edges. An algorithm is described that constructs the 2.1-D sketch of an image, and gives results for several example images. The algorithm yields the same interpretations of optical illusions as the human visual system