Fast Edge Integration

Abstract

A two-dimensional variational explanation for the Marr-Hildreth and the Haralick-Canny like edge detectors was recentckly presented in [280, 281]. For example, the zero crossings of the image Laplacian were shown to be optimal edge integration curves that solve a geometric problem. These are the curves whose normals best align with the image gradient field. Based on these observations, an improved active contour model was suggested, and its performances were shown to be better than classical geodesic active contours when directional information about the edge location is provided. We present a general model that incorporates the alignment as part of other driving forces of an active contour, together with the geodesic active contour model for regularization, and the minimal variance criterion suggested by Chan and Vese [100]. The minimal variance functional is related to segmentation by a threshold and to the Max-Lloyd quantization procedure. Here, we integrate all these geometric measures as part of one unified framework. Finally, we introduce unconditionally stable and simple numerical schemes for efficiently implementing the improved geometric active contour edge integration procedure.