Optimal algorithm for detecting two-dimensional images

In this paper, we present a new two-dimensional (2D) edge detection algorithm. The algorithm detects edges in 2D images by a curve segment based edge detection functional that uses the zero crossing contours of the Laplacian of Gaussian (LOG) as initial conditions to approach the true edge locations. We prove that the proposed edge detection functional is optimal in terms of signal-to-noise ratio and edge localization accuracy for detecting general 2D edges. In addition, the detected edge candidates preserve the nice scaling behavior that is held uniquely by the LOG zero crossing contours in scale space. The algorithm also provides: (1) an edge regularization procedure that enhances the continuity and smoothness of the detected edges; (2) an adaptive edge thresholding procedure that is based on a robust global noise estimation approach and two physiologically originated criteria to help generate edge detection results similar to those perceived by human visual systems; and (3) a scale space combination procedure that reliably combines edge candidates detected from different scales.