Optimizing Edge Detectors for Robust Automatic Threshold Selection: Coping with Edge Curvature and Noise

Abstract

The Robust Automatic Threshold Selection algorithm was introduced as a threshold selection based on a simple image statistic. The statistic is an average of the grey levels of the pixels in an image weighted by the response at each pixel of a specific edge detector. Other authors have suggested that many edge detectors may be used within the context of this method instead. A simple proof of this is given, including an extension to any number of image dimensions, and it is shown that in noiseless images with straight line edges these statistics all yield an optimum threshold. Biases caused by curvature of edges and by noise (uniform Gaussian and Poisson) are explored theoretically and on synthetic 2-D images. It is shown that curvature bias may be avoided by proper selection of the edge detector, and a comparison of two noise bias reduction schemes is given. Criteria for optimizing edge detectors are given and the performances of eight edge detectors are investigated in detail. The best results were obtained using two edge detectors which compute an approximation of the square of the gradient. It is shown that this conclusion can be extended to 3-D. Least sensitivity to noise was obtained when using 3 × 3 Sobel filter kernels to approximate partial derivatives inxandy.