Optimal Scale for Edge Detection

摘要

Many problems in early vision are ill posed. Edge detection is a typical example. This paper applies regularization techniques to the problem of edge detection. The authors derive an optimal filter for edge detection with a size controlled by the regularization parameter lambda and compare it to the Gaussian filter. A formula relating the signal-to-noise ratio to the parameter lambda is derived from regularization analysis for the case of small values of lambda. Also discussed is the method of Generalized Cross Validation for obtaining the optimal filter scale. Finally, the authors use their framework to explain two perceptual phenomena: coarsely quantized images becoming recognizable by either blurring or adding noise. Keywords: Numerical differentiation. (kr)