Edge Detection and Surface Reconstruction Using Refined Regularization
IEEE Transactions on Pattern Analysis and Machine Intelligence
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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. We 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 $\lambda$. We also discuss the method of Generalized Cross Validation for obtaining the optimal filter scale. Finally, we use our framework to explain two perceptual phenomena: coarsely quantized images becoming recognizable by either blurring or adding noise.