Adaptive window size gradient estimation for image edge detection
Abstract: New adaptive varying window size estimation methods for edge detection are presented in this work. The nonparametric Local Polynomial Approximation (<i>LPA</i>) method is used to define gradient estimation kernels or masks, which in conjunction with varying adaptive window size selection, carried out by the Intersection of Confidence Intervals (<i>ICI</i>) for each pixel, let us obtain algorithms which are adaptive to unknown smoothness and nearly optimal in the point-wise risk for estimating the intensity function and its derivatives. Several existing strategies using a constant window size of the convolutional kernel of edge detection have been upgraded to become varying window size techniques, first through the use of <i>LPA </i>for defining the gradient convolutional kernels of different sizes and second through <i>ICI</i> for the selection of the best estimate which balances the bias-variance trade-off in a point wise fashion for the whole stream of data. Comparisons with invariant window size edge detection schemes show the superiority of the presented methods, even over computationally more expensive techniques of edge detection.
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