Estimation of Edge Parameters and Image Blur Using Polynomial Transforms

Abstract

A method is presented for detecting blurred edges in images and for estimating the following edge parameters: position, orientation, amplitude, mean value, and edge slope. The method is based on a local image decomposition technique called a polynomial transform. The information that is made explicit by the polynomial transform is well suited to detect image features, such as edges, and to estimate feature parameters. By using the relationship between the polynomial coefficients of a blurred feature and those of the a priori assumed (unblurred) feature in the scene, the parameters of the blurred feature can be estimated. The performance of the proposed edge parameter estimation method in the presence of image noise has been analyzed. An algorithm is presented for estimating the spread of a position-invariant Gaussian blurring kernel, using estimates at different edge locations over the image. First a single-scale algorithm is developed in which one polynomial transform is used. A critical parameter of the single-scale algorithm is the window size, which has to be chosen a priori. Since the reliability of the estimate for the spread of the blurring kernel depends on the ratio of this spread to the window size, it is difficult to choose a window of appropriate size a priori. The problem is overcome by a multiscale blur estimation algorithm where several polynomial transforms at different scales are applied, and the appropriate scale for analysis is chosen a posteriori. By applying the blur estimation algorithm to natural and synthetic images with different amounts of blur and noise, it is shown that the algorithm gives reliable estimates for the spread of the blurring kernel even at low signal-to-noise ratios.