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Line finding is a very basic and important step in the low level vision process. Lines are important because they represent the border between two regions and thus help to define and distinguish the region. Lines may also represent physical objects in themselves (at low resolution a tank barrel looks like a ridge line). In the past, ad hoc approaches to line finding have been most prevalent. Recently, Canny has taken a more rigorous approach to edge detection. He has developed an optimal edgel (i.e., individual edge pixel) detector. This detector is optimal under the assumption of additive Gaussian noise and with the constraint that multiple responses from the same edge should be minimized. For a step edge in white Gaussian noise this operator can be closely approximated by convolving the image with a Gaussian mask and then calculating the gradient. A non-maximal suppression operation (in the direction of the gradient at each pixel) is applied to the image. The resulting image is then thresholded. The width of the smoothing Gaussian and the threshold are determined by performance constraints: probability of detection; probability of false alarm; and localization error of the edge. If one accepts the edge model and performance criteria given by Canny, this operator is optimal for detecting and estimating the amplitude and direction of individual edgels (i.e., it is optimal for detecting the 1D edge profile). Unfortunately, Canny's method of grouping individual edgels into lines is not optimal and is in fact quite ad hoc. We have taken a more rigorous approach to extending the Canny 1D edgel detector into a optimal 2D edge detector. Our method applies optimal detection and estimation techniques to the 2D problem. Optimality is determined with respect to the universally most powerful (UNIP) 2 detector for 2D edge. We have been able to develop the optimal detector for a number of edge models. A detector for a constant but unknown amplitude, straight edge model has been implemented. In the implementation we closely approximate the UNIP detector. This paper describes our approach to the problem.
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