An edge is a set of connected pixels lying on the boundary between two regions in an image that differs in pixel intensity. Accordingly, several gradient-based edge detectors have been developed that are based on measuring local changes in gray value; a pixel is declared to be an edge pixel if the change is significant. However, the minimum value of intensity change that may be considered to be significant remains a question. Therefore, it makes sense to calculate the edge-strength at every pixel on the basis of the intensity gradient at that pixel point. This edge-strength gives a measure of the potentiality of a pixel to be an edge pixel. In this paper, we propose to use a set of fuzzy rules to estimate the edge-strength. This is followed by selecting a threshold; only pixels having edge-strength above the threshold are considered to be edge pixels. This threshold is selected such that the overall probability of error in identifying edge pixels, that is, the sum of the probability of misdetection and the probability of false alarm, is minimum. This minimization is achieved via particle swarm optimization (PSO). Experimental results demonstrate the effectiveness of our proposed edge detection method over some other standard gradient-based methods. 1. Introduction Edge detection is an essential and important first step in object identification. An edge may be defined as a set of connected pixels lying at the boundary between the foreground and the background. Therefore, edge detection algorithms generally rely on detecting discontinuities within an image. Several gradient-based edge detectors are available in the literature which are based on measuring local changes in gray value; a pixel is declared to be an edge pixel if the change is significant. Accordingly, the underlying principle in most edge detection techniques is to compute the first- or second-order derivative of the intensity function within the image-detectors based on the first derivative looks for points where the derivative value is large while those using the second-order derivative find edges at zero-crossings of the image [1]. Several gradient operators, such as the Roberts, Prewitt, Sobel, and the Laplacian masks, exist which are used to estimate the first- and the second-order derivatives [2]. However, these detectors are generally very sensitive to noise and hence perform poorly in case of noisy images. In [3], Canny proposed a method to counter this noise problem by convolving the image with the first-order derivatives of Gaussian filter prior to edge detection. Some other edge
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