A pattern recognition approach to the detection of complex edges

Abstract We treat edge detection as a supervised pattern recognition problem, in which the edge is modeled as a linear combination of basis functions. We show both theoretically and analytically that our selection of Constant, Step and Gaussian as the basis functions is optimal in the sense of mininizing the RMS fitting error. The parameters of these basis functions are learned during the training phase, and the recognition phase uses these learned parameters to locate pixels that belong to edges. This modeling of edges is suitable to edges found in radiographs, which are more complex than step functions. Since edges may appear in any direction, we first show how to determine the gradient direction of the edge. We present the basis functions selected for modeling edges in bone radiographs and show both theoretically and experimentally that they are optimal in the sense that they are the most suitable combination for approximating the bone edge when compared to polynomials with more parameters. We then compute the relevant coefficients and parameters to be used for discriminating between edge and non-edge pixels.