Optimal edgebased shape detection

Abstract—We propose an approach to accurately detecting two-dimensional (2-D) shapes. The cross section of the shape boundary is modeled as a step function. We first derive a one-dimensional (1-D) optimal step edge operator, which minimizes both the noise power and the mean squared error between the input and the filter output. This operator is found to be the derivative of the double exponential (DODE) function, originally derived by Ben-Arie and Rao [5]. We define an operator for shape detection by extending the DODE filter along the shape’s boundary contour. The responses are accumulated at the centroid of the operator to estimate the like-lihood of the presence of the given shape. This method of detecting a shape is in fact a natural extension of the task of edge detection at the pixel level to the problem of global contour detection. This simple filtering scheme also provides a tool for a systematic anal-ysis of edge-based shape detection. We investigate how the error is propagated by the shape geometry. We have found that, under gen-eral assumptions, the operator is locally linear at the peak of the re-sponse. We compute the expected shape of the response and derive some of its statistical properties. This enables us to predict both its localization and detection performance and adjust its parameters according to imaging conditions and given performance specifica-tions. Applications to the problem of vehicle detection in aerial im-ages, human facial feature detection, and contour tracking in video are presented. Index Terms—Boundary detection, contour tracking, edge de-tection, facial feature detection, localization, shape detection, step edge, vehicle detection. I