Object Detection Using an Optimal Shape Operator

We propose an approach to accurately detecting two dimensional shapes. The cross-section of the shape boundary is mo deled as a step function. We first derive a one-dimensional opt imal step edge operator, which minimizes both the noise power and the mean squared error between the input and the filter output. Th is operator is found to be the derivative of the double exponent ial (DODE) function. 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 operato r to estimate the likelihood of the presence of the given shape. T his method of detecting a shape is in fact a natural extension of t he task of edge detection at the pixel level to the problem of glo ba contour detection. This simple filtering scheme also provid es a tool for a systematic analysis of edge-based shape detectio n. We investigate how the error is propagated by the shape geometr y, by computing the expected shape of the response and deriving so me of its statistical properties. Applications to the problem of human facial feature detection are presented. keywords Shape detection, Edge, Facial feature, Contour