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 modeled as a step function. We first derive a one-dimensional 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. 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 likelihood 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 analysis of edge-based shape detection. We investigate how the error is propagated by the shape geometry, by computing the expected shape of the response and deriving some of its statistical properties. Applications to the problem of human facial feature detection are presented. keywords Shape detection, Edge, Facial feature, Contour