Optimal shape detection

We present a new approach for accurate detection of two-dimensional shapes. We first derive an optimal smoothing filter, which minimizes both the noise power and the mean squared error between the input and the filter output. This operator is found to be a 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. We find that this filtering scheme is equivalent to integrating gradients along the hypothetical shape boundary, but our method turns out to be more robust than conventional edge detection followed by edge grouping. This approach also provides a tool for a systematic analysis of edge-based shape detection. We investigate how the error is propagated by the shape geometry. This enables us to predict both its localization and detection performance. Application to vehicle detection in aerial images and human facial feature detection are provided