The Nonlinear Prefiltering and Difference of Estimates Approaches to Edge Detection: Applications of Stack Filters

The theory of stack filtering, which is a generalization of median filtering, is used in two different approaches to the detection of intensity edges in noisy images. The first approach is a generalization of median prefiltering: a stack filter or another median-type filter is used to smooth an image before a standard gradient estimator is applied. These prefiltering schemes retain the robustness of the median prefilter, but allow resolution of finer detail. The second approach, called the Difference of Estimates (DoE) approach, is a new formulation of a morphological scheme [Lee et al., IEEE Trans. Robotics Automat. RA-3, Apr. 1987, 142-156, Maragos and Ziff, IEEE Trans. Pattern Anal. Mach. Intell. 12(5), May 1990.] which has proven to be very sensitive to impulsive noise. In this approach, stack filters are applied to a noisy image to obtain local estimates of the dilated and eroded versions of the noise-free image. Thresholding the difference between these two estimates yields the edge map. We find, for example, that this approach yields results comparable to those obtained with the Canny operator for images with additive Gaussian noise, but works much better when the noise is impulsive. In both approaches, the stack filters employed are trained to be optimal on images and noise that are "typical" examples of the target image. The robustness of stack filters leads to good performance for the target image, even when the statistics of the noise and/or image vary from those used in training. This is verified with extensive simulations.