Stack filters: Design algorithms and applications

Jisang Yoo, Purdue University

Abstract

Both the theory and application of stack filters are considered. The results obtained include new approaches to edge detection, new insights into the properties and proper uses of stack filters, and a new fast algorithm for training stack filters. The first approach to edge detection using stack filters is a generalization of median prefiltering: a stack 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 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. By defining the notion of a statistically symmetric image, an efficient design method called the Symmetric Difference of Estimates (SDoE) approach was proposed. In the SDoE approach, we can design the DoE operator with just one training run, and we can obtain unbiased estimates because of the symmetry constraint on the training data. The dual stack filters obtained under the SDoE approach are shown to be comparable. This property leads to a new scheme we call the Threshold Boolean Filter (TBF) approach. In the TBF approach, a Boolean function which may not be positive is used as a binary edge operator. This approach requires less training time but produces operators which are less robust than those produced by the DoE and SDoE approaches. Finally, to accelerate the training process for the design of stack filters, a new adaptive stack filtering algorithm is developed. The new algorithm retains the iterative nature of the present adaptive algorithms, but significantly reduces the number of iterations required in the training process. Also, due to the parallel nature of the new algorithm, the training process is much accelerated when it is implemented on the MasPar MP-1 parallel computer. The convergence property of the new algorithm is proved and the performance comparisons are made with the present adaptive algorithms.

Degree

Ph.D.

Advisors

Coyle, Purdue University.

Subject Area

Electrical engineering

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