A new class of nonlinear filters called Vector Median Rational Hybrid Filters (VMRHF) for multispectral image processing is introduced and applied to color image filtering problems. These filters are based on Rational Functions (RF). The VMRHF filter is a two-stage filter, which exploits the features of the vector median filter and those of the rational operator. The filter output is a result of vector rational function operating on the output of three sub-functions. Two vector median (VMF) sub-filters and one center weighted vector median filter (CWVMF) are proposed to be used here due to their desirable properties, such as, edge and details preservation and accurate chromaticity estimation. Experimental results show that the new VMRHF outperforms a number of widely known nonlinear filters for multispectral image processing such as the Vector Median ilter (VMF) and Distance Directional Filters (DDf) with respect to all criteria used.

We propose a motion estimation algorithm using less gray level images, which are composed of bits pixels lower than 8 bits pixels. Threshold values for generating low bits pixels from 8 bits pixels are simply determined as median values of pixels in a macro block. The proposed algorithm reduces the computational complexity of motion estimation at less expense of video quality. Moreover, median cut quantization can be applied to multilevel images and combined with a lot of fast algorithms to obtain more effective algorithms.

In this paper, quasi-Gaussian filter, quasi-median filter and locally adaptive filters are introduced. A new adaptive vector filter based on noise estimate is proposed to suppress Gaussian and/or impulse noise. To estimate the type and degree of noise corruption, a noise detector and an edge detector are introduced, and two key parameters are obtained to characterize noise in color image. After globally estimating the type and degree of noise corruption, different locally adaptive filters are properly chosen for image enhancement. All noisy images, used to test filters in experiments, are generated by PaintShopPro and Photoshop software. Experimental results show that the new adaptive filter performs better in suppressing noise and preserving details than the filter in Photoshop software and other filters.

We propose a robust detection scheme by employing an order statistic filter as a preprocessor of the input signal. For ease of design, the variance of the order statistic filtered output is modeled by proposing an approximate upper bound. The detector is analytically designed using a fixed sample size (FSS) test scheme. The performance of the proposed detector is compared to that of other robust detectors in terms of the sample size required for given false alarm and miss detection probabilities. Finally, analytical results are verified by computer simulation.

An analog circuit is devised which selects and outputs the kth largest element among n input voltages. The circuit is composed of n basic transconductance amplifiers connected mutually with an O(n) length wire, thus the complexity of the circuit is O(n). The circuit becomes particularly simple for the case of the selection of the median of inputs.

A two-cascaded image processing approach to enhance the subtle differences in X-ray CT image is proposed. In the method, an asymmetrical non-linear subfilter is introduced to reduce the noise inherent in the image while preserving local edges and directional structural information. Then, a subfilter is used to compress the global dynamic range of the image and emphasize the details in the homogeneous regions by performing a modular transformation on local image den-sities. The modular transformation is based on a dynamically defined contrast fator and the histogram distributions of the image. The local contrast factor is described in accordance with Weber's fraction by a two-layer neighborhood system where the relative variances of the medians for eight directions are computed. This method is suitable for low contrast images with wide dynamic ranges. Experiments on X-ray CT images of the head show the validity of the method.

An algorithm is presented for selecting the k-th smallest element of a totally ordered (but not sorted) set of n elements, 1kn, in the case that a special-purpose sorter is used as a coprocessor. When the pipeline merge sorter is used as the special-purpose sorter, we analyze the comparison complexity of the algorithm for the given capacity of the sorter. The comparison complexity of the algorithm is 1.4167no(n), provided that the capacity of the sorter is 256 elements. The comparison complexity of the algorithm decreases as the capacity of the sorter increases.

The purpose of our research is to get further improvement in the performance of order statistic filters. The basic idea found in our research is the use of a robust median estimator to obtain median differential order information which the classes of order statistic filter required in order to sort the input signal in the filter window. In order to give the motivation for using a median estimator in the classes of order statistic filters, we derive theorems characterizing the median filters and prove them theoretically using the characteristic that the order statistic filter has the performance for a monotonic signal equivalent with the FIR linear filter. As an application of median operation, we propose and investigate the Median Differential Order Statistic Filter to reduce impulsive noise as well as Gaussian noise and regard it as a subclass of the Order Statistic Filter. Moreover, we introduce the piecewise linear function in the Median Differential Order Statistic Filter to improve performance in terms of edge preservation. We call it the Piecewise Linear Median Differential Order Statistic Filter. The effectiveness of proposed filters is verified theoretically by computing the output Mean Square Error of the filters in parts of edge signals, impulsive noise, small amplitude noise and their combination. Computer simulations also show that the proposed filter can improve the performance in both noise (small-amplitude Gaussian noise and impulsive noise) reduction and edge preservation for one-dimensional signals.