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This paper presents a new concept of removing impulse noise through primary implicant elimination (PIE) applied to a logical system representation of the data. Applicable to binary and grayscale images, errors are corrected efficiently, in terms of the number of computations and memory requirements, while the fine details of the image are mostly preserved. Three filtering algorithms are presented: a general form in addition to iterative and switching variations. Experimental results on salt-and-pepper impulse noise, as well as on random-valued impulse noise, are compared against the performance of traditional median-based filters (both regular and switching) and are shown to be most successful in the often difficult case of when the original image contains many detailed patterns. Index Terms--Logical transform, median filter, random-valued impulse noise, salt-and-pepper impulse noise, switching filter.

Varying scene illumination poses many challenging problems for machine vision systems. One such issue is developing global enhancement methods that work effectively across the varying illumination. In this paper, we introduce two novel image enhancement algorithms: edge-preserving contrast enhancement, which is able to better preserve edge details while enhancing contrast in images with varying illumination, and a novel multi-histogram equalization method which utilizes the human visual system (HVS) to segment the image, allowing a fast and efficient correction of nonuniform illumination. We then extend this HVS-based multihistogram equalization approach to create a general enhancement method that can utilize any combination of enhancement algorithms for an improved performance. Additionally, we propose new quantitative measures of image enhancement, called the logarithmic Michelson contrast measure (AME) and the logarithmic AME by entropy. Many image enhancement methods require selection of operating parameters, which are typically chosen using subjective methods, but these new measures allow for automated selection. We present experimental results for these methods and make a comparison against other leading algorithms. Index Terms--Enhancement measure, human visual system (HVS), image enhancement, logarithmic image processing.

Three methods of image enhancement, based on the properties of the logarithmic transform domain histogram and histogram equalization are proposed. A human visual system-based quantitative measurement of image contrast improvement has helped in choosing the best parameters and transform for each enhancement.

Tensor algorithms for calculating the two-dimensional (2-D) discrete cosine transform (DCT) are examined. The approach used is based on the concept of partitions revealing transforms that leads the tensor representation of the 2-D DCT and effective tensor algorithms for computing the 2-D DCT with arbitrary orders.

Split manageable efficient algorithms have been developed for computing unitary transforms of arbitrary orders by using different partitioning in the frequency domain and new paired representation of the transforms. These are for the so-called paired transforms. The algorithms are described for the one-dimensional case and use the special partitioning in the frequency domain.

The signed binary number representation (SBNR) is used to reduce the number of PBF calculation stages in stack filters. The approach is based on the possibility of minimization of signed power-of-two terms in the SBNR representation of input data. A coder and a decoder for the mutual transformation of binary-weighted code and the minimal SBNR are proposed. An efficient algorithm and a processor structure for stack filtering based on the minimal SBNR are presented. The time complexity of the proposed filter is of order k[T.sub.P B F], where k is the number of bits in the input signals and [T.sub.P B F] is the delay in the incorporated circuit for the positive Boolean function (PBF). A stack filtering algorithm for the generalized nonadjacent form (GNAF) of signed digit number representation (SDNR) is also presented. Index Terms - Digital arithmetic, digital filters, nonlinear filters, stack filters.

Use of Fibonacci p-codes enables the development of an VLSI architecture and a parallel decomposition algorithm to determine the output of a nonlinear digital stack filter. A running stack filtering VLSI architecture and algorithm are derived for a subclass of positive Boolean functions.

In this paper, an effective column(row)-wise algorithm for computing the two-dimensional discrete Hadamard transform (2-D DHAT) of size [2.sup.r] x [2.sup.r], r [is greater than] 1, by using the paired algorithm of the one-dimensional DHAT, is considered. A new class of so-called discrete paired transforms, which split the [2.sup.r]-point DHAT, r [is greater than] 1, into a set of smaller [2.sup.r-i]-point transforms, i = 1: n, is introduced. Based on such splitting, the algorithm for computing the 2-D DHAT requires on average no more than 12 operations of additions per sample. Index Terms--Fast algorithms, Hadamard transform, paired functions.

In this brief, two different approaches to compute the 2-D discrete Hadamard transform (DHAT) of sizes [2.sup.r] X [2.sup.r], r [is greater than] 1 are presented. The both are based on the so-called 1-D discrete paired transforms, which split the [2.sup.r]-point DHAT into a set of smaller [2.sup.r-[Iota]]-point transforms, [Iota] = r : r. The first approach is a column(row)-wise algorithm which requires, on average, no more than 12 operations of additions per sample. The second approach is a splitting algorithm, in which the [2.sup.r] X [2.sup.r]-point DHAT is reduced to the computation of [2.sup.r-1] 3 1-D DHATs instead of [2.sup.r+1] 1-D DHAT's in the column(row)-wise algorithm, but requires more operations of additions. Examples and comparison of the proposed algorithms with the known algorithms are provided. Index Terms--Fast algorithms, Hadamard transform, paired functions.

A new concept is presented for calculating fast discrete orthogonal transforms that leads to a general split manageable algorithm for computing discrete unitary transforms. A fast Fourier transform (FFT) algorithm is developed with less arithmetical complexity by replacing some of the arithmetical operations by others, such as shifting operations.

A new class of the frequency domain-based signal/image enhancement algorithms is presented. These algorithms have been applied for detection and visualization on objects within an image.