Recursive pyramids and their use for image coding

Recursive pyramidal image representation in image coding algorithms through the use of the pyramid structure, and recursive two-dimensional scannings are introduced. Two approaches to the decorrelation of the picture elements in such a data structure are considered. Properties of different two-dimensional scannings as well as statistical properties of the recursive pyramid and their use for the development of image coding algorithms are shown. Experimental results demonstrating the achieved compression ratio and distortions are provided.     

Adaptive morphological filters for color image enhancement

In this paper, we investigate the performance of an adaptive morphological filter on color image processing, and we develop fast algorithms for the operation. The adaptive filter is based on a new type of opening (NOP) and closing operators (NCP). The operational window of the NOP and NCP can alter its shape according to the local geometry of the processed images. Our experimental results show the effect of the geometric-based adaptivity in preserving the edges, details, highlights, smoothness and color appearance, while removing noise from color images.     

A study on the effect of morphological filters on computer-aided medical image diagnosis

We have developed several morphological image filters that can be useful for computer-aided medical image diagnosis. Several computer-aided diagnosis (CAD) systems for lung cancer and breast cancer have been developed to assist the radiologist’s diagnostic work. The CAD systems for lung cancer can automatically detect pathological changes (pulmonary nodules) with a high true-positive rate (TP) even under low false-positive rate (FP) conditions. On the other hand, the conventional CAD systems for breast cancer can automatically detect some pathological changes (calcifications and masses), but the TP for other changes, such as architectural distortion, is still very low. Motivated by the radiologist’s cognitive processes to increase TP for breast cancer, we propose new methods to extract novel morphological features from X-ray mammography. Simulation results demonstrate the effectiveness of the morphological methods for detecting tumor shadows.     

The design of transverse filters and their use in visual electrograms

The subject under study is a digital filtering method which combines the advantages of both theoretical precision and great flexibility of use. This method has enabled us to develop transverse filters which respect the principle of causality and offer a fast and simple solution in the filtering of electrophysiological potentials. Here we present both the design of transverse filters and their application to visual electrophysiological signals.     

M-idempotent and self-dual morphological filters

In this paper, we present a comprehensive analysis of self-dual and m-idempotent operators. We refer to an operator as m-idempotent if it converges after m iterations. We focus on an important special case of the general theory of lattice morphology: spatially variant morphology, which captures the geometrical interpretation of spatially variant structuring elements. We demonstrate that every increasing self-dual morphological operator can be viewed as a morphological center. Necessary and sufficient conditions for the idempotence of morphological operators are characterized in terms of their kernel representation. We further extend our results to the representation of the kernel of m-idempotent morphological operators. We then rely on the conditions on the kernel representation derived and establish methods for the construction of m-idempotent and self-dual morphological operators. Finally, we illustrate the importance of the self-duality and m-idempotence properties by an application to speckle noise removal in radar images.     

Self-dual morphological operators and filters

The median operator is a nonlinear image transformation celebrated for its noise cleaning capacities. It treats the foreground and background of an image identically, i.e., it is self-dual. Unfortunately, the median operator has one major drawback: it is not idempotent. Even worse, subsequent iterations of a given image may lead to oscillations. This paper describes a general method for the construction of morphological operators which are self-dual. This construction is based upon the concept of a switch operator. Subsequently, the paper treats a class of operators, the so-called activity-extensive operators, which have the intriguing property that every sequence of iterates of a given image is pointwise monotone and therefore convergent. The underlying concept is that of the activity ordering. Every increasing, self-dual operator can be modified in such a way that it becomes activity-extensive. The sequence of iterates of this modification converges to a self-dual morphological filter.     

On various eigen fuzzy sets and their application to image reconstruction

In this study, we formulate and solve a problem of image reconstruction using eigen fuzzy sets. Treating images as fuzzy relations, we propose two algorithms of generating eigen fuzzy sets that are used in the reconstruction process. The first one corresponds to a convex combination of eigen fuzzy set equations, i.e., fuzzy relational equations involving convex combination of max-min and min-max compositions. In the case of the first algorithm, various eigen fuzzy sets can be generated by changing the parameter controlling the convex combination of the corresponding equations. The second algorithm generates various eigen fuzzy sets with respect to the original fuzzy relation using a permutation matrix. A thorough comparison of the proposed algorithms and a conventional algorithm which reconstructs an image using the greatest and smallest eigen fuzzy sets is presented as well. In the experiments, 10,000 artificial images of size 5 × 5 pixels. The approximation error in the case of the first/second algorithm is decreased to 68.2%/97.9% of that of the conventional algorithm, respectively. Furthermore, through the experimentation using real images extracted from Standard Image DataBAse (SIDBA), it is confirmed that the approximation error of the first algorithm is decreased to 41.5% of that of the conventional one.     

Asymptotic behavior of morphological filters

The connection between morphological and stack filters is used in the analysis of the statistical properties of morphological filters. Closed-form expressions for the output distributions of morphological filters are given, and their statistical symmetry properties are analyzed. Asytotically tight bounds on the expectations of two-dimensional morphological filters, and asymptotic formulas for the variances of one-dimensional morphological filters are derived. These results form the basis for analyzing general asymptotic properties of morphological filters.     

Max-plus algebra-based wavelet transforms and their FPGA implementation for image coding

In the present paper, we propose new image coding methods based on max-plus algebra-based wavelet transforms (MP-Wavelets). Max-plus algebra is an algebraic structure on the set of integers, endowed with maximum, minimum and standard addition as operations. The proposed wavelet decomposition schemes are novel classes of morphological wavelets which, in contrast to the existing approaches, involve only integers and only max, min and addition in their computation. Since they do not involve floating point calculations and multiplications, MP-Wavelets have a very low computational complexity and they are suitable for efficient hardware implementation. Through image coding experiments using 10,000 images extracted from low resolution web-crawled misc database, the characteristics of the proposed MP-Wavelets are presented. Furthermore, we show a computational complexity analysis to compare MP-Wavelets to one of the fastest wavelet transforms, the conventional Haar wavelet. The applicability of MP-Wavelets in video coding is also confirmed by image coding experiments using residual frames. Finally, the field programmable gate arrays (FPGA) implementation of MP-Wavelets is presented to confirm suitability of MP-Wavelets for hardware implementation.     

Parallel implementation of sequential morphological filters

Many useful morphological filters are built as more or less long concatenations of erosions and dilations: openings, closings, size distributions, sequential filters, etc. An efficient implementation of these concatenations would allow all the sequentially concatenated operators run simultaneously, on the time-delayed data. A recent algorithm (see below) for the morphological dilation/erosion allows such inter-operator parallelism. This paper introduces an additional, intra-operator level of parallelism in this dilation/erosion algorithm. Realized in a dedicated hardware, for rectangular structuring elements with programmable size, such an implementation allows obtaining previously unachievable, real-time performances for these traditionally costly operators. Low latency and memory requirements are the main benefits when the performance is not deteriorated even for long concatenations or high-resolution images.     

Identification of protein coding regions using antinotch filters

A major area of research in genomic sequence analysis is the identification of protein coding regions using the period-3 property. Previously antinotch filter has been used for this purpose. In this paper, three antinotch filters, namely conjugate suppression antinotch filter, antinotch filter followed by moving average filter and harmonic suppression antinotch filter are proposed to improve the identification accuracy. Conjugate suppression antinotch filter suppresses the conjugate frequency component, antinotch filter followed by moving average filter reduces the background noise and harmonic suppression antinotch filter suppresses the harmonic frequency component. Several existing DNA to numerical mapping techniques are compared for GENSCAN test set and based on the result one mapping technique is recommended so that detailed analysis can be performed using various datasets. The computational complexity of the antinotch filters is evaluated in comparison with the ST-DFT method and it is found that the computational load is reduced to a greater extent in antinotch filter. The identification accuracy of the proposed antinotch filter methods is compared with the existing antinotch filter method at the nucleotide level for benchmark datasets. The results show that proposed methods outperform the existing method, giving improved identification of the protein coding regions.     

Range filters: Localintensity subrange filters and their properties

A local filter which uses the local-intensity subrange of pixel intensity values within a window is described. The range filter is an extension of the rank filter and has been found useful for detecting edges. The deterministic and noise properties of the range filter are described and compared with those of the commonly used Sobel filter.     

Fourier coding of image boundaries

A transform coding scheme for closed image boundaries on a plane is described. The given boundary is approximated by a series of straight line segments. Depending on the shape, the boundary is represented by the (x-y) coordinates of the endpoints of the line segments or by the magnitude of the successive radii vectors that are equispaced in angle around the given boundary. Due to the circularity present in the data, the discrete Fourier transform is used to exactly decorrelate the finite boundary data. By fitting a Gaussian circular autoregressive model to represent the boundary data, estimates of the variances of the Fourier coefficients are obtained. Using the variances of the Fourier coefficients and the MAX quantizer, the coding scheme is implemented. The scheme is illustrated by an example.     

Natural image statistics and efficient coding

Natural images contain characteristic statistical regularities that set them apart from purely random images. Understanding what these regularities are can enable natural images to be coded more efficiently. In this paper, we describe some of the forms of structure that are contained in natural images, and we show how these are related to the response properties of neurons at early stages of the visual system. Many of the important forms of structure require higher-order (i.e. more than linear, pairwise) statistics to characterize, which makes models based on linear Hebbian learning, or principal components analysis, inappropriate for finding efficient codes for natural images. We suggest that a good objective for an efficient coding of natural scenes is to maximize the sparseness of the representation, and we show that a network that learns sparse codes of natural scenes succeeds in developing localized, oriented, bandpass receptive fields similar to those in the mammalian striate cortex.     

The three-dimensional fuzzy sets and their cut sets

In this paper, a new kind of L-fuzzy set is introduced which is called the three-dimensional fuzzy set. We first put forward four kinds of cut sets on the three-dimensional fuzzy sets which are defined by the 4-valued fuzzy sets. Then, the definitions of 4-valued order nested sets and 4-valued inverse order nested sets are given. Based on them, the decomposition theorems and representation theorems are obtained. Furthermore, the left interval-valued intuitionistic fuzzy sets and the right interval-valued intuitionistic fuzzy sets are introduced. We show that the lattices constructed by these two special L-fuzzy sets are not equivalent to sublattices of lattice constructed by the interval-valued intuitionistic fuzzy sets. Finally, we show that the three-dimensional fuzzy set is equivalent to the left interval-valued intuitionistic fuzzy set or the right interval-valued intuitionistic fuzzy set.     

The effect of morphological filters on texture boundarylocalization

We extend the theoretical results obtained by Stevenson et al. (1987) to two distributions and provide a quantitative comparison of 1D morphological filter edge localization with two classical types of kernel-based smoothing filters (the mean and the close relative to morphological filters, the median filter). Implications in the context of statistical texture segmentation are briefly discussed     

Application of morphological filters to tackle discretisation artefacts

A post-processing technique for removing discretisation artefacts (jaggies) is described. It is based on the detection of a jaggy by means of a suitable morphological filter and then using a heuristic algorithm to compute a probable density distribution, which is applied to the pixels adjacent to the jaggy. Also dashed lines are recognized and interpreted as possible discretisation artefacts. The method applies to both spatial and temporal aliasing.     

Implementation of morphological filters using coordinate logic operations

In this paper we present a methodology for performing morphological operations using coordinate logic operations. Coordinate logic operations are simple and fast because they are logic operations among the corresponding binary values of the image pixels. Coordinate logic (CL) filters are a family of fast non-increasing, non-linear filters, which are based on coordinate logic operations. CL filters exhibit analogous properties to those of the morphological filters but due to their different definition they display slightly different response. This is revoked in this paper by using appropriate image gray level quantization and mapping of the resulting levels to a specific set of decimal numbers. Based on this approach some fast efficient implementations of morphological filters using CL operators are proposed.     

提升小波变换的零树分形混合编码算法

为改善图像压缩的效果,在讨论小波提升算法的基本原理与实现流程的基础上,提出了一种改进的基于提升小波变换的零树分形混合图像编码算法。在基本小波提升算法的基础上,考虑到在对小波子树匹配预测时,经提升小波变换后的高分辨率子带自相似性不强的特点,不对高分辨率子块进行分形匹配,而直接用前几个较低分辨子带的匹配结果作为小波子树的匹配结果,改进了基于提升小波系数零树结构的分形预测图像编码方法及过程。实验结果表明,这种改进显著加快了编码速度,编码所花费时间仅为常规方法的十分之一。最后,阐明了小波与分形进行图像压缩相结合的本质和仍需改进的方向。