Novel uncertainty principles associated with 2D quaternion Fourier transforms

Mathematical morphology is a powerful tool for image processing and analysis of binary, greyscale and colour images. In the paper, an efficient new fuzzy model for morphological colour image processing is introduced. A new vector-ordering scheme that uses fuzzy if–then rules is proposed, and then the basic morphological operations of erosion and dilation are defined. The morphological operators presented, which are vector preserving, are less sensitive to image distortion and perform significantly better in noise removal problems than other reported morphological operators. Experimental results demonstrate these advantageous characteristics on real images. Additionally, illustrative examples that exhibit the applicability of the proposed framework to edge-detection problems are given.

Visual assessment, black & white image analysis and colour image analysis of the severity of powdery mildew (Sphaerotheca fuliginea) infection on leaves of cucumber (Cucumis sativus) were compared. The extent of infection with powdery mildew was expressed as the number of spores per cm2. Statistical treatment of the data showed colour image analysis to be superior to the other two methods of evaluation. Major veins, light reflections and variations in the colour of leaves can degrade the accuracy of colour image analysis somewhat. These problems are, however, surmountable. Colour image analysis qualifies as a valuable new tool for accurate, objective, reproducible and detailed quantitative assessment of disease on leaves of plants.

segmentation divides an image into several constituent components such as color, structure, shape, and texture. It forms a major research topic for many image processing researchers as the applications are endless. Its applications include image enhancement, object detection, image retrieval, image compression, and medical image processing to name a few. The segmentation of color images is necessary for efficient pattern recognition and feature extraction involving various color spaces such as RGB, HSV and CIE L*A*B*, etc. This paper describes the different cluster based segmentation techniques used for segmenting the different color images and the resultant is analyzed with subjective and objective measures. Initially, registered color images are considered as input. Then the cluster based segmentation techniques namely K-Means clustering, Pillar-Kmeans clustering and Fuzzy C-means (FCM) clustering techniques are applied. Further, the segmented image is analyzed with measures such as compactness and execution time. From the experimental results, it has been observed that K-means and Pillar-Kmeans are the most suitable techniques for RGB, HSV and LAB color spaces than the FCM technique.

Phone cameras are currently used in various medical fields for processing color images. Today they can play an important role in facilitating access to some diagnostic services because they are available to many people, including doctors and patients who do not have access to advanced imaging systems. Image enhancement via cell phones is a highly desired preprocessing tool because many pictures and images are poor in quality. Processing of color images in one of the known color models, such as RGB, XYZ, or HSV15 is a very difficult task and has attracted much research interest in the last decade. In traditional color image processing, each color channel (red, green, and blue in the RGB color space, for example) is separately considered, then the color image is composed. In such a simple approach, the inherent correlation between the components are not taken into account; this fact results in color artifacts. For another approach that simultaneously processes the color components of the image,19 the most promising tool is the theory of quaternion algebra with 2D quaternion transforms, such as the Fourier, Hadamard, and cosine transforms. The 2D discrete Fourier transform (DFT) is still the primary transform used in image enhancement and filtration. Therefore, we will focus on an extension of this transform in quaternion arithmetic. The color image as a three-component image is mapped into pure quaternion data and can be called a color-in-quaternion image. This quaternion-transform-based approach can effectively be used in different applications of color science. First introduced by Hamilton,quaternion numbers now are used in bioinformatics, navigation systems,6 image and video processing, and in a number of studies on quaternions in color image processing. Here, we note that since quaternion multiplication is not commutative, different definitions of quaternion Fourier transforms can be used in color image processing.

Based on experimental data, obtained in vitro from reflectance measurements and in vivo from digital analysis of color images of human irises, melanin content in human and bovine eye irises has been estimated. Reflectance measurements have been performed using commercially available optical multichannel spectrometer LESA-5 (BioSpec, Russia). For registration of color images digital camera Olympus C-5060 has been used. Analysis of the reflectance spectra has been performed by the method used for determination of melanin content in skin. For digital analysis of iris color images, decomposition of the images in RGB-color-coordinate system has been performed. The images have been obtained both from irises of health volunteers as from irises of patients with glaucoma. Original computer program based on Mathcad software has been developed for the analysis. The results obtained from spectral and color measurements have a good agreement each to other. In eye irises of patients with glaucoma, smaller melanin content has been obtained, and the result has been useful for development of novel and optimization of already existing methods of glaucoma diagnostics.

A recent trend in color image processing combines the quaternion algebra with dictionary learning methods. This paper aims to present a generalization of the quaternion dictionary learning method by using the octonion algebra. The octonion algebra combined with dictionary learning methods is well suited for representation of multispectral images with up to 7 color channels. Opposed to the classical dictionary learning techniques that treat multispectral images by concatenating spectral bands into a large monochrome image, we treat all the spectral bands simultaneously. Our approach leads to better preservation of color fidelity in true and false color images of the reconstructed multispectral image. To show the potential of the octonion based model, experiments are conducted for image reconstruction and denoising of color images as well as of extensively used Landsat 7 images.

Approximation of the Karhunen–Loève transformation and its application to colour images

Fracta1 techniques are widely explored to quantity and recognize texture patterns in digital images. Among the different types of fractal techniques, one that stands out is the Higuchi fractal dimension. The Higuchi fractal dimension allows determining how much space is filled in a two-dimensional image through the projection of the image in 1D signals. This property provides the possibility to calculate the Higuchi fractal dimension of specific regions of an image. The main drawback of this technique is that it does not allow the analysis of color images. In this work, a new Higuchi fractal dimension model is presented with the inclusion of multidimensional and multiscale strategies to expand the traditional Higuchi dimension for texture analysis in color images. The multidimensional approach was applied considering each pixel of the color image as an n-dimensional vector. The multiscale strategy was defined using different scales of observation. The proposed model was applied to a set of 151 colorectal histological images to test its ability to quantity and separate the benign and malignant groups from colorectal cancer. The performance of the proposed model was compared with that provided by consolidated fractal dimension techniques. The results obtained are promising and indicate that the proposal contributes significantly to the literature focused on the quantification and recognition of texture patterns with fractal techniques.

The color logarithmic image processing (CoLIP) is a mathematical framework for the representation and processing of color images. It is psychophysically well justified since it is consistent with several human visual perception laws and characteristics. It is mathematically and computationally relevant since it allows to consider color images as vectors in an abstract linear space, contrary to the classical color spaces (e.g., RGB and \(L^*a^*b^*\)). The first purpose of this chapter is to present the mathematical fundamentals of the CoLIP together with its main psychophysical connections (Grasmann’s law, color matching functions, chromaticity diagram, and the Maxwell triangle). The second purpose is to present some basic image processing and analysis techniques for contrast enhancement (histogram equalization, dynamic range maximization, and toggle contrast calculation), white balance correction, color transfer, K-means clustering, and filtering. Most of them are applied on various original color images in a comparative way between CoLIP, RGB, and \(L^*a^*b^*\) color spaces.

A color image processing technique has been applid to measure the temperature on a wall cooled by a cold air jet. Temperature distribution on the wall was visualized by a thereto-sensitive liquid crystal sheet. To achieve the color image analysis, the optical characteristics affecting to the temperature measure-ments, e.g, intensity of refractive light, relative angle between camera, crys-tal sheet and illumination, media configurations between camera and the crystal sheet, were quantitatively evaluated. The reflected colors from the liquid crys-tal-sheet were captured through a 3-tips color TV camera and the temperature distribution was obtained through a neural network color-temperature calibration scheme. This color image analysis is capable of measuring the spatial distribu-tion of mean temperature on the wall.

Multi-layer security of color image based on chaotic system combined with RP2DFRFT and Arnold Transform

Hyperbolic linear canonical transforms of quaternion signals and uncertainty

Image segmentation is the process of dividing an image into homogenous regions. It is an essential step towards high-level image processing task such as image analysis, pattern recognition and computer vision. Processing of color images has become an important issue due to its huge usage in computer vision applications. It is observed that most of the color image segmentation techniques are derived from monochrome image segmentation. The techniques for segmentation of monochrome images are based on the principles of histogram thresholding, edge detection, region growing etc. Many color image segmentation algorithms using different color models and these principles are proposed. Extraction of objects within an image without a prior knowledge is one of the important issues in segmentation area. Novel approaches such as fuzzy set theory, neural network and neuro-fuzzy based segmentation are coming up to tackle this problem. This paper is an endeavor to review various algorithms and recent advances in color image segmentation.

Spectral characteristics of a color image is conventionally obtained by multi-spectral imaging(1,2). A color image is illuminated by series of light having narrow spectral band equally divided in the visible spectral region. Spectral distribution for each pixel is directly determined by intensity distribution of images for each illuminating light.

An uncertainty principle for quaternion Fourier transform