Three-dimensional block matching using orthonormal tree-structured haar transform for multichannel images

Multichannel images, i.e., images of the same object or scene taken in different spectral bands or with different imaging modalities/settings, are common in many applications. For example, multispectral images contain several wavelength bands and hence, have richer information than color images. Multichannel magnetic resonance imaging and multichannel computed tomography images are common in medical imaging diagnostics, and multimodal images are also routinely used in art investigation. All the methods for grayscale images can be applied to multichannel images by processing each channel/band separately. However, it requires vast computational time, especially for the task of searching for overlapping patches similar to a given query patch. To address this problem, we propose a three-dimensional orthonormal tree-structured Haar transform (3D-OTSHT) targeting fast full search equivalent for three-dimensional block matching in multichannel images. The use of a three-dimensional integral image significantly saves time to obtain the 3D-OTSHT coefficients. We demonstrate superior performance of the proposed block matching

A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.Comment: 65 pages, 33 figures, 303 reference

Wavelets and their use

This review paper is intended to give a useful guide for those who want to apply discrete wavelets in their practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous proofs of mathematical statements are omitted, and the reader is just referred to corresponding literature. The multiresolution analysis and fast wavelet transform became a standard procedure for dealing with discrete wavelets. The proper choice of a wavelet and use of nonstandard matrix multiplication are often crucial for achievement of a goal. Analysis of various functions with the help of wavelets allows to reveal fractal structures, singularities etc. Wavelet transform of operator expressions helps solve some equations. In practical applications one deals often with the discretized functions, and the problem of stability of wavelet transform and corresponding numerical algorithms becomes important. After discussing all these topics we turn to practical applications of the wavelet machinery. They are so numerous that we have to limit ourselves by some examples only. The authors would be grateful for any comments which improve this review paper and move us closer to the goal proclaimed in the first phrase of the abstract.Comment: 63 pages with 22 ps-figures, to be published in Physics-Uspekh

The multi-level and multi-dimensional quantum wavelet packet transforms

© 2018, The Author(s). The classical wavelet packet transform has been widely applied in the information processing field. It implies that the quantum wavelet packet transform (QWPT) can play an important role in quantum information processing. In this paper, we design quantum circuits of a generalized tensor product (GTP) and a perfect shuffle permutation (PSP). Next, we propose multi-level and multi-dimensional (1D, 2D and 3D) QWPTs, including a Haar QWPT (HQWPT), a D4 QWPT (DQWPT) based on the periodization extension and their inverse transforms for the first time, and prove the correctness based on the GTP and PSP. Furthermore, we analyze the quantum costs and the time complexities of our proposed QWPTs and obtain precise results. The time complexities of HQWPTs is at most 6 on 2n elements, which illustrates high-efficiency of the proposed QWPTs. Simulation experiments demonstrate that the proposed QWPTs are correct and effective

An Investigation of Orthogonal Wavelet Division Multiplexing Techniques as an Alternative to Orthogonal Frequency Division Multiplex Transmissions and Comparison of Wavelet Families and Their Children

Recently, issues surrounding wireless communications have risen to prominence because of the increase in the popularity of wireless applications. Bandwidth problems, and the difficulty of modulating signals across carriers, represent significant challenges. Every modulation scheme used to date has had limitations, and the use of the Discrete Fourier Transform in OFDM (Orthogonal Frequency Division Multiplex) is no exception. The restriction on further development of OFDM lies primarily within the type of transform it uses in the heart of its system, Fourier transform. OFDM suffers from sensitivity to Peak to Average Power Ratio, carrier frequency offset and wasting some bandwidth to guard successive OFDM symbols. The discovery of the wavelet transform has opened up a number of potential applications from image compression to watermarking and encryption. Very recently, work has been done to investigate the potential of using wavelet transforms within the communication space. This research will further investigate a recently proposed, innovative, modulation technique, Orthogonal Wavelet Division Multiplex, which utilises the wavelet transform opening a new avenue for an alternative modulation scheme with some interesting potential characteristics. Wavelet transform has many families and each of those families has children which each differ in filter length. This research consider comprehensively investigates the new modulation scheme, and proposes multi-level dynamic sub-banding as a tool to adapt variable signal bandwidths. Furthermore, all compactly supported wavelet families and their associated children of those families are investigated and evaluated against each other and compared with OFDM. The linear computational complexity of wavelet transform is less than the logarithmic complexity of Fourier in OFDM. The more important complexity is the operational complexity which is cost effectiveness, such as the time response of the system, the memory consumption and the number of iterative operations required for data processing. Those complexities are investigated for all available compactly supported wavelet families and their children and compared with OFDM. The evaluation reveals which wavelet families perform more effectively than OFDM, and for each wavelet family identifies which family children perform the best. Based on these results, it is concluded that the wavelet modulation scheme has some interesting advantages over OFDM, such as lower complexity and bandwidth conservation of up to 25%, due to the elimination of guard intervals and dynamic bandwidth allocation, which result in better cost effectiveness

Sonar image interpretation for sub-sea operations

Mine Counter-Measure (MCM) missions are conducted to neutralise underwater explosives. Automatic Target Recognition (ATR) assists operators by increasing the speed and accuracy of data review. ATR embedded on vehicles enables adaptive missions which increase the speed of data acquisition. This thesis addresses three challenges; the speed of data processing, robustness of ATR to environmental conditions and the large quantities of data required to train an algorithm. The main contribution of this thesis is a novel ATR algorithm. The algorithm uses features derived from the projection of 3D boxes to produce a set of 2D templates. The template responses are independent of grazing angle, range and target orientation. Integer skewed integral images, are derived to accelerate the calculation of the template responses. The algorithm is compared to the Haar cascade algorithm. For a single model of sonar and cylindrical targets the algorithm reduces the Probability of False Alarm (PFA) by 80% at a Probability of Detection (PD) of 85%. The algorithm is trained on target data from another model of sonar. The PD is only 6% lower even though no representative target data was used for training. The second major contribution is an adaptive ATR algorithm that uses local sea-floor characteristics to address the problem of ATR robustness with respect to the local environment. A dual-tree wavelet decomposition of the sea-floor and an Markov Random Field (MRF) based graph-cut algorithm is used to segment the terrain. A Neural Network (NN) is then trained to filter ATR results based on the local sea-floor context. It is shown, for the Haar Cascade algorithm, that the PFA can be reduced by 70% at a PD of 85%. Speed of data processing is addressed using novel pre-processing techniques. The standard three class MRF, for sonar image segmentation, is formulated using graph-cuts. Consequently, a 1.2 million pixel image is segmented in 1.2 seconds. Additionally, local estimation of class models is introduced to remove range dependent segmentation quality. Finally, an A* graph search is developed to remove the surface return, a line of saturated pixels often detected as false alarms by ATR. The A* search identifies the surface return in 199 of 220 images tested with a runtime of 2.1 seconds. The algorithm is robust to the presence of ripples and rocks

Application of Wavelets and Principal Component Analysis in Image Query and Mammography

Breast cancer is currently one of the major causes of death for women in the U.S. Mammography is currently the most effective method for detection of breast cancer and early detection has proven to be an efficient tool to reduce the number of deaths. Mammography is the most demanding of all clinical imaging applications as it requires high contrast, high signal to noise ratio and resolution with minimal x-radiation. According to studies [36], 10% to 30% of women having breast cancer and undergoing mammography, have negative mammograms, i.e. are misdiagnosed. Furthermore, only 20%-40% of the women who undergo biopsy, have cancer. Biopsies are expensive, invasive and traumatic to the patient. The high rate of false positives is partly because of the difficulties in the diagnosis process and partly due to the fear of missing a cancer. These facts motivate research aimed to enhance the mammogram images (e.g. by enhancement of features such as clustered calcification regions which were found to be associated with breast cancer) , to provide CAD (Computer Aided Diagnostics) tools that can alert the radiologist to potentially malignant regions in the mammograms and to develope tools for automated classification of mammograms into benign and malignant classes. In this paper we apply wavelet and Principal Component analysis, including the approximate Karhunen Loeve aransform to mammographic images, to derive feature vectors used for classification of mammographic images from an early stage of malignancy. Another area where wavelet analysis was found useful, is the area of image query. Image query of large data bases must provide a fast and efficient search of the query image. Lately, a group of researchers developed an algorithm based on wavelet analysis that was found to provide fast and efficient search in large data bases. Their method overcomes some of the difficulties associated with previous approaches, but the search algorithm is sensitive to displacement and rotation of the query image due to the fact that wavelet analysis is not invariant under displacement and rotation. In this study we propose the integration of the Hotelling transform to improve on this sensitivity and provide some experimental results in the context of the standard alphabetic characters

Visual Object Tracking Approach Based on Wavelet Transforms

In this Thesis, a new visual object tracking (VOT) approach is proposed to overcome the main challenging problem encountered within the existing approaches known as the significant appearance changes which is due mainly to the heavy occlusion and illumination variations. Indeed, the proposed approach is based on combining the deep convolutional neural networks (CNN), the histograms of oriented gradients (HOG) features, and the discrete wavelet packet transform to ensure the implementation of three ideas. Firstly, solving the problem of illumination variation by incorporating the coefficients of the image discrete wavelet packet transform instead of the image template to handle the case of images with high saturation in the input of the used CNN, whereas the inverse discrete wavelet packet transform is used at the output for extracting the CNN features. Secondly, by combining four learned correlation filters with convolutional features, the target location is deduced using multichannel correlation maps at the CNNs output. On the other side, the maximum value of the resulting maps from correlation filters with convolutional features produced by HOG feature of the image template previously obtained are calculated and which are used as an updating parameter of the correlation filters extracted from CNN and from HOG where the major aim is to ensure long-term memory of target appearance so that the target item may be recovered if tracking fails. Thirdly, to increase the performance of HOG, the coefficients of the discrete packet wavelet transform are employed instead of the image template. Finally, for the validation and the evaluation of the proposed tracking approach performance based on specific performance metrics in comparison to the state-of-the-art counterparts, extensive simulation experiments on benchmark datasets have been conducted out, such as OTB50, OTB100 , TC128 ,and UAV20. The obtained results clearly prove the validity of the proposed approach in solving the encountered problems of visual object tracking in almost the experiment cases presented in this thesis compared to other existing tracking approaches

Colour image coding with wavelets and matching pursuit

This thesis considers sparse approximation of still images as the basis of a lossy compression system. The Matching Pursuit (MP) algorithm is presented as a method particularly suited for application in lossy scalable image coding. Its multichannel extension, capable of exploiting inter-channel correlations, is found to be an efficient way to represent colour data in RGB colour space. Known problems with MP, high computational complexity of encoding and dictionary design, are tackled by finding an appropriate partitioning of an image. The idea of performing MP in the spatio-frequency domain after transform such as Discrete Wavelet Transform (DWT) is explored. The main challenge, though, is to encode the image representation obtained after MP into a bit-stream. Novel approaches for encoding the atomic decomposition of a signal and colour amplitudes quantisation are proposed and evaluated. The image codec that has been built is capable of competing with scalable coders such as JPEG 2000 and SPIHT in terms of compression ratio