Fourier Transform

The application of Fourier transform (FT) in signal processing and physical sciences has increased in the past decades. Almost all the textbooks on signal processing or physics have a section devoted to the FT theory. For this reason, this book focuses on signal processing and physical sciences. The book chapters are related to fast hybrid recursive FT based on Jacket matrix, acquisition algorithm for global navigation satellite system, determining the sensitivity of output parameters based on FFT, convergence of integrals of products based on Riemann-Lebesgue Lemma function, extending the real and complex number fields for treating the FT, nonmaterial structure, Gabor transform, and chalcopyrite bioleaching. The book provides applications oriented to signal processing and physics written primarily for engineers, mathematicians, physicians and graduate students, will also find it useful as a reference for their research activities

A Relaxation Scheme for Mesh Locality in Computer Vision.

Parallel processing has been considered as the key to build computer systems of the future and has become a mainstream subject in Computer Science. Computer Vision applications are computationally intensive that require parallel approaches to exploit the intrinsic parallelism. This research addresses this problem for low-level and intermediate-level vision problems. The contributions of this dissertation are a unified scheme based on probabilistic relaxation labeling that captures localities of image data and the ability of using this scheme to develop efficient parallel algorithms for Computer Vision problems. We begin with investigating the problem of skeletonization. The technique of pattern match that exhausts all the possible interaction patterns between a pixel and its neighboring pixels captures the locality of this problem, and leads to an efficient One-pass Parallel Asymmetric Thinning Algorithm (OPATA\sb8). The use of 8-distance in this algorithm, or chessboard distance, not only improves the quality of the resulting skeletons, but also improves the efficiency of the computation. This new algorithm plays an important role in a hierarchical route planning system to extract high level typological information of cross-country mobility maps which greatly speeds up the route searching over large areas. We generalize the neighborhood interaction description method to include more complicated applications such as edge detection and image restoration. The proposed probabilistic relaxation labeling scheme exploit parallelism by discovering local interactions in neighboring areas and by describing them effectively. The proposed scheme consists of a transformation function and a dictionary construction method. The non-linear transformation function is derived from Markov Random Field theory. It efficiently combines evidences from neighborhood interactions. The dictionary construction method provides an efficient way to encode these localities. A case study applies the scheme to the problem of edge detection. The relaxation step of this edge-detection algorithm greatly reduces noise effects, gets better edge localization such as line ends and corners, and plays a crucial rule in refining edge outputs. The experiments on both synthetic and natural images show that our algorithm converges quickly, and is robust in noisy environment

Unified Theory for Biorthogonal Modulated Filter Banks

Modulated filter banks (MFBs) are practical signal decomposition tools for M -channel multirate systems. They combine high subfilter selectivity with efficient realization based on polyphase filters and block transforms. Consequently, the O(M 2 ) burden of computations in a general filter bank (FB) is reduced to O(M log2 M ) - the latter being a complexity order comparable with the FFT-like transforms.Often hiding from the plain sight, these versatile digital signal processing tools have important role in various professional and everyday life applications of information and communications technology, including audiovisual communications and media storage (e.g., audio codecs for low-energy music playback in portable devices, as well as communication waveform processing and channelization). The algorithmic efficiency implies low cost, small size, and extended battery life, bringing the devices close to our skins.The main objective of this thesis is to formulate a generalized and unified approach to the MFBs, which includes, in addition to the deep theoretical background behind these banks, both their design by using appropriate optimization techniques and efficient algorithmic realizations. The FBs discussed in this thesis are discrete-time time-frequency decomposition/reconstruction, or equivalently, analysis-synthesis systems, where the subfilters are generated through modulation from either a single or two prototype filters. The perfect reconstruction (PR) property is a particularly important characteristics of the MFBs and this is the core theme of this thesis. In the presented biorthogonal arbitrary-delay exponentially modulated filter bank (EMFB), the PR property can be maintained also for complex-valued signals.The EMFB concept is quite flexible, since it may respond to the various requirements given to a subband processing system: low-delay PR prototype design, subfilters having symmetric impulse responses, efficient algorithms, and the definition covers odd and even-stacked cosine-modulated FBs as special cases. Oversampling schemes for the subsignals prove out to be advantageous in subband processing problems requiring phase information about the localized frequency components. In addition, the MFBs have strong connections with the lapped transform (LT) theory, especially with the class of LTs grounded in parametric window functions.<br/

A VISION-BASED QUALITY INSPECTION SYSTEM FOR FABRIC DEFECT DETECTION AND CLASSIFICATION

Published ThesisQuality inspection of textile products is an important issue for fabric manufacturers. It is desirable to produce the highest quality goods in the shortest amount of time possible. Fabric faults or defects are responsible for nearly 85% of the defects found by the garment industry. Manufacturers recover only 45 to 65% of their profits from second or off-quality goods. There is a need for reliable automated woven fabric inspection methods in the textile industry. Numerous methods have been proposed for detecting defects in textile. The methods are generally grouped into three main categories according to the techniques they use for texture feature extraction, namely statistical approaches, spectral approaches and model-based approaches. In this thesis, we study one method from each category and propose their combinations in order to get improved fabric defect detection and classification accuracy. The three chosen methods are the grey level co-occurrence matrix (GLCM) from the statistical category, the wavelet transform from the spectral category and the Markov random field (MRF) from the model-based category. We identify the most effective texture features for each of those methods and for different fabric types in order to combine them. Using GLCM, we identify the optimal number of features, the optimal quantisation level of the original image and the optimal intersample distance to use. We identify the optimal GLCM features for different types of fabrics and for three different classifiers. Using the wavelet transform, we compare the defect detection and classification performance of features derived from the undecimated discrete wavelet and those derived from the dual-tree complex wavelet transform. We identify the best features for different types of fabrics. Using the Markov random field, we study the performance for fabric defect detection and classification of features derived from different models of Gaussian Markov random fields of order from 1 through 9. For each fabric type we identify the best model order. Finally, we propose three combination schemes of the best features identified from the three methods and study their fabric detection and classification performance. They lead generally to improved performance as compared to the individual methods, but two of them need further improvement

Discrete Wavelet Transforms

The discrete wavelet transform (DWT) algorithms have a firm position in processing of signals in several areas of research and industry. As DWT provides both octave-scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. The present book: Discrete Wavelet Transforms: Algorithms and Applications reviews the recent progress in discrete wavelet transform algorithms and applications. The book covers a wide range of methods (e.g. lifting, shift invariance, multi-scale analysis) for constructing DWTs. The book chapters are organized into four major parts. Part I describes the progress in hardware implementations of the DWT algorithms. Applications include multitone modulation for ADSL and equalization techniques, a scalable architecture for FPGA-implementation, lifting based algorithm for VLSI implementation, comparison between DWT and FFT based OFDM and modified SPIHT codec. Part II addresses image processing algorithms such as multiresolution approach for edge detection, low bit rate image compression, low complexity implementation of CQF wavelets and compression of multi-component images. Part III focuses watermaking DWT algorithms. Finally, Part IV describes shift invariant DWTs, DC lossless property, DWT based analysis and estimation of colored noise and an application of the wavelet Galerkin method. The chapters of the present book consist of both tutorial and highly advanced material. Therefore, the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications

Retinal vessel segmentation using textons

Segmenting vessels from retinal images, like segmentation in many other medical image domains, is a challenging task, as there is no unified way that can be adopted to extract the vessels accurately. However, it is the most critical stage in automatic assessment of various forms of diseases (e.g. Glaucoma, Age-related macular degeneration, diabetic retinopathy and cardiovascular diseases etc.). Our research aims to investigate retinal image segmentation approaches based on textons as they provide a compact description of texture that can be learnt from a training set. This thesis presents a brief review of those diseases and also includes their current situations, future trends and techniques used for their automatic diagnosis in routine clinical applications. The importance of retinal vessel segmentation is particularly emphasized in such applications. An extensive review of previous work on retinal vessel segmentation and salient texture analysis methods is presented. Five automatic retinal vessel segmentation methods are proposed in this thesis. The first method focuses on addressing the problem of removing pathological anomalies (Drusen, exudates) for retinal vessel segmentation, which have been identified by other researchers as a problem and a common source of error. The results show that the modified method shows some improvement compared to a previously published method. The second novel supervised segmentation method employs textons. We propose a new filter bank (MR11) that includes bar detectors for vascular feature extraction and other kernels to detect edges and photometric variations in the image. The k-means clustering algorithm is adopted for texton generation based on the vessel and non-vessel elements which are identified by ground truth. The third improved supervised method is developed based on the second one, in which textons are generated by k-means clustering and texton maps representing vessels are derived by back projecting pixel clusters onto hand labelled ground truth. A further step is implemented to ensure that the best combinations of textons are represented in the map and subsequently used to identify vessels in the test set. The experimental results on two benchmark datasets show that our proposed method performs well compared to other published work and the results of human experts. A further test of our system on an independent set of optical fundus images verified its consistent performance. The statistical analysis on experimental results also reveals that it is possible to train unified textons for retinal vessel segmentation. In the fourth method a novel scheme using Gabor filter bank for vessel feature extraction is proposed. The ii method is inspired by the human visual system. Machine learning is used to optimize the Gabor filter parameters. The experimental results demonstrate that our method significantly enhances the true positive rate while maintaining a level of specificity that is comparable with other approaches. Finally, we proposed a new unsupervised texton based retinal vessel segmentation method using derivative of SIFT and multi-scale Gabor filers. The lack of sufficient quantities of hand labelled ground truth and the high level of variability in ground truth labels amongst experts provides the motivation for this approach. The evaluation results reveal that our unsupervised segmentation method is comparable with the best other supervised methods and other best state of the art methods