Directional edge and texture representations for image processing

An efficient representation for natural images is of fundamental importance in image processing and analysis. The commonly used separable transforms such as wavelets axe not best suited for images due to their inability to exploit directional regularities such as edges and oriented textural patterns; while most of the recently proposed directional schemes cannot represent these two types of features in a unified transform. This thesis focuses on the development of directional representations for images which can capture both edges and textures in a multiresolution manner. The thesis first considers the problem of extracting linear features with the multiresolution Fourier transform (MFT). Based on a previous MFT-based linear feature model, the work extends the extraction method into the situation when the image is corrupted by noise. The problem is tackled by the combination of a "Signal+Noise" frequency model, a refinement stage and a robust classification scheme. As a result, the MFT is able to perform linear feature analysis on noisy images on which previous methods failed. A new set of transforms called the multiscale polar cosine transforms (MPCT) are also proposed in order to represent textures. The MPCT can be regarded as real-valued MFT with similar basis functions of oriented sinusoids. It is shown that the transform can represent textural patches more efficiently than the conventional Fourier basis. With a directional best cosine basis, the MPCT packet (MPCPT) is shown to be an efficient representation for edges and textures, despite its high computational burden. The problem of representing edges and textures in a fixed transform with less complexity is then considered. This is achieved by applying a Gaussian frequency filter, which matches the disperson of the magnitude spectrum, on the local MFT coefficients. This is particularly effective in denoising natural images, due to its ability to preserve both types of feature. Further improvements can be made by employing the information given by the linear feature extraction process in the filter's configuration. The denoising results compare favourably against other state-of-the-art directional representations

Probabilistic modeling of wavelet coefficients for processing of image and video signals

Statistical estimation and detection techniques are widely used in signal processing including wavelet-based image and video processing. The probability density function (PDF) of the wavelet coefficients of image and video signals plays a key role in the development of techniques for such a processing. Due to the fixed number of parameters, the conventional PDFs for the estimators and detectors usually ignore higher-order moments. Consequently, estimators and detectors designed using such PDFs do not provide a satisfactory performance. This thesis is concerned with first developing a probabilistic model that is capable of incorporating an appropriate number of parameters that depend on higher-order moments of the wavelet coefficients. This model is then used as the prior to propose certain estimation and detection techniques for denoising and watermarking of image and video signals. Towards developing the probabilistic model, the Gauss-Hermite series expansion is chosen, since the wavelet coefficients have non-compact support and their empirical density function shows a resemblance to the standard Gaussian function. A modification is introduced in the series expansion so that only a finite number of terms can be used for modeling the wavelet coefficients with rendering the resulting PDF to become negative. The parameters of the resulting PDF, called the modified Gauss-Hermite (NIGH) PDF, are evaluated in terms of the higher-order sample-moments. It is shown that the MGH PDF fits the empirical density function better than the existing PDFs that use a limited number of parameters do. The proposed MGH PDF is used as the prior of image and video signals in designing maximum a posteriori and minimum mean squared error-based estimators for denoising of image and video signals and log-likelihood ratio-based detector for watermarking of image signals. The performance of the estimation and detection techniques are then evaluated in terms of the commonly used metrics. It is shown through extensive experimentations that the estimation and detection techniques developed utilizing the proposed MGH PDF perform substantially better than those that utilize the conventional PDFs. These results confirm that the superior fit of the MGH PDF to the empirical density function resulting from the flexibility of the MGH PDF in choosing the number of parameters, which are functions of higher-order moments of data, leads to the better performance. Thus, the proposed MGH PDF should play a significant role in wavelet-based image and video signal processin

Signal processing algorithms for enhanced image fusion performance and assessment

The dissertation presents several signal processing algorithms for image fusion in noisy multimodal conditions. It introduces a novel image fusion method which performs well for image sets heavily corrupted by noise. As opposed to current image fusion schemes, the method has no requirements for a priori knowledge of the noise component. The image is decomposed with Chebyshev polynomials (CP) being used as basis functions to perform fusion at feature level. The properties of CP, namely fast convergence and smooth approximation, renders it ideal for heuristic and indiscriminate denoising fusion tasks. Quantitative evaluation using objective fusion assessment methods show favourable performance of the proposed scheme compared to previous efforts on image fusion, notably in heavily corrupted images. The approach is further improved by incorporating the advantages of CP with a state-of-the-art fusion technique named independent component analysis (ICA), for joint-fusion processing based on region saliency. Whilst CP fusion is robust under severe noise conditions, it is prone to eliminating high frequency information of the images involved, thereby limiting image sharpness. Fusion using ICA, on the other hand, performs well in transferring edges and other salient features of the input images into the composite output. The combination of both methods, coupled with several mathematical morphological operations in an algorithm fusion framework, is considered a viable solution. Again, according to the quantitative metrics the results of our proposed approach are very encouraging as far as joint fusion and denoising are concerned. Another focus of this dissertation is on a novel metric for image fusion evaluation that is based on texture. The conservation of background textural details is considered important in many fusion applications as they help define the image depth and structure, which may prove crucial in many surveillance and remote sensing applications. Our work aims to evaluate the performance of image fusion algorithms based on their ability to retain textural details from the fusion process. This is done by utilising the gray-level co-occurrence matrix (GLCM) model to extract second-order statistical features for the derivation of an image textural measure, which is then used to replace the edge-based calculations in an objective-based fusion metric. Performance evaluation on established fusion methods verifies that the proposed metric is viable, especially for multimodal scenarios

Sparse image approximation with application to flexible image coding

Natural images are often modeled through piecewise-smooth regions. Region edges, which correspond to the contours of the objects, become, in this model, the main information of the signal. Contours have the property of being smooth functions along the direction of the edge, and irregularities on the perpendicular direction. Modeling edges with the minimum possible number of terms is of key importance for numerous applications, such as image coding, segmentation or denoising. Standard separable basis fail to provide sparse enough representation of contours, due to the fact that this kind of basis do not see the regularity of edges. In order to be able to detect this regularity, a new method based on (possibly redundant) sets of basis functions able to capture the geometry of images is needed. This thesis presents, in a first stage, a study about the features that basis functions should have in order to provide sparse representations of a piecewise-smooth image. This study emphasizes the need for edge-adapted basis functions, capable to accurately capture local orientation and anisotropic scaling of image structures. The need of different anisotropy degrees and orientations in the basis function set leads to the use of redundant dictionaries. However, redundant dictionaries have the inconvenience of giving no unique sparse image decompositions, and from all the possible decompositions of a signal in a redundant dictionary, just the sparsest is needed. There are several algorithms that allow to find sparse decompositions over redundant dictionaries, but most of these algorithms do not always guarantee that the optimal approximation has been recovered. To cope with this problem, a mathematical study about the properties of sparse approximations is performed. From this, a test to check whether a given sparse approximation is the sparsest is provided. The second part of this thesis presents a novel image approximation scheme, based on the use of a redundant dictionary. This scheme allows to have a good approximation of an image with a number of terms much smaller than the dimension of the signal. This novel approximation scheme is based on a dictionary formed by a combination of anisotropically refined and rotated wavelet-like mother functions and Gaussians. An efficient Full Search Matching Pursuit algorithm to perform the image decomposition in such a dictionary is designed. Finally, a geometric image coding scheme based on the image approximated over the anisotropic and rotated dictionary of basis functions is designed. The coding performances of this dictionary are studied. Coefficient quantization appears to be of crucial importance in the design of a Matching Pursuit based coding scheme. Thus, a quantization scheme for the MP coefficients has been designed, based on the theoretical energy upper bound of the MP algorithm and the empirical observations of the coefficient distribution and evolution. Thanks to this quantization, our image coder provides low to medium bit-rate image approximations, while it allows for on the fly resolution switching and several other affine image transformations to be performed directly in the transformed domain

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

Entropy in Image Analysis II

Image analysis is a fundamental task for any application where extracting information from images is required. The analysis requires highly sophisticated numerical and analytical methods, particularly for those applications in medicine, security, and other fields where the results of the processing consist of data of vital importance. This fact is evident from all the articles composing the Special Issue "Entropy in Image Analysis II", in which the authors used widely tested methods to verify their results. In the process of reading the present volume, the reader will appreciate the richness of their methods and applications, in particular for medical imaging and image security, and a remarkable cross-fertilization among the proposed research areas