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

The development of the quaternion wavelet transform

The purpose of this article is to review what has been written on what other authors have called quaternion wavelet transforms (QWTs): there is no consensus about what these should look like and what their properties should be. We briefly explain what real continuous and discrete wavelet transforms and multiresolution analysis are and why complex wavelet transforms were introduced; we then go on to detail published approaches to QWTs and to analyse them. We conclude with our own analysis of what it is that should define a QWT as being truly quaternionic and why all but a few of the “QWTs” we have described do not fit our definition

Facial Expression Recognition Using Multiresolution Analysis

Facial expression recognition from images or videos attracts interest of research community owing to its applications in human-computer interaction and intelligent transportation systems. The expressions cause non-rigid motions of the face-muscles thereby changing the orientations of facial curves. Wavelets and Gabor wavelets have been used effectively for recognition of these oriented features. Although wavelets are the most popular multiresolution method, they have limited orientation-selectivity/directionality. Gabor wavelets are highly directional but they are not multiresolution methods in the true sense of the term. Proposed work is an effort to apply directional multiresolution representations like curvelets and contourlets to explore the multiresolution space in multiple ways for extracting effective facial features. Extensive comparisons between different multiresolution transforms and state of the art methods are provided to demonstrate the promise of the work. The problem of drowsiness detection, a special case of expression recognition, is also addressed using a proposed feature extraction method

NOVEL OFDM SYSTEM BASED ON DUAL-TREE COMPLEX WAVELET TRANSFORM

The demand for higher and higher capacity in wireless networks, such as cellular, mobile and local area network etc, is driving the development of new signaling techniques with improved spectral and power efficiencies. At all stages of a transceiver, from the bandwidth efficiency of the modulation schemes through highly nonlinear power amplifier of the transmitters to the channel sharing between different users, the problems relating to power usage and spectrum are aplenty. In the coming future, orthogonal frequency division multiplexing (OFDM) technology promises to be a ready solution to achieving the high data capacity and better spectral efficiency in wireless communication systems by virtue of its well-known and desirable characteristics. Towards these ends, this dissertation investigates a novel OFDM system based on dual-tree complex wavelet transform (D

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

Statistical Characterization of Morphodynamic Signals Using Wavelet Analysis

Morphodynamic and hydrodynamic properties are concomitantly part of the entire dynamic of river systems and commonly present both temporal and spatial persistent variability. Therefore, the study of both river morphodynamic signals (e.g. bed forms and meandering and anabranching river morphometrics) and hydrodynamic signals (e.g. velocity fields, sediment concentrations) requires both temporal and spatial multi-scale signal representations. The present research is focused on the former type of signals and it is a first attempt to discriminate such signals and, subsequently, develop the theoretical background to link these processes at different spatial and temporal scales and determine the scales that have more influence on river evolution. The main contribution of this study are: [1] to design a methodology to discriminate bed form features (e.g. bars, dunes and ripples) via the combined application of robust spline filters and one-dimensional continuous wavelet transforms, allowing the quantitative recognition of bed form hierarchies. The methodology was tested by using synthetic bed form signals and subsequently applied to the analysis of bed form features from the Parana River, Argentina. [2] To develop a methodology for the statistical analysis of the spatial distribution of meandering rivers morphometrics by coupling the capabilities of one-dimensional wavelet transforms, principal component analysis and Frechet distance. A universal river classification method is also proposed. [3] To perform a novel study of the planimetric configuration of confluences in tropical free meandering rivers located in the upper Amazon catchment. River confluences in tropical environments represent areas where biota is concentrated; therefore, a better understanding and characterization of these features has a particular importance for the Amazonian ecosystem. [4] To evaluate the potential of two-dimensional wavelet transforms in the analysis of bed form features. The broader impact will be an improved understanding of river morphodynamics of the upper Amazon River for practical applications such as navigability. Furthermore, the project will provide an updated statistical analysis of the meandering rivers dynamics for practical applications, including erosion control, river ecology, and habitat restoration. The developed statistical tool will be included as an application of the RVR Meander platform (www.rvrmeander.org), which is a broadly used software for river restoration