MULTIRIDGELETS FOR TEXTURE ANALYSIS

Directional wavelets have orientation selectivity and thus are able to efficiently represent highly anisotropic elements such as line segments and edges. Ridgelet transform is a kind of directional multi-resolution transform and has been successful in many image processing and texture analysis applications. The objective of this research is to develop multi-ridgelet transform by applying multiwavelet transform to the Radon transform so as to attain attractive improvements. By adapting the cardinal orthogonal multiwavelets to the ridgelet transform, it is shown that the proposed cardinal multiridgelet transform (CMRT) possesses cardinality, approximate translation invariance, and approximate rotation invariance simultaneously, whereas no single ridgelet transform can hold all these properties at the same time. These properties are beneficial to image texture analysis. This is demonstrated in three studies of texture analysis applications. Firstly a texture database retrieval study taking a portion of the Brodatz texture album as an example has demonstrated that the CMRT-based texture representation for database retrieval performed better than other directional wavelet methods. Secondly the study of the LCD mura defect detection was based upon the classification of simulated abnormalities with a linear support vector machine classifier, the CMRT-based analysis of defects were shown to provide efficient features for superior detection performance than other competitive methods. Lastly and the most importantly, a study on the prostate cancer tissue image classification was conducted. With the CMRT-based texture extraction, Gaussian kernel support vector machines have been developed to discriminate prostate cancer Gleason grade 3 versus grade 4. Based on a limited database of prostate specimens, one classifier was trained to have remarkable test performance. This approach is unquestionably promising and is worthy to be fully developed

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

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

Curvelets and Ridgelets

International audienceDespite the fact that wavelets have had a wide impact in image processing, they fail to efficiently represent objects with highly anisotropic elements such as lines or curvilinear structures (e.g. edges). The reason is that wavelets are non-geometrical and do not exploit the regularity of the edge curve. The Ridgelet and the Curvelet [3, 4] transforms were developed as an answer to the weakness of the separable wavelet transform in sparsely representing what appears to be simple building atoms in an image, that is lines, curves and edges. Curvelets and ridgelets take the form of basis elements which exhibit high directional sensitivity and are highly anisotropic [5, 6, 7, 8]. These very recent geometric image representations are built upon ideas of multiscale analysis and geometry. They have had an important success in a wide range of image processing applications including denoising [8, 9, 10], deconvolution [11, 12], contrast enhancement [13], texture analysis [14, 15], detection [16], watermarking [17], component separation [18], inpainting [19, 20] or blind source separation[21, 22]. Curvelets have also proven useful in diverse fields beyond the traditional image processing application. Let’s cite for example seismic imaging [10, 23, 24], astronomical imaging [25, 26, 27], scientific computing and analysis of partial differential equations [28, 29]. Another reason for the success of ridgelets and curvelets is the availability of fast transform algorithms which are available in non-commercial software packages following the philosophy of reproducible research, see [30, 31]

Face Recognition Using Curvelet and Waveatom Transform

The field of digital image processing is continually evolving. Nowadays, there is a significant increase in the level of interest in image morphology, neural networks, full-color image processing, image data compression and image recognition. This work deals with image recognition with the application of face recognition. Some people think that face recognition is an easy task for computer system as for humans, but in reality most of the face recognition systems can’t achieve a complete reliable performance because there are many factors affect on the process of recognition like: large variations in facial approach, head size and orientation, and change in environmental conditions, all these factors makes face recognition one of the fundamental problems in pattern analysis, other factors that impact the performance are the accuracy of face location stage and the number of actual face recognition techniques used in each system. So face recognition from still and video images is emerging as an active research area with numerous commercial and law enforcement application. This research identifies two techniques for face features extraction based on two different multiresolution analysis tools; the first called Curvelet transform while the second is waveatom transform. The resultant features are inputted to train via two famous classifiers; one of them is the artificial neural network (ANN) and the other is hidden Markov model (HMM). Experiments are carried out on two well-known datasets; AT&T dataset consists of 400 images corresponding to 40 people, and Essex Grimace dataset consists of 360 images corresponding to 18 people. Experimental results show the strength of both curvelets and waveatom features. On one hand, waveatom features obtained the highest accuracy rate of 99% and 100% with HMM classifier, and 98% and 100% with ANN classifier, for AT&T and Essex Grimace datasets, respectively. On the other hand, two levels Curvelet features achieved accuracy rate of 98% and 100% with HMM classifier, and 97% and 100% with ANN classifier, for AT&T and Essex Grimace datasets, respectively. A comparative study for waveatom with wavelet-based, curvelet-based, and traditional Principal Component Analysis (PCA) techniques is also presented. The proposed techniques supersede all of them. And shows the robustness of feature extraction methods used against included and occluded effects. Also, indicates the potential of HMM over ANN, as they are classifiers

Biometric Applications Based on Multiresolution Analysis Tools

This dissertation is dedicated to the development of new algorithms for biometric applications based on multiresolution analysis tools. Biometric is a unique, measurable characteristic of a human being that can be used to automatically recognize an individual or verify an individual\u27s identity. Biometrics can measure physiological, behavioral, physical and chemical characteristics of an individual. Physiological characteristics are based on measurements derived from direct measurement of a part of human body, such as, face, fingerprint, iris, retina etc. We focussed our investigations to fingerprint and face recognition since these two biometric modalities are used in conjunction to obtain reliable identification by various border security and law enforcement agencies. We developed an efficient and robust human face recognition algorithm for potential law enforcement applications. A generic fingerprint compression algorithm based on state of the art multiresolution analysis tool to speed up data archiving and recognition was also proposed. Finally, we put forth a new fingerprint matching algorithm by generating an efficient set of fingerprint features to minimize false matches and improve identification accuracy. Face recognition algorithms were proposed based on curvelet transform using kernel based principal component analysis and bidirectional two-dimensional principal component analysis and numerous experiments were performed using popular human face databases. Significant improvements in recognition accuracy were achieved and the proposed methods drastically outperformed conventional face recognition systems that employed linear one-dimensional principal component analysis. Compression schemes based on wave atoms decomposition were proposed and major improvements in peak signal to noise ratio were obtained in comparison to Federal Bureau of Investigation\u27s wavelet scalar quantization scheme. Improved performance was more pronounced and distinct at higher compression ratios. Finally, a fingerprint matching algorithm based on wave atoms decomposition, bidirectional two dimensional principal component analysis and extreme learning machine was proposed and noteworthy improvements in accuracy were realized

Auswertung und Charakterisierung dreidimensionaler Messdaten technischer Oberflächen mit Riefentexturen

Im Rahmen dieser Arbeit werden Charakterisierung optisch erfasster 3D-Oberflächendaten untersucht. Für eine effiziente Auswertung ist es nötig, die Texturkomponenten zu zerlegen. Zwei Ansätze zur Separation von Riefentexturen werden vorgestellt, die auf einer geometrischen bzw. spektralen Modellierung beruhen. Auf Basis der Separation wird die Charakterisierung vorgestellt, deren robuste und zuverlässige Kenngrößen zur Beurteilung der Oberflächenqualität herangezogen werden können

Fast Fourier Transform at Nonequispaced Nodes and Applications

The direct computation of the discrete Fourier transform at arbitrary nodes requires O(NM) arithmetical operations, too much for practical purposes. For equally spaced nodes the computation can be done by the well known fast Fourier transform (FFT) in only O(N log N) arithmetical operations. Recently, the fast Fourier transform for nonequispaced nodes (NFFT) was developed for the fast approximative computation of the above sums in only O(N log N + M log 1/e), where e denotes the required accuracy. The principal topics of this thesis are generalizations and applications of the NFFT. This includes the following subjects: - Algorithms for the fast approximative computation of the discrete cosine and sine transform at nonequispaced nodes are developed by applying fast trigonometric transforms instead of FFTs. - An algorithm for the fast Fourier transform on hyperbolic cross points with nonequispaced spatial nodes in 2 and 3 dimensions based on the NFFT and an appropriate partitioning of the hyperbolic cross is proposed. - A unified linear algebraic approach to recent methods for the fast computation of matrix-vector-products with special dense matrices, namely the fast multipole method, fast mosaic-skeleton approximation and H-matrix arithmetic, is given. Moreover, the NFFT-based summation algorithm by Potts and Steidl is further developed and simplified by using algebraic polynomials instead of trigonometric polynomials and the error estimates are improved. - A new algorithm for the characterization of engineering surface topographies with line singularities is proposed. It is based on hard thresholding complex ridgelet coefficients combined with total variation minimization. The discrete ridgelet transform is designed by first using a discrete Radon transform based on the NFFT and then applying a dual-tree complex wavelet transform. - A new robust local scattered data approximation method is introduced. It is an advancement of the moving least squares approximation (MLS) and generalizes an approach of van den Boomgard and van de Weijer to scattered data. In particular, the new method is space and data adaptive