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

Dual-tree Complex Wavelet Transform based Local Binary Pattern Weighted Histogram Method for Palmprint Recognition

In the paper, we improve the Local Binary Pattern Histogram (LBPH) approach and combine it with Dual-Tree Complex Wavelet Transform (DT-CWT) to propose a Dual-Tree Complex Wavelet Transform based Local Binary Pattern Weighted Histogram (DT-CWT based LBPWH) method for palmprint representation and recognition. The approximate shift invariant property of the DT-CWT and its good directional selectively in 2D make it a very appealing choice for palmprint representation. LBPH is a powerful texture description method, which considers both shape and texture information to represent an image. To enhance the representation capability of LBPH, a weight set is computed and assigned to the finial feature histogram. Here we needn't construct a palmprint model by a train sample set, which is not like some methods based on subspace discriminant analysis or statistical learning. In the approach, a palmprint image is first decomposed into multiple subbands by using DT-CWT. After that, each subband in complex wavelet domain is divided into non-overlapping sub-regions. Then LBPHs are extracted from each sub-region in each subband, and lastly, all of LBPHs are weighted and concatenated into a single feature histogram to effectively represent the palmprint image. A Chi square distance is used to measure the similarity of different feature histograms and the finial recognition is performed by the nearest neighborhood classifier. A group of optimal parameters is chosen by 20 verification tests on our palmprint database. In addition, the recognition results on our palmprint database and the database from the Hong Kong Polytechnic University show the proposed method outperforms other methods

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

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

Matched wavelet construction and its application to target detection

This dissertation develops a new wavelet design technique that produces a wavelet that matches a desired signal in the least squares sense. The Wavelet Transform has become very popular in signal and image processing over the last 6 years because it is a linear transform with an infinite number of possible basis functions that provides localization in both time (space) and frequency (spatial frequency). The Wavelet Transform is very similar to the matched filter problem, where the wavelet acts as a zero mean matched filter. In pattern recognition applications where the output of the Wavelet Transform is to be maximized, it is necessary to use wavelets that are specifically matched to the signal of interest. Most current wavelet design techniques, however, do not design the wavelet directly, but rather, build a composite wavelet from a library of previously designed wavelets, modify the bases in an existing multiresolution analysis or design a multiresolution analysis that is generated by a scaling function which has a specific corresponding wavelet. In this dissertation, an algorithm for finding both symmetric and asymmetric matched wavelets is developed. It will be shown that under certain conditions, the matched wavelets generate an orthonormal basis of the Hilbert space containing all finite energy signals. The matched orthonormal wavelets give rise to a pair of Quadrature Mirror Filters (QMF) that can be used in the fast Discrete Wavelet Transform. It will also be shown that as the conditions are relaxed, the algorithm produces dyadic wavelets which when used in the Wavelet Transform provides significant redundancy in the transform domain. Finally, this dissertation develops a shift, scale and rotation invariant technique for detecting an object in an image using the Wavelet Radon Transform (WRT) and matched wavelets. The detection algorithm consists of two levels. The first level detects the location, rotation and scale of the object, while the second level detects the fine details in the object. Each step of the wavelet matching algorithm and the object detection algorithm is demonstrated with specific examples

Hybrid Discrete Wavelet Transform and Gabor Filter Banks Processing for Features Extraction from Biomedical Images

A new methodology for automatic feature extraction from biomedical images and subsequent classification is presented. The approach exploits the spatial orientation of high-frequency textural features of the processed image as determined by a two-step process. First, the two-dimensional discrete wavelet transform(DWT) is applied to obtain the HH high-frequency subband image. Then, a Gabor filter bank is applied to the latter at different frequencies and spatial orientations to obtain new Gabor-filtered image whose entropy and uniformity are computed. Finally, the obtained statistics are fed to a support vector machine (SVM) binary classifier. The approach was validated on mammograms, retina, and brain magnetic resonance (MR) images.The obtained classification accuracies show better performance in comparison to common approaches that use only the DWT or Gabor filter banks for feature extraction

Pattern detection and recognition using over-complete and sparse representations

Recent research in harmonic analysis and mammalian vision systems has revealed that over-complete and sparse representations play an important role in visual information processing. The research on applying such representations to pattern recognition and detection problems has become an interesting field of study. The main contribution of this thesis is to propose two feature extraction strategies - the global strategy and the local strategy - to make use of these representations. In the global strategy, over-complete and sparse transformations are applied to the input pattern as a whole and features are extracted in the transformed domain. This strategy has been applied to the problems of rotation invariant texture classification and script identification, using the Ridgelet transform. Experimental results have shown that better performance has been achieved when compared with Gabor multi-channel filtering method and Wavelet based methods. The local strategy is divided into two stages. The first one is to analyze the local over-complete and sparse structure, where the input 2-D patterns are divided into patches and the local over-complete and sparse structure is learned from these patches using sparse approximation techniques. The second stage concerns the application of the local over-complete and sparse structure. For an object detection problem, we propose a sparsity testing technique, where a local over-complete and sparse structure is built to give sparse representations to the text patterns and non-sparse representations to other patterns. Object detection is achieved by identifying patterns that can be sparsely represented by the learned. structure. This technique has been applied. to detect texts in scene images with a recall rate of 75.23% (about 6% improvement compared with other works) and a precision rate of 67.64% (about 12% improvement). For applications like character or shape recognition, the learned over-complete and sparse structure is combined. with a Convolutional Neural Network (CNN). A second text detection method is proposed based on such a combination to further improve (about 11% higher compared with our first method based on sparsity testing) the accuracy of text detection in scene images. Finally, this method has been applied to handwritten Farsi numeral recognition, which has obtained a 99.22% recognition rate on the CENPARMI Database and a 99.5% recognition rate on the HODA Database. Meanwhile, a SVM with gradient features achieves recognition rates of 98.98% and 99.22% on these databases respectivel

Directional multiresolution image representations

Efficient representation of visual information lies at the foundation of many image processing tasks, including compression, filtering, and feature extraction. Efficiency of a representation refers to the ability to capture significant information of an object of interest in a small description. For practical applications, this representation has to be realized by structured transforms and fast algorithms. Recently, it has become evident that commonly used separable transforms (such as wavelets) are not necessarily best suited for images. Thus, there is a strong motivation to search for more powerful schemes that can capture the intrinsic geometrical structure of pictorial information. This thesis focuses on the development of new "true" two-dimensional representations for images. The emphasis is on the discrete framework that can lead to algorithmic implementations. The first method constructs multiresolution, local and directional image expansions by using non-separable filter banks. This discrete transform is developed in connection with the continuous-space curvelet construction in harmonic analysis. As a result, the proposed transform provides an efficient representation for two-dimensional piecewise smooth signals that resemble images. The link between the developed filter banks and the continuous-space constructions is set up in a newly defined directional multiresolution analysis. The second method constructs a new family of block directional and orthonormal transforms based on the ridgelet idea, and thus offers an efficient representation for images that are smooth away from straight edges. Finally, directional multiresolution image representations are employed together with statistical modeling, leading to powerful texture models and successful image retrieval systems

Un descripteur efficace pour la reconnaissance des symboles graphiques basé sur la transformée de Radon

ISBN : 978-9973-37-582-7National audienceLe choix des descripteurs constitue un problème majeur dans les systèmes d'analyse d'images, car ces descripteurs conditionnent fortement le résultat final de la recherche ou de la classification. Dans cet article, après avoir proposé un nouveau descripteur invariant aux transformations géométriques usuelles, basé sur la transformée de Radon appelé phi-signature, un autre ensemble de descripteurs qui découle des transformations en ondelettes de ladite signature et de la R-signature, est présenté. Les résultats expérimentaux montrent l'efficacité de ces descripteurs, particulièrement pour des formes complexes non pleines de type symbole graphique