Graph Spectral Image Processing

Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains pixels that reside on a regularly sampled 2D grid, if one can design an appropriate underlying graph connecting pixels with weights that reflect the image structure, then one can interpret the image (or image patch) as a signal on a graph, and apply GSP tools for processing and analysis of the signal in graph spectral domain. In this article, we overview recent graph spectral techniques in GSP specifically for image / video processing. The topics covered include image compression, image restoration, image filtering and image segmentation

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

Locally Adaptive Frames in the Roto-Translation Group and their Applications in Medical Imaging

Locally adaptive differential frames (gauge frames) are a well-known effective tool in image analysis, used in differential invariants and PDE-flows. However, at complex structures such as crossings or junctions, these frames are not well-defined. Therefore, we generalize the notion of gauge frames on images to gauge frames on data representations $U:\mathbb{R}^{d} \rtimes S^{d-1} \to \mathbb{R}$ defined on the extended space of positions and orientations, which we relate to data on the roto-translation group $SE(d)$, $d=2,3$. This allows to define multiple frames per position, one per orientation. We compute these frames via exponential curve fits in the extended data representations in $SE(d)$. These curve fits minimize first or second order variational problems which are solved by spectral decomposition of, respectively, a structure tensor or Hessian of data on $SE(d)$. We include these gauge frames in differential invariants and crossing preserving PDE-flows acting on extended data representation $U$ and we show their advantage compared to the standard left-invariant frame on $SE(d)$. Applications include crossing-preserving filtering and improved segmentations of the vascular tree in retinal images, and new 3D extensions of coherence-enhancing diffusion via invertible orientation scores

A textural deep neural network architecture for mechanical failure analysis

Nowadays, many classification problems are approached with deep learning architectures, and the results are outstanding compared to the ones obtained with traditional computer vision approaches. However, when it comes to texture, deep learning analysis has not had the same success as for other tasks. The texture is an inherent characteristic of objects, and it is the main descriptor for many applications in the computer vision field, however due to its stochastic appearance, it is difficult to obtain a mathematical model for it. According to the state of the art, deep learning techniques have some limitations when it comes to learning textural features; and, to classify texture using deep neural networks, it is essential to integrate them with handcrafted features or develop an architecture that resembles these features. By solving this problem, it would be possible to contribute in different applications, such as fractographic analysis. To achieve the best performance in any industry, it is important that the companies have a failure analysis, able to show the flaws’ causes, offer applications and solutions and generate alternatives that allow the customers to obtain more efficient components and productions. The failure of an industrial element has consequences such as significant economic losses, and in some cases, even human losses. With this analysis it is possible to examine the background of the damaged piece in order to find how and why it fails, and to help prevent future failures, in order to implement safer conditions. The visual inspection is the basis for the generation of every fractographic process in failure analysis and it is the main tool for fracture classification. This process is usually done by non-expert personnel on the topic, and normally they do not have the knowledge or experience required for the job, which, without question, increases the possibilities of generating a wrong classification and negatives results in the whole process. This research focuses on the development of a visual computer system that implements a textural deep learning architecture. Several approaches were taken into account, including combining deep learning techniques with traditional handcrafted features, and the development of a new architecture based on the wavelet transform and the multiresolution analysis. The algorithm was test on textural benchmark datasets and on the classification of mechanical fractures with particular texture and marks on surfaces of crystalline materials.Actualmente, diferentes problemas computacionales utilizan arquitecturas de aprendizaje profundo como enfoque principal. Obteniendo resultados sobresalientes comparados con los obtenidos por métodos tradicionales de visión por computador. Sin embargo, cuando se trata de texturas, los análisis de textura no han tenido el mismo éxito que para otras tareas. La textura es una característica inherente de los objetos y es el descriptor principal para diferentes aplicaciones en el campo de la visión por computador. Debido a su apariencia estocástica difícilmente se puede obtener un modelo matemático para describirla. De acuerdo con el estado-del-arte, las técnicas de aprendizaje profundo presentan limitaciones cuando se trata de aprender características de textura. Para clasificarlas, se hace esencial combinarlas con características tradicionales o desarrollar arquitecturas de aprendizaje profundo que reseemblen estas características. Al solucionar este problema es posible contribuir a diferentes aplicaciones como el análisis fractográfico. Para obtener el mejor desempeño en cualquier tipo de industria es importante obtener análisis fractográfico, el cual permite determinar las causas de los diferentes fallos y generar las alternativas para obtener componentes más eficientes. La falla de un elemento mecánico tiene consecuencias importantes tal como pérdidas económicas y en algunos casos incluso pérdidas humanas. Con estos análisis es posible examinar la historia de las piezas dañadas con el fin de entender porqué y cómo se dio el fallo en primer lugar y la forma de prevenirla. De esta forma implementar condiciones más seguras. La inspección visual es la base para la generación de todo proceso fractográfico en el análisis de falla y constituye la herramienta principal para la clasificación de fracturas. El proceso, usualmente, es realizado por personal no-experto en el tema, que normalmente, no cuenta con el conocimiento o experiencia necesarios requeridos para el trabajo, lo que sin duda incrementa las posibilidades de generar una clasificación errónea y, por lo tanto, obtener resultados negativos en todo el proceso. Esta investigación se centra en el desarrollo de un sistema visual de visión por computado que implementa una arquitectura de aprendizaje profundo enfocada en el análisis de textura. Diferentes enfoques fueron tomados en cuenta, incluyendo la combinación de técnicas de aprendizaje profundo con características tradicionales y el desarrollo de una nueva arquitectura basada en la transformada wavelet y el análisis multiresolución. El algorítmo fue probado en bases de datos de referencia en textura y en la clasificación de fracturas mecánicas en materiales cristalinos, las cuales presentan texturas y marcas características dependiendo del tipo de fallo generado sobre la pieza.Fundación CEIBADoctorad

Selection of Wavelet Basis Function for Image Compression : a Review

Wavelets are being suggested as a platform for various tasks in image processing. The advantage of wavelets lie in its time frequency resolution. The use of different basis functions in the form of different wavelets made the wavelet analysis as a destination for many applications. The performance of a particular technique depends on the wavelet coefficients arrived after applying the wavelet transform. The coefficients for a specific input signal depends on the basis functions used in the wavelet transform. Hence in this paper toward this end, different basis functions and their features are presented. As the image compression task depends on wavelet transform to large extent from few decades, the selection of basis function for image compression should be taken with care. In this paper, the factors influencing the performance of image compression are presented

MASCOT : metadata for advanced scalable video coding tools : final report

The goal of the MASCOT project was to develop new video coding schemes and tools that provide both an increased coding efficiency as well as extended scalability features compared to technology that was available at the beginning of the project. Towards that goal the following tools would be used: - metadata-based coding tools; - new spatiotemporal decompositions; - new prediction schemes. Although the initial goal was to develop one single codec architecture that was able to combine all new coding tools that were foreseen when the project was formulated, it became clear that this would limit the selection of the new tools. Therefore the consortium decided to develop two codec frameworks within the project, a standard hybrid DCT-based codec and a 3D wavelet-based codec, which together are able to accommodate all tools developed during the course of the project

Wavelet Based Feature Extraction and Dimension Reduction for the Classification of Human Cardiac Electrogram Depolarization Waveforms

An essential task for a pacemaker or implantable defibrillator is the accurate identification of rhythm categories so that the correct electrotherapy can be administered. Because some rhythms cause a rapid dangerous drop in cardiac output, it is necessary to categorize depolarization waveforms on a beat-to-beat basis to accomplish rhythm classification as rapidly as possible. In this thesis, a depolarization waveform classifier based on the Lifting Line Wavelet Transform is described. It overcomes problems in existing rate-based event classifiers; namely, (1) they are insensitive to the conduction path of the heart rhythm and (2) they are not robust to pseudo-events. The performance of the Lifting Line Wavelet Transform based classifier is illustrated with representative examples. Although rate based methods of event categorization have served well in implanted devices, these methods suffer in sensitivity and specificity when atrial, and ventricular rates are similar. Human experts differentiate rhythms by morphological features of strip chart electrocardiograms. The wavelet transform is a simple approximation of this human expert analysis function because it correlates distinct morphological features at multiple scales. The accuracy of implanted rhythm determination can then be improved by using human-appreciable time domain features enhanced by time scale decomposition of depolarization waveforms. The purpose of the present work was to determine the feasibility of implementing such a system on a limited-resolution platform. 78 patient recordings were split into equal segments of reference, confirmation, and evaluation sets. Each recording had a sampling rate of 512Hz, and a significant change in rhythm in the recording. The wavelet feature generator implemented in Matlab performs anti-alias pre-filtering, quantization, and threshold-based event detection, to produce indications of events to submit to wavelet transformation. The receiver operating characteristic curve was used to rank the discriminating power of the feature accomplishing dimension reduction. Accuracy was used to confirm the feature choice. Evaluation accuracy was greater than or equal to 95% over the IEGM recordings