Spatially-Variant Directional Mathematical Morphology Operators Based on a Diffused Average Squared Gradient Field

International audienceThis paper proposes an approach for mathematical morphology operators whose structuring element can locally adapt its orientation across the pixels of the image. The orientation at each pixel is extracted by means of a diffusion process of the average squared gradient field. The resulting vector field, the average squared gradient vector flow, extends the orientation information from the edges of the objects to the homogeneous areas of the image. The provided orientation field is then used to perform a spatially variant filtering with a linear structuring element. Results of erosion, dilation, opening and closing spatially-variant on binary images prove the validity of this theoretical sound and novel approach

Adaptive morphological filters based on a multiple orientation vector field dependent on image local features

This paper addresses the formulation of adaptive morphological filters based on spatially-variant structuring elements. The adaptivity of these filters is achieved by modifying the shape and orientation of the structuring elements according to a multiple orientation vector field. This vector field is provided by means of a bank of directional openings which can take into account the possible multiple orientations of the contours in the image. After reviewing and formalizing the definition of the spatially-variant dilation, erosion, opening and closing, the proposed structuring elements are described. These spatially-variant structuring elements are based on ellipses which vary over the image domain adapting locally their orientation according to the multiple orientation vector field and their shape (the eccentricity of the ellipses) according to the distance to relevant contours of the objects. The proposed adaptive morphological filters are used on gray-level images and are compared with spatially-invariant filters, with spatially-variant filters based on a single orientation vector field, and with adaptive morphological bilateral filters. Results show that the morphological filters based on a multiple orientation vector field are more adept at enhancing and preserving structures which contains more than one orientation

Direction-adaptive grey-level morphology. Application to 3D vascular brain imaging

International audienceSegmentation and analysis of blood vessels is an important issue in medical imaging. In 3D cerebral angiographic data, the vascular signal is however hard to accurately detect and can, in particular, be disconnected. In this article, we present a procedure utilising both linear, Hessian-based and morphological methods for blood vessel edge enhancement and reconnection. More specifically, multi-scale second-order derivative analysis is performed to detect candidate vessels as well as their orientation. This information is then fed to a spatially-variant morphological filter for reconnection and reconstruction. The result is a fast and effective vessel-reconnecting method

Estimación de la orientación múltiple mediante un banco de filtros y su uso en el desarrollo de aplicaciones de procesado de imagen

Mención Europeo / Mención Internacional: Concedido.[SPA] Esta tesis doctoral se presenta bajo la modalidad de compendio de publicaciones. En las últimas décadas, la estimación de orientación se ha convertido en una tarea clave del procesado de imagen, dada su capacidad para extraer características de bajo nivel y su aplicación en el análisis de datos. Existen un gran número de aplicaciones donde la estimación de orientación juega un papel fundamental como son: el análisis de huellas dactilares, extracción de puntos característicos, bifurcaciones, esquinas o intersecciones, filtrado adaptativo o seguimiento de objetos, entre otras. Sin embargo, con el paso del tiempo han aparecido diferentes problemas asociados a la estimación de orientación que pueden complicar este proceso. Los más importantes a destacar son los siguientes: las limitaciones que presentan muchos de los métodos de estimación en estructuras complejas, por ejemplo, estructuras con varias orientaciones asociadas, el incremento de la complejidad computacional de los métodos más modernos o la dependencia de éstos a solo unas determinadas aplicaciones. Resulta en estos momentos, por tanto, una tarea clave conseguir métodos de estimación que sean lo más globales y genéricos posibles, en otras palabras, lo más independientes del tipo de imagen con la que se trabaje y del campo de aplicación. En esta Tesis doctoral, en primer lugar, se aborda una revisión de los conceptos más importantes de la estimación de orientación, como es el concepto de estructura, orientación y sus propiedades principales. También se describen los métodos de estimación de orientaciones más importantes: tensor estructural, bancos de filtros, gradiente al cuadrado promediado, etc. Y las aplicaciones más importantes como la detección de texturas, extracción de características, análisis de huellas dactilares, filtrado variante o seguimiento de objetos, entre otras. Las contribuciones principales a esta Tesis son dos. En primer lugar, la propuesta de un marco de trabajo (de estimación de orientaciones) capaz de sistematizar el proceso de estimación de orientaciones, independientemente del tipo de estructuras o el tipo de aplicación. El marco propuesto está basado en una de las técnicas de estimación de orientación más usadas, los bancos de filtros. Durante este trabajo, éstos han sido probados en multitud de escenarios mientras se consideraban diferentes familias de filtros para su aplicación. En segundo lugar, se abordan casos prácticos de aplicación del marco de trabajo propuesto con el objetivo de mostrar sus excelentes capacidades en aplicaciones muy dispares, mostrando su potencial en multitud de posibilidades. Dado que el método de presentación de la presente Tesis doctoral es mediante un compendio de artículos, la organización de esta memoria constará de un primer capítulo de introducción y estado del arte. Seguidamente se mostrarán, de forma coherente y organizada, los artículos con los resultados obtenidos durante el periodo de investigación de la Tesis, con una introducción para cada uno de los artículos incluidos en este compendio. Finalmente, el capítulo de conclusiones y trabajo futuro cierra la Tesis.[ENG] This doctoral dissertation has been presented in the form of thesis by publication. In the last decades, image orientation estimation has become in a fundamental task of image processing, due to its ability to extract low level features and its application to data analysis. There are a wide number of applications where the image orientation estimation plays and important role, some of these are: fingerprint analysis, feature extractions such as bifurcation, junction and corner, adaptive filtering or tracking applications. However, with the pass of time, different problems related to orientation estimation have appeared and they can complicate this process. The most important problems to highlight are: difficult of a wide number of methods to estimate the orientation of complex object structures, for example, structures with multiple orientations associated, high computational cost of modern methods or dependence on the application framework. Therefore, nowadays, the obtention of global and generics methods, in other words, methods as independent as possible from the image and the application, has become in a important task. In this Thesis, firstly, a review of main concepts of image orientation have been carried out, such as the concept of structure, orientation and their main properties. The most important methods have been described, as e.g., structural tensor, bank of filters, average square gradient, etc. And the most important applications based on image orientation estimation as texture analysis, feature extraction, fingerprint analysis, object tracking and space variant filtering, among others. The main contributions to this Thesis are two. First one is the proposal of a new framework for image orientation estimation, which can systematize this process, making it independent of image type and application. The proposed framework is based on one of the most used estimation orientation techniques, the bank of filters. Throughout this work, it have been tested in a wide variety of scenarios, considering different families of filters for their application. Secondly, the proposed framework has been evaluated in practical applications to show its ability and potential. This Thesis has been carried out by the method of compendium of publications, it has been organized as follows. Chapter one shows an introduction and a review of the state of art. Chapter two shows the journal papers and other contributions done during the research period of this Thesis. Finally, Chapter three shows the conclusion and future work.El trabajo de esta Tesis ha estado financiado parcialmente por el Ministerio de Economía, Industria y Competitividad (Proyecto PI17/00771) y la Universidad Politécnica de Valencia - Instituto Interuniversitario de Investigación en Bioingeniería y Tecnología Orientada al Ser Humano. Labhuman- conjuntamente con la Universidad Politécnica de Cartagena (Proyectos 4106/15TIC y 3626/13TIC).Los artículos y capítulos de libros que forman la tesis son los siguientes: Artículo 1: A.G. Legaz-Aparicio, R. Verdú-Monedero, J. Angulo, “Multiscale Estimation of Multiple Orientations based on Morphological Directional Openings”, Signal, Image and Video Processing, 2018, Accepted, (doi:10.1007/s11760-018-1276-y). ISI-JCR(2017): 1.643, Posición 163 de 260 (T2, Q3), cat ENGINEERING, ELECTRICAL & ELECTRONIC. Artículo 2: Álvar-Ginés Legaz-Aparicio, Rafael Verdú-Monedero, Juan Morales-Sanchez, Jorge Larrey- Ruiz, Jesús Angulo, “Detection of Retinal Vessel Bifurcation by Means of Multiple Orientation Estimation Based on Regularized Morphological Openings”. XIII Medierranean Confe-rence on Medical and Biological Engineering and Computing, Sevilla, 2013. Artículo 3: S. Morales, Á. Legaz-Aparicio, V. Naranjo, R. Verdú-Monedero, “Determination of Bifurcation Angles of the Retinal Vascular Tree through Multiple Orientation Estimation ba-sed on Regularized Morphological Openings”, International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS 2015), Lisbon (Portugal), January 2015. Artículo 4: S. Morales, V. Naranjo, J. Angulo, A.G. Legaz-Aparicio, R. Verdú-Monedero, “Retinal network characterization through fundus image processing: signicant point identication on vessel centerline”, Signal Processing: Image Communication, Vol. 59, pp. 50-64, November 2017. ISI-JCR(2017): 2.073, Posición 118 de 260 (T2, Q2), cat ENGINEERING, ELECTRICAL & ELEC-TRONIC. Artículo 5: A.G. Legaz-Aparicio, R. Verdú-Monedero, K. Engan, “Noise Robust and Ro-tation Invariant Framework for Texture Analysis and Classification”, Applied Mathematics and Computation, Volume 335, pp. 124 a 132, October 2018. ISI-JCR(2017): 2.300, Posición 21 de 252 (T1, Q1), cat MATHEMATICS, APPLIED. Artículo 6: Álvar-Ginés Legaz-Aparicio, Rafael Verdú-Monedero, Jesús Angulo, “Adaptive spatially variant morphological filters based on a multiple orientation vector field”, Mathematical modelling in Engineering & Human Behaviour 2016. Artículo 7: A.G. Legaz-Aparicio, R. Verdú-Monedero, J. Angulo, “Adaptive morphological filters based on a multiple orientation vector field dependent on image local features”, Journal of Computational and Applied Mathematics, Vol. 330, pp. 965-981, March 2018. ISI-JCR(2017): 1.632, Posición 49 de 252 (T1, Q1), cat MATHEMATICS, APPLIED.Escuela Internacional de Doctorado de la Universidad Politécnica de CartagenaUniversidad Politécnica de CartagenaPrograma de Doctorado en Tecnologías de la Información y las Comunicaciones por la Universidad Politécnica de Cartagen

Nonlocal smoothing and adaptive morphology for scalar- and matrix-valued images

In this work we deal with two classic degradation processes in image analysis, namely noise contamination and incomplete data. Standard greyscale and colour photographs as well as matrix-valued images, e.g. diffusion-tensor magnetic resonance imaging, may be corrupted by Gaussian or impulse noise, and may suffer from missing data. In this thesis we develop novel reconstruction approaches to image smoothing and image completion that are applicable to both scalar- and matrix-valued images. For the image smoothing problem, we propose discrete variational methods consisting of nonlocal data and smoothness constraints that penalise general dissimilarity measures. We obtain edge-preserving filters by the joint use of such measures rich in texture content together with robust non-convex penalisers. For the image completion problem, we introduce adaptive, anisotropic morphological partial differential equations modelling the dilation and erosion processes. They adjust themselves to the local geometry to adaptively fill in missing data, complete broken directional structures and even enhance flow-like patterns in an anisotropic manner. The excellent reconstruction capabilities of the proposed techniques are tested on various synthetic and real-world data sets.In dieser Arbeit beschäftigen wir uns mit zwei klassischen Störungsquellen in der Bildanalyse, nämlich mit Rauschen und unvollständigen Daten. Klassische Grauwert- und Farb-Fotografien wie auch matrixwertige Bilder, zum Beispiel Diffusionstensor-Magnetresonanz-Aufnahmen, können durch Gauß- oder Impulsrauschen gestört werden, oder können durch fehlende Daten gestört sein. In dieser Arbeit entwickeln wir neue Rekonstruktionsverfahren zum zur Bildglättung und zur Bildvervollständigung, die sowohl auf skalar- als auch auf matrixwertige Bilddaten anwendbar sind. Zur Lösung des Bildglättungsproblems schlagen wir diskrete Variationsverfahren vor, die aus nichtlokalen Daten- und Glattheitstermen bestehen und allgemeine auf Bildausschnitten definierte Unähnlichkeitsmaße bestrafen. Kantenerhaltende Filter werden durch die gemeinsame Verwendung solcher Maße in stark texturierten Regionen zusammen mit robusten nichtkonvexen Straffunktionen möglich. Für das Problem der Datenvervollständigung führen wir adaptive anisotrope morphologische partielle Differentialgleichungen ein, die Dilatations- und Erosionsprozesse modellieren. Diese passen sich der lokalen Geometrie an, um adaptiv fehlende Daten aufzufüllen, unterbrochene gerichtet Strukturen zu schließen und sogar flussartige Strukturen anisotrop zu verstärken. Die ausgezeichneten Rekonstruktionseigenschaften der vorgestellten Techniken werden anhand verschiedener synthetischer und realer Datensätze demonstriert

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

Estimación de la orientación múltiple en imágenes mediante morfología matemática y técnicas de regularización

El presente trabajo describe un novedoso método de estimación de orientaciones múltiples para imágenes. Este método combina la estimación de las orientaciones múltiples de las estructuras de los objetos de la imagen con la difusión de la información de las orientaciones, de esta forma se consigue obtener las orientaciones múltiples en todos los píxeles de la imagen. Para evaluación de las prestaciones se emplean imágenes tanto sintéticas como reales con diversos tipos de escenarios. Por último se presentan las conclusiones y se describen las líneas futuras.Escuela Técnica Superior de Ingeniería de TelecomunicaciónUniversidad Politécnica de Cartagen

Development of High Angular Resolution Diffusion Imaging Analysis Paradigms for the Investigation of Neuropathology

Diffusion weighted magnetic resonance imaging (DW-MRI), provides unique insight into the microstructure of neural white matter tissue, allowing researchers to more fully investigate white matter disorders. The abundance of clinical research projects incorporating DW-MRI into their acquisition protocols speaks to the value this information lends to the study of neurological disease. However, the most widespread DW-MRI technique, diffusion tensor imaging (DTI), possesses serious limitations which restrict its utility in regions of complex white matter. Fueled by advances in DW-MRI acquisition protocols and technologies, a group of exciting new DW-MRI models, developed to address these concerns, are now becoming available to clinical researchers. The emergence of these new imaging techniques, categorized as high angular resolution diffusion imaging (HARDI), has generated the need for sophisticated computational neuroanatomic techniques able to account for the high dimensionality and structure of HARDI data. The goal of this thesis is the development of such techniques utilizing prominent HARDI data models. Specifically, methodologies for spatial normalization, population atlas building and structural connectivity have been developed and validated. These methods form the core of a comprehensive analysis paradigm allowing the investigation of local white matter microarcitecture, as well as, systemic properties of neuronal connectivity. The application of this framework to the study of schizophrenia and the autism spectrum disorders demonstrate its sensitivity sublte differences in white matter organization, as well as, its applicability to large population DW-MRI studies

Development and validation of computational fluid dynamics models for the coupled simulation of heat transfer and fluid flow in the coral microenvironments

This thesis explored the temperature deviations between coral surface temperature and ambient seawater temperature that likely determines the microscale processes involved in coral bleaching. The work presented here applied Computational Fluid Dynamics (CFD) technique coupled with hydrodynamic modelling and ray-tracing to predict coral surface warming due to the effects of stressors. This thesis demonstrates that modelling microscale temperature could yield important insights into thermoregulation in corals, which may lead to a more effective reef management