1,940 research outputs found

    Riemannian mathematical morphology

    No full text
    This paper introduces mathematical morphology operators for real-valued images whose support space is a Riemannian manifold. The starting point consists in replacing the Euclidean distance in the canonic quadratic structuring function by the Riemannian distance used for the adjoint dilation/erosion. We then extend the canonic case to a most general framework of Riemannian operators based on the notion of admissible Riemannian structuring function. An alternative paradigm of morphological Riemannian operators involves an external structuring function which is parallel transported to each point on the manifold. Besides the definition of the various Riemannian dilation/erosion and Riemannian opening/closing, their main properties are studied. We show also how recent results on Lasry-Lions regularization can be used for non-smooth image filtering based on morphological Riemannian operators. Theoretical connections with previous works on adaptive morphology and manifold shape morphology are also considered. From a practical viewpoint, various useful image embedding into Riemannian manifolds are formalized, with some illustrative examples of morphological processing real-valued 3D surfaces

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

    Get PDF
    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

    Amoeba Techniques for Shape and Texture Analysis

    Full text link
    Morphological amoebas are image-adaptive structuring elements for morphological and other local image filters introduced by Lerallut et al. Their construction is based on combining spatial distance with contrast information into an image-dependent metric. Amoeba filters show interesting parallels to image filtering methods based on partial differential equations (PDEs), which can be confirmed by asymptotic equivalence results. In computing amoebas, graph structures are generated that hold information about local image texture. This paper reviews and summarises the work of the author and his coauthors on morphological amoebas, particularly their relations to PDE filters and texture analysis. It presents some extensions and points out directions for future investigation on the subject.Comment: 38 pages, 19 figures v2: minor corrections and rephrasing, Section 5 (pre-smoothing) extende

    Unsupervised Multi Class Segmentation of 3D Images with Intensity Inhomogeneities

    Full text link
    Intensity inhomogeneities in images constitute a considerable challenge in image segmentation. In this paper we propose a novel biconvex variational model to tackle this task. We combine a total variation approach for multi class segmentation with a multiplicative model to handle the inhomogeneities. Our method assumes that the image intensity is the product of a smoothly varying part and a component which resembles important image structures such as edges. Therefore, we penalize in addition to the total variation of the label assignment matrix a quadratic difference term to cope with the smoothly varying factor. A critical point of our biconvex functional is computed by a modified proximal alternating linearized minimization method (PALM). We show that the assumptions for the convergence of the algorithm are fulfilled by our model. Various numerical examples demonstrate the very good performance of our method. Particular attention is paid to the segmentation of 3D FIB tomographical images which was indeed the motivation of our work

    Model order reduction of coupled thermo-hydro-mechanical processes in geo-environmental applications

    Get PDF
    Tesi en modalitat de cotutela: Universitat Politècnica de Catalunya i Université libre de BruxellesIn a large number of geo-environmental applications, it is essential to model coupled processes that depend on several design parameters such as material properties and geometrical features. Thermo-hydro-mechanical (THM) processes are, among others, key effects to consider in critical applications such as deep geological repository of hazardous waste. This thesis proposes novel model order reduction strategies to evaluate the thermo-hydro-mechanical response of the material, taking into account the complexities involved in the coupled processes for such applications. To include variability of some design parameters, an a-posteriori model order reduction approach with reduced basis methods is applied to solve the high-dimensional parametric THM system. The reduction is based on an offline-online stage strategy. In the offline stage, reduced subspaces are constructed by a greedy adaptive procedure and in the online stage, multi-subspace projection is performed to quickly obtain the coupled THM response at any value of the design parameter. At the core of the greedy adaptive strategy is a goal-oriented error estimator that guides the selection of optimal design parameters where snapshots are evaluated. To tackle nonlinearity in the form of elasto-plastic material behaviour, the multi-subspace reduced basis method is combined with sub-structuring by domain decomposition. The effectiveness of the model reduction strategies are demonstrated on inverse problems involving large-scale geomodels that depict the coupled response of host rocks in potential deep geological repository sites. Two types of scenarios are considered: (i) the host rock undergoing geomorphological process is investigated as glacier advances over it for a period lasting over thousands of years and (ii) the clay response of an underground research laboratory is modelled numerically to support and validate in-situ heating experiments.En un gran número de aplicaciones geoambientales, es esencial modelar procesos acoplados que dependen de varios parámetros de diseño, como las propiedades de los materiales y las características geométricas. Los procesos termohidromecánicos (THM) son, entre otros, efectos clave a considerar en aplicaciones críticas como los depósitos geológicos profundos de residuos peligrosos. Esta tesis propone novedosas estrategias de reducción de orden del modelo para evaluar la respuesta termo-hidromecánica del material, teniendo en cuenta las complejidades que implican los procesos acoplados para dichas aplicaciones. Para incluir la variabilidad de algunos parámetros de diseño, se aplica un enfoque de reducción de orden del modelo a-posteriori con métodos de base reducida para resolver el sistema paramétrico THM de alta dimensión. La reducción se basa en una estrategia de etapas offline-online. En la etapa offline, los subespacios reducidos se construyen mediante un procedimiento adaptativo codicioso y en la etapa online, se realiza una proyección multisubespacio para obtener rápidamente la respuesta THM acoplada a cualquier valor del parámetro de diseño. El núcleo de la estrategia adaptativa 'greedy' es un 'goal-oriented error estimator' a objetivos que guía la selección de los parámetros de diseño óptimos donde se evalúan las 'snapshots'. Para hacer frente a la no linealidad en forma de comportamiento elastoplástico del material, se combina el método de bases reducidas multisuperficie con 'domain decomposition sub-structuring'. La eficacia de las estrategias de reducción de modelos se demuestra en problemas inversos de problemas inversos que implican geomodelos a gran escala que representan la respuesta acoplada de las rocas anfitrionas en posibles emplazamientos de depósitos geológicos profundos. Se consideran dos tipos de escenarios: (i) se investiga la roca sometida a un proceso geomorfológico a medida que el glaciar avanza sobre ella durante un período de miles de años y (ii) se modela numéricamente la respuesta de la arcilla de un laboratorio de investigación subterráneo para apoyar y validar los experimentos de "in situ heating"Postprint (published version
    • …
    corecore