Morphological bilateral filtering

International audienceA current challenging topic in mathematical morphology is the construction of locally adaptive operators; i.e., structuring functions that are dependent on the input image itself at each position. Development of spatially-variant filtering is well established in the theory and practice of Gaussian filtering. The aim of the first part of the paper is to study how to generalize these convolution-based approaches in order to introduce adaptive nonlinear filters that asymptotically correspond to spatially-variant morphological dilation and erosion. In particular, starting from the bilateral filtering framework and using the notion of counter-harmonic mean, our goal is to propose a new low complexity approach to define spatially-variant bilateral structuring functions. Then, in the second part of the paper, an original formulation of spatially-variant flat morphological filters is proposed, where the adaptive structuring elements are obtained by thresholding the bilateral structuring functions. The methodological results of the paper are illustrated with various comparative examples

Attribute Controlled Reconstruction and Adaptive Mathematical Morphology

ISBN : 978-3-642-38293-2International audienceIn this paper we present a reconstruction method controlled by the evolution of attributes. The process begins from a marker, propagated over increasing quasi-flat zones. The evolution of several increasing and non-increasing attributes is studied in order to select the appropriate region. Additionally, the combination of attributes can be used in a straightforward way. To demonstrate the performance of our method, three applications are presented. Firstly, our method successfully segments connected objects in range images. Secondly, input-adaptive structuring elements (SE) are defined computing the controlled propagation for each pixel on a pilot image. Finally, input-adaptive SE are used to assess shape features on the image. Our approach is multi-scale and auto-dual. Compared with other methods, it is based on a given attribute but does not require a size parameter in order to determine appropriate regions. It is useful to extract objects of a given shape. Additionally, our reconstruction is a connected operator since quasi-flat zones do not create new contours on the image

Adaptive hit or miss transform

International audienceThe Hit or Miss Transform is a fundamental morphological operator, and can be used for template matching. In this paper, we present a framework for adaptive Hit or Miss Transform, where structuring elements are adaptive with respect to the input image itself. We illustrate the difference between the new adaptive Hit or Miss Transform and the classical Hit or Miss Transform. As an example of its usefulness, we show how the new adaptive Hit or Miss Transform can detect particles in single molecule imaging

Riemannian mathematical morphology

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

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

Beyond scalar quasi-arithmetic means: Quasi-arithmetic averages and quasi-arithmetic mixtures in information geometry

We generalize quasi-arithmetic means beyond scalars by considering the gradient map of a Legendre type real-valued function. The gradient map of a Legendre type function is proven strictly comonotone with a global inverse. It thus yields a generalization of strictly mononotone and differentiable functions generating scalar quasi-arithmetic means. Furthermore, the Legendre transformation gives rise to pairs of dual quasi-arithmetic averages via the convex duality. We study the invariance and equivariance properties under affine transformations of quasi-arithmetic averages via the lens of dually flat spaces of information geometry. We show how these quasi-arithmetic averages are used to express points on dual geodesics and sided barycenters in the dual affine coordinate systems. We then consider quasi-arithmetic mixtures and describe several parametric and non-parametric statistical models which are closed under the quasi-arithmetic mixture operation.Comment: 20 page

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