Multiscale local multiple orientation estimation using mathematical morphology and B-spline interpolation

Presentation available at http://www.tic.upct.es/rafael.verdu/slides/slides2011ispa.pdfInternational audienceThis paper introduces a novel multiscale approach to estimate local multiple orientations, which are underlying in the discrete grid of an image. The basic ingredients are two: on the one hand, multiscale directional openings by line segments of variable length, which produce directional signatures for various scales, with the estimation of the orientation properties; and on the other hand, multiple peak detection by means of b-spline interpolation of the directional signatures. Experimental results on real and synthetic images show the applications of the proposed method based on mathematical morphology, which can detect local multiple orientations in textured images at different scales with high accuracy

Retinal network characterization through fundus image processing: Significant point identification on vessel centerline

[EN] This paper describes a new approach for significant point identification on vessel centerline. Significant points such as bifurcations and crossovers are able to define and characterize the retinal vascular network. In particular, hit-or-miss transformation is used to detect terminal, bifurcation and simple crossing points but a post-processing stage is needed to identify complex intersections. This stage focuses on the idea that the intersection of two vessels creates a sort of close loop formed by the vessels and this effect can be used to differentiate a bifurcation from a crossover. Experimental results show quantitative improvements by increasing the number of true positives and reducing the false positives and negatives in the significant point detection when the proposed method is compared with another state-of-the-art work. A sensitivity equal to 1 and a predictive positive value of 0.908 was achieved in the analyzed cases. Hit-or-miss transformation must be applied on a binary skeleton image. Therefore, a method to extract the vessel skeleton in a direct way is also proposed. Although the identification of the significant points of the retinal tree can be useful by itself for multiple applications such as biometrics and image registration, this paper presents an algorithm that makes use of the significant points to measure the bifurcation angles of the retinal network which can be related to cardiovascular risk determination.This work was supported by the Ministerio de Economia y Conipetitividad of Spain, Project ACRIMA (TIN2013-46751-R). The authors would like to thank people who provide the public databases used in this work (DRIVE, STARE and VARIA).Morales, S.; Naranjo Ornedo, V.; Angulo, J.; Legaz-Aparicio, A.; Verdu-Monedero, R. (2017). Retinal network characterization through fundus image processing: Significant point identification on vessel centerline. Signal Processing: Image Communication. 59:50-64. https://doi.org/10.1016/j.image.2017.03.013S50645

Comparison of orientated and spatially variant morphological filters vs mean/median filters for adaptive image denoising

Presentation available at http://www.tic.upct.es/rafael.verdu/slides/slides2010icip.pdfISBN: 978-142447994-8International audienceThis paper shows a comparison of spatially-variant discrete operators for denoising gray-level images. These non-iterative operators use a neighborhood that varies over space, adapting their shape and orientation according to the data of the image under study. The orientation of the neighborhood is computed by means of a diffusion process of the average square gradient field, which regularizes and extends the orientation information from the edges of the objects to the homogeneous areas of the image; and the shape of the orientated neighborhood can be either a linear segment or a rectangle of anisotropy given by the distance to relevant edges of the objects. Results on gray-level images show the ability of spatially-variant morphological operators for adaptively preserving the main structures in the image while reducing the noise

Spatially-Variant Anisotropic Morphological Filters Driven By Gradient Fields

ISBN : 978-3-642-03612-5International audienceThis paper deals with the theory and applications of spatially-variant mathematical morphology. We formalize the definition of spatially variant dilation/erosion and opening/closing for gray-level images using exclusively the structuring function, without resorting to complement. This sound theoretical framework allows to build morphological operators whose structuring elements can locally adapt their orientation across the dominant direction of image structures. The orientation at each pixel is extracted by means of a diffusion process of the average square gradient field, which regularizes and extends the orientation information from the edges of the objects to the homogeneous areas of the image. The proposed filters are used for enhancement of anisotropic images features such as coherent, flow-like structures

Anisotropic morphological filters with spatially-variant structuring elements based on image-dependent gradient fields

International audienceThis paper deals with the theory and applications of spatially-variant discrete mathematical morphology. We review and formalize the definition of spatially variant dilation/erosion and opening/closing for binary and gray-level images using exclusively the structuring function, without resorting to complement. This theoretical framework allows to build morphological operators whose structuring elements can locally adapt their shape and orientation across the dominant direction of the structures in the image. The shape and orientation of the structuring element at each pixel are extracted from the image under study: the orientation is given by means of a diffusion process of the average square gradient field, which regularizes and extends the orientation information from the edges of the objects to the homogeneous areas of the image; and the shape of the orientated structuring elements can be linear or it can be given by the distance to relevant edges of the objects. The proposed filters are used on binary and gray-level images for enhancement of anisotropic features such as coherent, flow-like structures. Results of spatially-variant erosions/dilations and openings/closings-based filters 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.

International audienceThis 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

Multiscale estimation of multiple orientations based on morphological directional openings

International audienceThis paper introduces a novel approach to estimate multiple orientations at each pixel of a gray image at different scales. The main orientations are provided by a bank of directional openings. Gathering the responses of the filtered directional openings provide at each pixel a discrete sequence which is the directional signature. Then, the directional signature is interpolated by cubic B-splines, and the multiple orientations at each pixel are obtained by means of peak detection in the continuous directional signature. This procedure is performed using structuring elements with different lengths which results in a multiscale approach. The comparison with other existing methods as well as the experimental results on images shows the ability of the proposed method to detect multiple orientations in textured images at different scales with high accuracy

Towards Morphological Image Regularization Using the Counter-Harmonic Mean

ISBN : 978-3-642-38293-2International audienceThe introduction of nonlinear filters which approximate flat dilation and erosion is an issue that has been studied during the past years. In the literature, we can find works which involve the definition of robust morphological-like filters from well-known operators such as the Counter-Harmonic Mean (CHM). The main goal of this paper is to provide the reader with a morphological CHM-based regularization which simultaneously preserve both the structural information in areas of the image with high gradient and the morphological effect in the areas with low gradient. With this purpose, we introduce a suitable mathematical framework and then deal with the variational formulation which is derived from it. Practical aspects of the implementation are discussed and some results are provided to illustrate the behaviour of our approach

Frequency domain regularization of d-dimensional structure tensor-based directional fields

Available online 25 June 2011International audienceThe present work is intended to address two of the major difficulties that can be found when tackling the estimation of the local orientation of the data in a scene, a task which is usually accomplished by means of the computation of the structure tensor-based directional field. On one hand, the orientation information only exists in the non-homogeneous regions of the dataset, while it is zero in the areas where the gradient (i.e. the first-order intensity variation) remains constant. Due to this lack of information, there are many cases in which the overall shape of the represented objects cannot be precisely inferred from the directional field. On the other hand, the orientation estimation is highly dependent on the particular choice of the averaging window used for its computation (since a collection of neighboring gradient vectors is needed to obtain a dominant orientation), typically resulting in vector fields which vary from very irregular (thus yielding a noisy estimation) to very uniform (but at the expense of a loss of angular resolution). The proposed solution to both drawbacks is the regularization of the directional field; this process extends smoothly the previously computed vectors to the whole dataset while preserving the angular information of relevant structures. With this purpose, the paper introduces a suitable mathematical framework and deals with the d-dimensional variational formulation which is derived from it. The proposed formulation is finally translated into the frequency domain in order to obtain an increase of insight on the regularization problem, which can be understood as a low-pass filtering of the directional field. The frequency domain point of view also allows for an efficient implementation of the resulting iterative algorithm. Simulation experiments involving datasets of different dimensionality prove the validity of the theoretical approach