161 research outputs found
Amoeba Techniques for Shape and Texture Analysis
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
Analysis of Amoeba Active Contours
Subject of this paper is the theoretical analysis of structure-adaptive
median filter algorithms that approximate curvature-based PDEs for image
filtering and segmentation. These so-called morphological amoeba filters are
based on a concept introduced by Lerallut et al. They achieve similar results
as the well-known geodesic active contour and self-snakes PDEs. In the present
work, the PDE approximated by amoeba active contours is derived for a general
geometric situation and general amoeba metric. This PDE is structurally similar
but not identical to the geodesic active contour equation. It reproduces the
previous PDE approximation results for amoeba median filters as special cases.
Furthermore, modifications of the basic amoeba active contour algorithm are
analysed that are related to the morphological force terms frequently used with
geodesic active contours. Experiments demonstrate the basic behaviour of amoeba
active contours and its similarity to geodesic active contours.Comment: Revised version with several improvements for clarity, slightly
extended experiments and discussion. Accepted for publication in Journal of
Mathematical Imaging and Visio
A graph-based mathematical morphology reader
This survey paper aims at providing a "literary" anthology of mathematical
morphology on graphs. It describes in the English language many ideas stemming
from a large number of different papers, hence providing a unified view of an
active and diverse field of research
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
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
Cell-cell signalling in sexual chemotaxis: a basis for gametic differentiation, mating types and sexes
While sex requires two parents, there is no obvious need for them to be differentiated into distinct mating types or sexes. Yet this is the predominate state of nature. Here, we argue that mating types could play a decisive role because they prevent the apparent inevitability of self-stimulation during sexual signalling. We rigorously assess this hypothesis by developing a model for signaller-detector dynamics based on chemical diffusion, chemotaxis and cell movement. Our model examines the conditions under which chemotaxis improves partner finding. Varying parameter values within ranges typical of protists and their environments, we show that simultaneous secretion and detection of a single chemoattractant can cause a multifold movement impediment and severely hinder mate finding. Mutually exclusive roles result in faster pair formation, even when cells conferring the same roles cannot pair up. This arrangement also allows the separate mating types to optimize their signalling or detecting roles, which is effectively impossible for cells that are both secretors and detectors. Our findings suggest that asymmetric roles in sexual chemotaxis (and possibly other forms of sexual signalling) are crucial, even without morphological differences, and may underlie the evolution of gametic differentiation among both mating types and sexes
Contents lists available at ScienceDirect Pattern Recognition
journal homepage: www.elsevier.com/locate/pr Edge-preserving smoothing using a similarity measure in adaptive geodesi
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