602 research outputs found
Stochastic spectral-spatial permutation ordering combination for nonlocal morphological processing
International audienceThe extension of mathematical morphology to mul-tivariate data has been an active research topic in recent years. In this paper we propose an approach that relies on the consensus combination of several stochastic permutation orderings. The latter are obtained by searching for a smooth shortest path on a graph representing an image. The construction of the graph can be based on both spatial and spectral information and naturally enables patch-based nonlocal processing
Nonlinear operators on graphs via stacks
International audienceWe consider a framework for nonlinear operators on functions evaluated on graphs via stacks of level sets. We investigate a family of transformations on functions evaluated on graph which includes adaptive flat and non-flat erosions and dilations in the sense of mathematical morphology. Additionally, the connection to mean motion curvature on graphs is noted. Proposed operators are illustrated in the cases of functions on graphs, textured meshes and graphs of images
Random projection depth for multivariate mathematical morphology
International audienceThe open problem of the generalization of mathematical morphology to vector images is handled in this paper using the paradigm of depth functions. Statistical depth functions provide from the "deepest" point a "center-outward ordering" of a multidimensional data distribution and they can be therefore used to construct morphological operators. The fundamental assumption of this data-driven approach is the existence of "background/foreground" image representation. Examples in real color and hyperspectral images illustrate the results
Differentiated cell behavior: a multiscale approach using measure theory
This paper deals with the derivation of a collective model of cell
populations out of an individual-based description of the underlying physical
particle system. By looking at the spatial distribution of cells in terms of
time-evolving measures, rather than at individual cell paths, we obtain an
ensemble representation stemming from the phenomenological behavior of the
single component cells. In particular, as a key advantage of our approach, the
scale of representation of the system, i.e., microscopic/discrete vs.
macroscopic/continuous, can be chosen a posteriori according only to the
spatial structure given to the aforesaid measures. The paper focuses in
particular on the use of different scales based on the specific functions
performed by cells. A two-population hybrid system is considered, where cells
with a specialized/differentiated phenotype are treated as a discrete
population of point masses while unspecialized/undifferentiated cell aggregates
are represented with a continuous approximation. Numerical simulations and
analytical investigations emphasize the role of some biologically relevant
parameters in determining the specific evolution of such a hybrid cell system.Comment: 25 pages, 6 figure
Cellular neural networks, Navier-Stokes equation and microarray image reconstruction
Copyright @ 2011 IEEE.Although the last decade has witnessed a great deal of improvements achieved for the microarray technology, many major developments in all the main stages of this technology, including image processing, are still needed. Some hardware implementations of microarray image processing have been proposed in the literature and proved to be promising alternatives to the currently available software systems. However, the main drawback of those proposed approaches is the unsuitable addressing of the quantification of the gene spot in a realistic way without any assumption about the image surface. Our aim in this paper is to present a new image-reconstruction algorithm using the cellular neural network that solves the NavierâStokes equation. This algorithm offers a robust method for estimating the background signal within the gene-spot region. The MATCNN toolbox for Matlab is used to test the proposed method. Quantitative comparisons are carried out, i.e., in terms of objective criteria, between our approach and some other available methods. It is shown that the proposed algorithm gives highly accurate and realistic measurements in a fully automated manner within a remarkably efficient time
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Invasion and adaptive evolution for individual-based spatially structured populations
The interplay between space and evolution is an important issue in population
dynamics, that is in particular crucial in the emergence of polymorphism and
spatial patterns. Recently, biological studies suggest that invasion and
evolution are closely related. Here we model the interplay between space and
evolution starting with an individual-based approach and show the important
role of parameter scalings on clustering and invasion. We consider a stochastic
discrete model with birth, death, competition, mutation and spatial diffusion,
where all the parameters may depend both on the position and on the trait of
individuals. The spatial motion is driven by a reflected diffusion in a bounded
domain. The interaction is modelled as a trait competition between individuals
within a given spatial interaction range. First, we give an algorithmic
construction of the process. Next, we obtain large population approximations,
as weak solutions of nonlinear reaction-diffusion equations with Neumann's
boundary conditions. As the spatial interaction range is fixed, the
nonlinearity is nonlocal. Then, we make the interaction range decrease to zero
and prove the convergence to spatially localized nonlinear reaction-diffusion
equations, with Neumann's boundary conditions. Finally, simulations based on
the microscopic individual-based model are given, illustrating the strong
effects of the spatial interaction range on the emergence of spatial and
phenotypic diversity (clustering and polymorphism) and on the interplay between
invasion and evolution. The simulations focus on the qualitative differences
between local and nonlocal interactions
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
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