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Segmentation d'Images Vectorielles par Partitions de Voronoï Généralisées Vector-Valued Image Segmentation by Generalized Voronoi Tessellations
Abstract
We address the issue of low-level segmentation for vector- valued images, focusing on color images. The proposed approach relies on the formulation of the problem as a generalized Voronoi tessellation of the image domain. In this context, the issue is transferred to the definition of an appropriated pseudo-metric and the selection of a set of sources. Two types of pseudo-metrics are considered ; the first one is based on energy minimizing paths and the se- cond is associated to the families of nested partitions of the image domain. We discuss specific applications of our approach to pre-segmentation, edge detection and hierar- chical segmentation on color images.
... Thouis R [3] segments the microscope images of cells by controlling its local features, and calculates the approximate value of Voronoi region, but it exits segment error for improper selection of image features. P. Arbelaez [4] proposes a method that takes color images as Voronoi tessellations to outline the border of images by combining texture and contours. Sinclair [5] use voronoi diagram to decompose boundary of photographs, it can segment the border clearly by the discrete features merging of texture modal, but it still exits the such problems as over-segmentation and can't distinguish sub-goal and background. ...
... Thouis R [3] segments the microscope images of cells by controlling its local features, and calculates the approximate value of Voronoi region, but it exits segment error for improper selection of image features. P. Arbelaez [4] proposes a method that takes color images as Voronoi tessellations to outline the border of images by combining texture and contours. Sinclair [5] use voronoi diagram to decompose boundary of photographs, it can segment the border clearly by the discrete features merging of texture modal, but it still exits the such problems as over-segmentation and can't distinguish sub-goal and background. ...
By taking the advantages of the Voronoi-based segmentation method in detecting the thin edges and the region growing segmentation method in segmenting regions more completely, we proposed a novel segmentation algorithm by combining the Voronoi diagrams and region growing to deal with the medical images in this paper. Firstly, the region growing segmentation algorithm is used to produce a rough partition, and then the Voronoi-based method is applied to the initial partition for further iterative processing to get a clearer border. Segmentation results on CT and MR images show that our method can segment the target area completely and accurately. Especially, it can effectively preserve the high frequency information in the edge area. Furthermore, we found that the proposed method behaved better on MR images than on CT images.
In this article we provide a framework for optimal placement or deployment of facilities in a region of interest. We present a generalization of Voronoi partition, where functions modeling the effectiveness of facilities are used in the place of the usual distance measure used in the standard Voronoi partition and its variations. We illustrate the usefulness of the generalization in designing strategies for optimal deployment of multiple vehicles equipped with sensors, optimal placement of base stations in a cellular network design problem, and locational optimization of power plants.
We address the issue of low-level segmentation of vector-valued images, focusing on the case of color natural images. The proposed approach relies on the formulation of the problem in the metric framework, as a Voronoi tessellation of the image domain. In this context, a segmentation is determined by a distance transform and a set of sites. Our method consists in dividing the segmentation task in two successive sub-tasks: pre-segmentation and hierarchical representation. We design specific distances for both sub-problems by considering low-level image attributes and, particularly, color and lightness information. Then, the interpretation of the metric formalism in terms of boundaries allows the definition of a soft contour map that has the property of producing a set of closed curves for any threshold. Finally, we evaluate the quality of our results with respect to ground-truth segmentation data.
The prelims comprise: Properties of infinite Voronoi diagramsProperties of Poisson Voronoi diagramsUses of Poisson Voronoi diagramsSimulating Poisson Voronoi and Delaunay cellsProperties of Poisson Voronoi cellsStochastic processes induced by Poisson VoronoidiagramsSectional Voronoi diagramsAdditively weighted Poisson Voronoi diagrams: the Johnson-Mehl modelHigher order Poisson Voronoi diagramsPoisson Voronoi diagrams on the surface of a sphereProperties of Poisson Delaunay cellsOther random Voronoi diagrams
On a grey level image, extrema correspond to zones of uniform altitude
whose neighboring pixels have a strictly lower (maxima) or strictly
higher (minima) altitude. If an image is seen as a relief, minima are
located at the bottom of valleys or pits (structures darker than the
background) and maxima are located at the top of plateaus, pics, or
domes (structures lighter than the background). The detection of extrema
is often used as the first step of a segmentation process when we just
need to roughly located objects of interest. Unfortunately, the noise
sensitivity of this transformation makes it uneasy to use. We propose in
this paper a transformation which valuates the extrema on a contrast
criterion: the dynamics. The selection of the minima of interest is
easier with this contrast information. The dynamics is a measure at the
scale of the structure. It does not characterize the extremum itself or
its catchment basin but the structure containing the extremum. An
original aspect of the dynamics is that this transformation does not
consider the size and the shape of the structures. We do not need to
know a priori the size of the structures to evaluate their contrast.
That is not the case for contrast feature extraction like the top-hat
transformation. The computation of the dynamics is not straight forward
from its definition. We propose a technique of computation based on
flooding simulations. Using last algorithmical developments, this
implementation is particularly efficient. That will help to develop the
use of the promising transformations based on the dynamics.
This paper deals with the class of extensive operators in the lattice of partitions. These operators are merging techniques. They can be used as filtering tools or as segmentation algorithms. In the first case, they are known as connected operators and, in the second case, they are region growing techniques. This paper discusses the basic elements that have to be defined to create a merging algorithm: merging order, merging criterion and region model. This analysis highlights the similarity and differences between a filtering tool, such as a connected operator, and a segmentation algorithm. Taking benefit from the filtering and segmentation viewpoints, we propose a general merging algorithm that can be used to create new connected operators (in particular self-dual operators) and efficient segmentation algorithms (robust criteria and efficient implementation).
