Color Image Segmentation by Voronoi Partitions

We address the issue of low-level segmentation of color images. The proposed approach is based on the formulation of the problem as a generalized Voronoi partition of the image domain. In this context, a segmentation is determined by the definition of a distance between points of the image and the selection of a set of sites. The distance is defined by considering the low-level attributes of the image and, particularly, the color information. We divide the segmentation task in three successive sub-tasks, treated in the framework of Voronoi partitions : pre-segmentation, hierarchical representation and contour extraction.Nous étudions le problème de la segmentation de bas niveau pour les images couleur. L'approche proposée consiste à modéliser la segmentation d'une image comme une partition de Voronoï généralisée de son domaine. Dans ce contexte, segmenter une image couleur revient à définir une distance appropriée entre points de l'image et à choisir un ensemble de sites. La distance est définie en considérant les attributs de bas niveau de l'image et, en particulier, l'information fournie par la couleur. La démarche adoptée repose sur la division du problème de la segmentation en trois sous-tâches successives, traitées dans le cadre des partitions de Voronoï : la pré-segmentation, la représentation hiérarchique et l'extraction de contours

A Smirnov-Bickel-Rosenblatt theorem for compactly-supported wavelets

In nonparametric statistical problems, we wish to find an estimator of an unknown function f. We can split its error into bias and variance terms; Smirnov, Bickel and Rosenblatt have shown that, for a histogram or kernel estimate, the supremum norm of the variance term is asymptotically distributed as a Gumbel random variable. In the following, we prove a version of this result for estimators using compactly-supported wavelets, a popular tool in nonparametric statistics. Our result relies on an assumption on the nature of the wavelet, which must be verified by provably-good numerical approximations. We verify our assumption for Daubechies wavelets and symlets, with N = 6, ..., 20 vanishing moments; larger values of N, and other wavelet bases, are easily checked, and we conjecture that our assumption holds also in those cases

THE TIGHT-BINDING APPROACH TO THE DIELECTRIC RESPONSE IN THE MULTIBAND SYSTEMS

Starting from the random phase approximation for the weakly coupled multiband tightly-bounded electron systems, we calculate the dielectric matrix in terms of intraband and interband transitions. The advantages of this representation with respect to the usual plane-wave decomposition are pointed out. The analysis becomes particularly transparent in the long wavelength limit, after performing the multipole expansion of bare Coulomb matrix elements. For illustration, the collective modes and the macroscopic dielectric function for a general cubic lattice are derived. It is shown that the dielectric instability in conducting narrow band systems proceeds by a common softening of one transverse and one longitudinal mode. Furthermore, the self-polarization corrections which appear in the macroscopic dielectric function for finite band systems, are identified as a combined effect of intra-atomic exchange interactions between electrons sitting in different orbitals and a finite inter-atomic tunneling.Comment: 20 pages, LaTeX, no figure

Binary data corruption due to a Brownian agent

We introduce a model of binary data corruption induced by a Brownian agent (active random walker) on a d-dimensional lattice. A continuum formulation allows the exact calculation of several quantities related to the density of corrupted bits \rho; for example the mean of \rho, and the density-density correlation function. Excellent agreement is found with the results from numerical simulations. We also calculate the probability distribution of \rho in d=1, which is found to be log-normal, indicating that the system is governed by extreme fluctuations.Comment: 39 pages, 10 figures, RevTe

Globally optimal geodesic active contours

An approach to optimal object segmentation in the geodesic active contour framework is presented with application to automated image segmentation. The new segmentation scheme seeks the geodesic active contour of globally minimal energy under the sole restriction that it contains a specified internal point p_int. This internal point selects the object of interest and may be used as the only input parameter to yield a highly automated segmentation scheme. The image to be segmented is represented as a Riemannian space S with an associated metric induced by the image. The metric is an isotropic and decreasing function of the local image gradient at each point in the image, encoding the local homogeneity of image features. Optimal segmentations are then the closed geodesics which partition the object from the background with minimal similarity across the partitioning. An efficient algorithm is presented for the computation of globally optimal segmentations and applied to cell microscopy, x-ray, magnetic resonance and cDNA microarray images

The moral reasoning abilities of Australian and Malaysian accounting students : a comparative analysis

If national culture is a significant determinant of ethical attitudes, it is not unreasonable to expect ethical decision-making to be influenced by one\u27s culture. However, problems arise when the notion of right differs from one culture to another. The question addressed in this paper is whether the moral reasoning abilities of Australian and Malaysian accounting students in their final year of study differ because of their cultural upbringing. This study uses primary data collected from 34 final year accounting students (12 Australian and 22 Malaysian) enrolled in an Australian degree program. The test scores collected at the beginning and end of the academic year indicate that culture and other explanatory variables do not have an affect on students\u27 moral judgment. The findings in this study suggest that culture as an independent variable does not influence the way accounting students analyse and resolve ethical dilemmas.<br /

Some peculiarities of motion of neutral and charged test particles in the field of a spherically symmetric charged object in General Relativity

We propose the method of investigation of radial motions for charged and neutral test particles in the Reissner-Nordstr\"{o}m field by means of mass potential. In this context we analyze special features of interaction of charges and their motions in General Relativity and construct the radial motion classification. For test particles and a central source with charges $q$ and $Q$, respectively, the conditions of attraction (when $qQ>0$) and repulsion (when $qQ<0$) are obtained. The conditions of motionless test particle states with respect to the central source are investigated and, in addition, stability conditions for such static equilibrium states are found. It is shown that stable states are possible only for the bound states of weakly charged particles in the field of a naked singularity. Frequencies of small oscillations of test particles near their equilibrium positions are also found.Comment: 15 pages, 9 figure

Globally optimal 3D image reconstruction and segmentation via energy minimisation techniques

This paper provides an overview of a number of techniques developed within our group to perform 3D reconstruction and image segmentation based of the application of energy minimisation concepts. We begin with classical snake techniques and show how similar energy minimisation concepts can be extended to derive globally optimal segmentation methods. Then we discuss more recent work based on geodesic active contours that can lead to globally optimal segmentations and reconstructions in 2D. Finally we extend the work to 3D by introducing continuous flow globally minimal surfaces. Several applications are discussed to show the wide applicability and suitability of these techniques to several difficult image analysis problems

Bcc 4^4He as a Coherent Quantum Solid

In this work we investigate implications of the quantum nature of bcc $^{4}$% He. We show that it is a unique solid phase with both a lattice structure and an Off-Diagonal Long Range Order of coherently oscillating local electric dipole moments. These dipoles arise from the local motion of the atoms in the crystal potential well, and oscillate in synchrony to reduce the dipolar interaction energy. The dipolar ground-state is therefore found to be a coherent state with a well defined global phase and a three-component complex order parameter. The condensation energy of the dipoles in the bcc phase stabilizes it over the hcp phase at finite temperatures. We further show that there can be fermionic excitations of this ground-state and predict that they form an optical-like branch in the (110) direction. A comparison with 'super-solid' models is also discussed.Comment: 12 pages, 8 figure

Anderson localization of polaron states

Using the vanishing of the typical polaron tunneling rate as an indicator of the breakdown of itinerancy, we study the localization of polaron states in a generic model for a disordered polaronic material. We find that extremely small disorder causes an Anderson localization of small polaron states. However, the ratio between the critical disorder strength needed to localize all states in the polaron band and the renormalized bandwidth is not necessarily smaller than for a bare electron.Comment: 4 pages, 3 figure