Domagoj Kovačević

Generalized Poincaré algebras, Hopf algebras and κ-Minkowski spacetime

Abstract We propose a generalized description for the κ-Poincare–Hopf algebra as a symmetry quantum group of underlying κ-Minkowski spacetime. We investigate all the possible implementations of (deformed) Lorentz algebras which are compatible with the given choice of κ-Minkowski algebra realization. For the given realization of κ-Minkowski spacetime there is a unique κ-Poincare–Hopf algebra with undeformed Lorentz algebra. We have constructed a three-parameter family of deformed Lorentz generators with κ-Poincare algebras which are related to κ-Poincare–Hopf algebra with undeformed Lorentz algebra. Known bases of κ-Poincare–Hopf algebra are obtained as special cases. Also deformation of igl ( 4 ) Hopf algebra compatible with the κ-Minkowski spacetime is presented. Some physical applications are briefly discussed.

Kappa-Minkowski spacetime, Kappa-Poincare Hopf algebra and realizations

We unify κ-Minkowki spacetime and Lorentz algebra in unique Lie algebra. Introducing commutative momenta, a family of κ-deformed Heisenberg algebras and κ-deformed Poincare algebras are defined. They are specified by the matrix depending on momenta. We construct all such matrices. Realizations and star product are defined and analyzed in general and specially, their relation to coproduct of momenta is pointed out. Hopf algebra of the Poincare algebra, related to the covariant realization, is presented in unified covariant form. Left–right dual realizations and dual algebra are introduced and considered. The generalized involution and the star inner product are analyzed and their properties are discussed. Partial integration and deformed trace property are obtained in general. The translation invariance of the star product is pointed out. Finally, perturbative approach up to the first order in a is presented in the appendix.

Quantitative intracerebral brain hemorrhage analysis

In this paper a system for 3-D quantitative analysis of human spontaneous intracerebral brain hemorrhage (ICH) is described. The purpose of the developed system is to perform quantitative 3-D measurements of the parameters of ICH region and from computed tomography (CT) images. The measured parameter in this phase of the system development is volume of the hemorrhage region. The goal of the project is to measure parameters for a large number of patients having ICH and to correlate measured parameters to patient morbidity and mortality.

Semi-automatic Active Contour Approach to Segmentation of Computed Tomography Volumes

In this paper a method for three-dimensional (3-D) semi- automatic segmentation of volumes of medical images is described. The method is semi-automatic in the sense that, in the initial phase, the user assistance is required for manual segmentation of a certain number of slices (cross-sections) of the volume. In the second phase, the algorithm for automatic segmentation is started. The segmentation algorithm is based on the active contour approach. A semi 3-D active contour algorithm is used in the sense that additional inter-slice forces are introduced in order to constrain the obtained solution. The energy function which is minimized is modified to exploit information provided by the manual segmentation of some of the slices performed by the user. The experiments have been performed using computed tomography (CT) scans of the abdominal region of the human body. In particular, CT images of abdominal aortic aneurysms have been segmented to determine the location of aorta. The experiments have shown the feasibility of the approach.© (2000) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Radial basis function-based image segmentation using a receptive field

The paper presents a novel method for CT head image automatic segmentation. The images are obtained from patients having a spontaneous intra-cerebral brain hemorrhage (ICH). The results of the segmentation are images partitioned into five regions of interest corresponding to four tissue classes (skull, brain, calcifications and ICH) and background. Once the images are segmented it is possible to calculate various hemorrhage region parameters such as size, position, etc. The segmentation is performed in three major steps. In the first phase feature extraction and normalization is performed using a receptive field (RF). Experiments were performed to determine the optimal RF structure. Pixels are classified in the second phase using the radial basis function (RBF) artificial neural network. Experiments with different RBF network topologies were performed in order to determine the optimal basis functions, network size and a training algorithm. The segmentation results obtained using the RBF network were compared with results obtained by multi-layer perceptron neural network (MLP). In the third phase the image regions obtained by the RBF network were labeled using an expert system. Experiments have shown that the proposed method successfully performs image segmentation.

Κ-Deformed Phase Space, Hopf Algebroid and Twisting

Hopf algebroid structures on the Weyl algebra (phase space) are presented. We define the coproduct for the Weyl generators from Leibniz rule. The codomain of the coproduct is modified in order to obtain an algebra structure. We use the dual base to construct the target map and antipode. The notion of twist is analyzed for -deformed phase space in Hopf algebroid setting. It is outlined how the twist in the Hopf algebroid setting reproduces the full Hopf algebra structure of -Poincar e algebra. Several examples of realizations are worked out in details.

Hermitian realizations of κ-Minkowski space–time

General realizations, star products and plane waves for κ-Minkowski space–time are considered. Systematic construction of general Hermitian realization is presented, with special emphasis on noncommutative plane waves and Hermitian star product. Few examples are elaborated and possible physical applications are mentioned.

Fuzzy expert system for edema segmentation

A method for segmentation of edema region in a computed tomography (CT) image of the brain is presented in this paper. The edema region is a dark region surrounding the intracerebral brain hemorrhage (ICH) region. Edema segmentation, in general, is difficult because of very subtle grayscale variations. The proposed edema segmentation procedure consists of two major parts. Fuzzy feature extraction is performed in the first part of the procedure. Extracted features include local contrast and distance from ICH region. The fuzzy features are then input into the rule-based expert system as fuzzy facts. In the second part, a fuzzy expert system is used to perform the actual segmentation. A set of rules is formulated to represent the knowledge about the possible image structure. The set of rules is constant and does not depend on the input image. The fuzzy facts extracted in the first part of the procedure are derived from the particular image to be segmented. Fuzzy-CLIPS software package has been used to derive a conclusion from the facts based on the rules. The conclusion represents the segmented edema region. Experiments have shown that the method can be used for edema segmentation.

CT image labeling using Hopfield neural network

A method for the computed tomography (CT) image labeling is presented. CT images used in this work are obtained from patients having the spontaneous intra-cerebral haemorrhage (ICH). The images are segmented into three tissue classes (skull, brain, and ICH) and the background. The method consists of two steps. In the the first step, the image is divided into a number of regions using the K-means clustering algorithm. Regions used are dark, medium dark and bright region. In the second step, the regions are labeled using the modified Hopfield (1985) neural network. The stable state of the network represents a possible solution to the labeling problem. Simulated annealing is used as algorithm for network simulation.

A GENERAL FORMULATION OF THE MOYAL AND VOROS PRODUCTS AND ITS PHYSICAL INTERPRETATION

A unifying perspective on the Moyal and Voros products and their physical meanings has been recently presented in the literature, where the Voros formulation admits a consistent physical interpretation. We define a star product ⋆, in terms of an antisymmetric fixed matrix Θ, and an arbitrary symmetric matrix Φ, that is a generalization of the Moyal and the Voros products. We discuss the quantum mechanics and the physical meaning of the generalized star product.