On the size of quadtrees generalized to d-dimensional binary pictures

AbstractSome results about the size of quadtrees and linear quadtrees, used to represent binary 2n × 2n digital pictures, are generalized to d-dimensional 2n × … × 2n pictures. Among these results are a comparison of the space-efficiency of linear vs regular trees, in terms of both the number of nodes of the tree and the number of bits needed to store each node, and an upper bound on the number of nodes as a function of n and the perimeter of the picture

High Speed Photon Transport in Monte Carlo Method

モンテカルロシミュレーションにおける光子輸送では通常小さいVOXELの組合せによって記述されたモデルを使用して実行される、Voxel-Based（VB）法と呼ばれるこのモデルの欠点は光子輸送に長い時間がかかることであり、この計算時間を短くするために我々は新光子輸送法を提案する。この方法では光子輸送の際、いちいち隣のVOXELに光子を動かさずに、異なる媒質の境界までまたは平均自由行程分だけ光子を動かす。この提案した方法と従来からの方法（VB法とQuadtree法）を比較した結果、新光子輸送法は計算時間をVB法の半分にまで減らすことが可能であることが明らかになった。Monte Carlo simulations in nuclear science and medicine are usually performed using a model which describes an object by a combination of small voxels. The model named voxel-based (VB) method takes long time to transport photons. To reduce the calculation time we proposed a new photon transportation method. In this method we do not move a photon to the next voxel, but move it to a boundary of different media directoly or by a mean free path. The proposed method was compared with the conventional methods (the VB method and the Quadtree method). The results showed the proposed method accomplished to reduce the calculation time to half of the VB method

Robot environment expert system

The Robot Environment Expert System uses a hexidecimal tree data structure to model a complex robot environment where not only the robot arm moves, but also the robot itself and other objects may move. The hextree model allows dynamic updating, collision avoidance and path planning over time, to avoid moving objects

Surface Shape Perception in Volumetric Stereo Displays

In complex volume visualization applications, understanding the displayed objects and their spatial relationships is challenging for several reasons. One of the most important obstacles is that these objects can be translucent and can overlap spatially, making it difficult to understand their spatial structures. However, in many applications, for example medical visualization, it is crucial to have an accurate understanding of the spatial relationships among objects. The addition of visual cues has the potential to help human perception in these visualization tasks. Descriptive line elements, in particular, have been found to be effective in conveying shape information in surface-based graphics as they sparsely cover a geometrical surface, consistently following the geometry. We present two approaches to apply such line elements to a volume rendering process and to verify their effectiveness in volume-based graphics. This thesis reviews our progress to date in this area and discusses its effects and limitations. Specifically, it examines the volume renderer implementation that formed the foundation of this research, the design of the pilot study conducted to investigate the effectiveness of this technique, the results obtained. It further discusses improvements designed to address the issues revealed by the statistical analysis. The improved approach is able to handle visualization targets with general shapes, thus making it more appropriate to real visualization applications involving complex objects

Search Tree Data Structures and Their Applications

This study concerns the discussion of search tree data structures and their applications. The thesis presents three new top-down updating algorithms for the concurrent data processing environment.Computing and Information Scienc

Representação, visualização e manipulação de dados médicos tridimensionais: um estudo sobre as bases da simulação cirúrgica imersiva

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico. Programa de Pós-Graduação em Ciência da Computação.Dados tridimensionais referentes a pacientes são utilizados em diversos setores médico-hospitalares, fornecendo embasamento à diagnósticos e orientação durante procedimentos cirúrgicos. No entanto, apesar de bastante úteis estes dados são bastante inflexíveis, não permitindo que o usuário interaja com estes ou os manipule. O emprego de técnicas de computação gráfica e realidade virtual para a representação destes dados sanaria estas dificuldades, gerando representações indivíduais e adaptadas para cada paciente e permitindo a realização de planejamentos cirúrgicos e cirurgias auxiliadas por computador, dentre outras possibilidades. A representação destes dados e as formas de manipulação devem conter um conjunto de elementos e obedecer alguns requisitos para que se obtenha realismo nas aplicações, caso contrário, o emprego destas técnicas não traria grandes vantagens. Analisando os elementos e requisitos a serem obedecidos, é construído um grafo de dependências que mostra as técnicas e estruturas computacionais necessárias para a obtenção de ambientes virtuais imersivos realistas. Tal grafo demonstra as estruturas de dados para representação de sólidos como peça chave para este tipo de aplicativos. Para suprir as necessidades destes, é apresentada uma estrutura de dado capaz de representar uma vasta classe de topologias espaciais, além de permitir rápido acesso a elementos e suas vizinhanças, bem como métodos para a construção de tal estrutura. É apresentada, também, uma aplicação para mensuração de artérias utilizando a estrutura e os métodos previamente mencionados e os resultados por obtidos por estes

Murray polygons as a tool in image processing

This thesis reports on some applications of murray polygons, which are a generalization of space filling curves and of Peano polygons in particular, to process digital image data. Murray techniques have been used on 2-dimensional and 3-dimensional images, which are in cartesian/polar co-ordinates. Attempts have been made to resolve many associated aspects of image processing, such as connected components labelling, hidden surface removal, scaling, shading, set operations, smoothing, superimposition of images, and scan conversion. Initially different techniques which involve quadtree, octree, and linear run length encoding, for processing images are reviewed. Several image processing problems which are solved using different techniques are described in detail. The steps of the development from Peano polygons via multiple radix arithmetic to murray polygons is described. The outline of a software implementation of the basic and fast algorithms are given and some hints for a hardware implementation are described The application of murray polygons to scan arbitrary images is explained. The use of murray run length encodings to resolve some image processing problems is described. The problem of finding connected components, scaling an image, hidden surface removal, shading, set operations, superimposition of images, and scan conversion are discussed. Most of the operations described in this work are on murray run lengths. Some operations on the images themselves are explained. The results obtained by using murray scan techniques are compared with those obtained by using standard methods such as linear scans, quadtrees, and octrees. All the algorithms obtained using murray scan techniques are finally presented in a menu format work bench. Algorithms are coded in PS-algol and the C language