We present a new algorithm, called marching cubes, that creates triangle models of constant density surfaces from 3D medical data. Using a divide-and-conquer approach to generate inter-slice connectivity, we create a case table that defines triangle topology. The algorithm processes the 3D medical data in scan-line order and calculates triangle vertices using linear interpolation. We find the gradient of the original data, normalize it, and use it as a basis for shading the models. The detail in images produced from the generated surface models is the result of maintaining the inter-slice connectivity, surface data, and gradient information present in the original 3D data. Results from computed tomography (CT), magnetic resonance (MR), and single-photon emission computed tomography (SPECT) illustrate the quality and functionality of marching cubes. We also discuss improvements that decrease processing time and add solid modeling capabilities.

/pdf/marching-cubes-a-high-resolution-3d-surface-construction-3ealswkmtb.pdf

Marching cubes: A high resolution 3D surface construction algorithm

Apercu sur les quadarbres et les structures de donnees hierarchiques. Elles sont basees sur le principe de decomposition recursive. L'accentuation est mise sur la representation de donnees dans les applications de traitement d'images, d'infographie, les systemes d'informations geographiques et la robotique. On examine en detail un certain nombre d'operations dans lesquelles de telles structures de donnees trouvent leur utilisation

/pdf/the-quadtree-and-related-hierarchical-data-structures-38sprs9bn9.pdf

The Quadtree and Related Hierarchical Data Structures

Three-dimensional models provide a volumetric representation of space which is important for a variety of robotic applications including flying robots and robots that are equipped with manipulators. In this paper, we present an open-source framework to generate volumetric 3D environment models. Our mapping approach is based on octrees and uses probabilistic occupancy estimation. It explicitly represents not only occupied space, but also free and unknown areas. Furthermore, we propose an octree map compression method that keeps the 3D models compact. Our framework is available as an open-source C++ library and has already been successfully applied in several robotics projects. We present a series of experimental results carried out with real robots and on publicly available real-world datasets. The results demonstrate that our approach is able to update the representation efficiently and models the data consistently while keeping the memory requirement at a minimum.

/pdf/octomap-an-efficient-probabilistic-3d-mapping-framework-3dp42nnofi.pdf

OctoMap: an efficient probabilistic 3D mapping framework based on octrees

The computer code system PENELOPE (version 2008) performs Monte Carlo simulation of coupled
electron-photon transport in arbitrary materials for a wide energy range, from a few hundred eV to
about 1 GeV. Photon transport is simulated by means of the standard, detailed simulation scheme.
Electron and positron histories are generated on the basis of a mixed procedure, which combines
detailed simulation of hard events with condensed simulation of soft interactions. A geometry package
called PENGEOM permits the generation of random electron-photon showers in material systems
consisting of homogeneous bodies limited by quadric surfaces, i.e., planes, spheres, cylinders, etc. This
report is intended not only to serve as a manual of the PENELOPE code system, but also to provide the
user with the necessary information to understand the details of the Monte Carlo algorithm.

/pdf/penelope-2006-a-code-system-for-monte-carlo-simulation-of-43nx3zmw6c.pdf

PENELOPE-2006: A Code System for Monte Carlo Simulation of Electron and Photon Transport

Three-dimensional models provide a volumetric representation of space which is important for a variety of robotic applications including flying robots and robots that are equipped with manipulators. In this paper, we present an open-source framework to generate volumetric 3D environ- ment models. Our mapping approach is based on octrees and uses probabilistic occupancy estimation. It explicitly repre- sents not only occupied space, but also free and unknown areas. Furthermore, we propose an octree map compression method that keeps the 3D models compact. Our framework is available as an open-source C++ library and has already been successfully applied in several robotics projects. We present a series of experimental results carried out with real robots and on publicly available real-world datasets. The re- sults demonstrate that our approach is able to update the representation efficiently and models the data consistently while keeping the memory requirement at a minimum.

Donald Meagher

Papers

Geometric modeling using octree encoding