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The theory, design, implementation and evaluation of a three-dimensional surface detection algorithm

Authors:

Gideon Frieder,

Gabor T. HermanAuthors Info & Claims

SIGGRAPH '80: Proceedings of the 7th annual conference on Computer graphics and interactive techniques

Pages 2 - 9

https://doi.org/10.1145/800250.807461

Published: 01 July 1980 Publication History

Abstract

In many three-dimensional imaging applications the three-dimensional scene is represented by a three-dimensional array of volume elements, or voxels for short. A subset Q of the voxels is specified by some property. The objects in the scene are then defined as subsets of Q formed by voxels which are “connected” in some appropriate sense. It is often of interest to detect and display the surface of an object in the scene, specified say by one of the voxels in it.

In this paper, the problem of surface detection is translated into a problem of traversal of a directed graph, G. The nodes of G correspond to faces separating voxels in Q from voxels not in Q. It has been proven that connected subgraphs of G correspond to surfaces of connected components of Q (i.e., of objects in the scene). Further properties of the directed graph have been proven, which allow us to keep the number of marked nodes (needed to avoid loops in the graph traversal) to a small fraction of the total number of visited nodes.

This boundary detection algorithm has been implemented. We discuss the interaction between the underlying mathematical theory and the design of the working software. We illustrate the software on some clinical studies in which the input is computed tomographic (CT) data and the output is dynamically rotating three-dimensional displays of isolated organs. Even though the medical application leads to very large scale problems, our theory and design allows us to use our method routinely on the minicomputer of a CT scanner.

References

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Artzy, E. Display of three-dimensional information in computed tomography. Comm. Grph. and Image Proc. 9, (Feb. 1979), 196-198.

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Artzy, E. and Herman, G.T., Boundary detection in 3-dimensions with a medical application. Comp. Graph., to appear.

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Robb, R.A., Ritman, E.L., Greenleaf, J.F., Sturm, R.E., Herman, G.T., Chevalier, P.A., Liu, H.K., and Wood, E.H., Quantitative imaging of dynamic structure and functions of the heart, lungs and circulation by computerized reconstruction and subtraction techniques. Proceedings of the 3rd Annual Conf. on Comp. Grph., Interactive Techniques and Image Processing (SIGGRAPH'76), Philadelphia, Pa. (July 1976), 246-256.

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Index Terms

The theory, design, implementation and evaluation of a three-dimensional surface detection algorithm
1. Computing methodologies
  1. Artificial intelligence
    1. Computer vision
      1. Image and video acquisition
        3D imaging
  2. Computer graphics
2. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory

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cover image ACM Conferences

SIGGRAPH '80: Proceedings of the 7th annual conference on Computer graphics and interactive techniques

July 1980

336 pages

ISBN:0897910214

DOI:10.1145/800250

ACM SIGGRAPH Computer Graphics Volume 14, Issue 3
July 1980
327 pages
ISSN:0097-8930
DOI:10.1145/965105
Issue’s Table of Contents

Copyright © 1980 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 01 July 1980

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SIGGRAPH '80 Paper Acceptance Rate 52 of 140 submissions, 37%;

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https://doi.org/10.3390/architecture3020010
Xia SLi XXu FChen LZhang Y(2019)Visualization Method for Arbitrary Cutting of Finite Element Data Based on Radial-Basis FunctionsInformation10.3390/info1007022910:7(229)Online publication date: 3-Jul-2019
https://doi.org/10.3390/info10070229
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