A reconstruction of an unknown 3-D surface from a collection of its cross sections; an implementation

In biological research, medical diagnosis and therapy, as well as in architecture, automobile, and ship design a three dimensional solid must be reconstructed from a set of sections, either to aid in the comprehension of the object's structure or to facilitate its automatic manipulation and ana...

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Bibliographic Details
Published in:International journal of computer mathematics Vol. 26; no. 3-4; pp. 143 - 160
Main Author: Livadas, Panos E.
Format: Journal Article
Language:English
Published: Abingdon Gordon and Breach Science Publishers 01.01.1989
Taylor and Francis
Subjects:
Algorithms
Applied sciences
Artificial intelligence
Computer science; control theory; systems
contour
D.1.0 Programming Techniques
data structures
E.1 Data Structures
Exact sciences and technology
F.2.0 Analysis of Algorithms
G.2.2 Graph Theory
graph
graphics pipeline
I.3.4 Graphics Utilities I.3.5 Object Modeling
I.4.0 Image Processing
image generation
J.3 Medical Sciences
object modeling
object reconstruction
Pattern recognition. Digital image processing. Computational geometry
sampling
Surface reconstruction
Medical imagery
Three dimensional representation
Algorithm
Edge boundary
Computer graphics
ISSN:0020-7160, 1029-0265
Online Access:Get full text
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Summary:In biological research, medical diagnosis and therapy, as well as in architecture, automobile, and ship design a three dimensional solid must be reconstructed from a set of sections, either to aid in the comprehension of the object's structure or to facilitate its automatic manipulation and analysis. This paper presents a mathematical solution to that problem which is due to Fuchs, Kedem and Uselton [3] and an algorithm that implements that solution; the solution of the problem requires the approximation of each lateral surface band delimited by two neighbouring contour lines by tiles. To determine the set of tiles needed to approximate each lateral band, one has to find a certain minimum cost cycle in a directed toroidal graph. It is shown that the search for this cycle could be restricted to a planar graph. An algorithm for finding that cycle is given and its implementation is presented.
ISSN:0020-7160
1029-0265
DOI:10.1080/00207168908803691