Piecewise Linear Digital Curve Representation and Compression Using Graph Theory and a Line Segment Alphabet

The use of an alphabet of line segments to compose a curve is a possible approach for curve data compression. Many approaches are developed with the drawback that they can process simple curves only. Curves having more sophisticated topology with self-intersections can be handled by methods consider...

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Bibliographic Details
Published in:IEEE transactions on image processing Vol. 17; no. 2; pp. 126 - 133
Main Authors: Hajdu, A., Pitas, I.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.02.2008
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Applied sciences
Chinese postman problem
Coding, codes
Computer Graphics
Computer Simulation
curve compression
curve partitioning
Data compression
Data Compression - methods
Digital images
Euler graph
Exact sciences and technology
Geometry
Graph theory
Graphics
Image coding
Image Enhancement - methods
Image Interpretation, Computer-Assisted - methods
Image processing
Image segmentation
Imaging, Three-Dimensional - methods
Information, signal and communications theory
Linear Models
optimal curve tracing
Piecewise linear approximation
Piecewise linear techniques
Reproducibility of Results
Sensitivity and Specificity
Signal and communications theory
Signal processing
Signal Processing, Computer-Assisted
Telecommunications and information theory
Topology
Alphabet
Performance evaluation
Euler equation
Partition method
Line segment
Data compression
Graph theory
Algorithm
Chinese postman problem
curve partitioning
optimal curve tracing
Recursive method
Chinese
curve compression
Euler graph
Piecewise linearization
ISSN:1057-7149, 1941-0042
Online Access:Get full text
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Description
Summary:The use of an alphabet of line segments to compose a curve is a possible approach for curve data compression. Many approaches are developed with the drawback that they can process simple curves only. Curves having more sophisticated topology with self-intersections can be handled by methods considering recursive decomposition of the canvas containing the curve. In this paper, we propose a graph theory-based algorithm for tracing the curve directly to eliminate the decomposition needs. This approach obviously improves the compression performance, as longer line segments can be used. We tune our method further by selecting optimal turns at junctions during tracing the curve. We assign a polygon approximation to the curve which consists of letters coming from an alphabet of line segments. We also discuss how other application fields can take advantage of the provided curve description scheme.
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ISSN:1057-7149
1941-0042
DOI:10.1109/TIP.2007.914202