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Piecewise linear digital curve representation and compression using graph theory and a line segment alphabet
1Department of Informatics, Aristotle University of Thessaloniki, Greece. hajdua@aiia.csd.auth.gr
Summary
This study introduces a graph theory algorithm for curve data compression, improving efficiency by directly tracing curves. The method enhances compression performance using longer line segments and optimal junction turns.
Area of Science:
- Computer Science
- Graph Theory
- Data Compression
Background:
- Curve data compression is essential for efficient storage and transmission.
- Existing methods struggle with complex curves featuring self-intersections.
- Recursive decomposition is a common but limited approach for complex curves.
Purpose of the Study:
- To develop a novel graph theory-based algorithm for direct curve tracing.
- To improve curve data compression performance, especially for complex topologies.
- To eliminate the need for canvas decomposition in curve processing.
Main Methods:
- A graph theory algorithm is proposed for direct curve tracing.
- The method optimizes turn selection at junctions during tracing.
- A polygon approximation using a line segment alphabet is assigned to the curve.
Main Results:
- The direct tracing approach significantly improves compression performance.
- Longer line segments are utilized, leading to greater efficiency.
- The algorithm effectively handles curves with complex topology and self-intersections.
Conclusions:
- The proposed graph theory algorithm offers a superior approach to curve data compression.
- This method overcomes limitations of existing techniques for complex curves.
- The curve description scheme has potential applications in various fields.
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