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Optimum uniform piecewise linear approximation of planar curves
1Department of Electrical Engineering, Southern Methodist University, Dallas, TX 75275.
IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 27, 2011
Summary
This study introduces an optimal algorithm for approximating digital curves with minimal piecewise linear segments. The new method ensures uniform error bounds while outperforming existing algorithms in segment count and execution speed.
Area of Science:
- Computer Vision
- Computational Geometry
- Digital Image Processing
Background:
- Uniform approximation of 2D digital curves is crucial in computer graphics and image analysis.
- Existing algorithms often yield suboptimal results in terms of segment count or computational efficiency.
- The need for precise and efficient curve approximation methods persists.
Purpose of the Study:
- To develop an algorithm for finding a piecewise linear approximation of a 2D digital curve.
- To minimize the number of linear segments used in the approximation.
- To ensure the approximation adheres to a uniform error bound with fixed endpoints.
Main Methods:
- An optimal algorithm is presented for piecewise linear curve approximation.
- The algorithm determines the minimal number of segments for a given uniform error tolerance.
- Comparison with suboptimal algorithms based on segment count and execution time.
Main Results:
- The proposed algorithm achieves the minimal number of segments for uniform approximation.
- It provides a more efficient approximation compared to several existing suboptimal methods.
- Performance is evaluated against alternative algorithms regarding segment count and computational cost.
Conclusions:
- The presented algorithm offers an optimal solution for approximating 2D digital curves with piecewise linear segments.
- It establishes a new benchmark for efficiency and accuracy in curve approximation tasks.
- This method is valuable for applications requiring precise digital curve representation.
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