Polygonal Approximation Techniques in Digital Curve Analysis
Summary
Polygonal approximation techniques seek to represent continuous or digital curves by sequences of linear segments. Traditional approaches include global methods that optimise a prespecified error metric over the entire curve and local strategies that iteratively fit segments to small curve portions. The Douglas–Peucker algorithm typifies local threshold-based methods, reducing vertices by recursively discarding points that lie within an error bound. Dynamic programming techniques, conversely, furnish optimal approximations by minimising cumulative error at the cost of higher computational overhead. More recent developments leverage metaheuristic optimisation—such as particle swarm and artificial bee colony algorithms—to balance approximation fidelity with vertex count. Curvature-driven schemes adaptively allocate more segments to high-curvature regions, improving local accuracy. These techniques find applications in computer vision, GIS, medical image analysis and shape recognition, where efficient representations of boundaries and contours are critical for subsequent processing and interpretation.
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Polygonal Approximation Techniques in Digital Curve Analysis publication trend
The graph below shows the total number of articles in polygonal approximation techniques in digital curve analysis across all publications each year (not limited to Nature Index journals).
Technical terms
Polygonal approximation: Representation of a continuous or digital curve by a sequence of straight-line segments.
Integrated square error: Sum of squared distances between the original curve and its polygonal approximation, used as an optimisation metric.
Threshold-based method: Technique that iteratively fits segments until a specified maximum deviation from the original curve is reached.
Metaheuristic optimisation: Search strategy employing high-level heuristics, such as swarm intelligence, to optimise a problem-specific objective function.
Curvature: Rate of change of the tangent direction along a curve, indicating how sharply it bends at a point.
References
- Polygonal Approximation Using an Artificial Bee Colony Algorithm. Mathematical Problems in Engineering (2015).
- Landmark Analysis Of Leaf Shape Using Polygonal Approximation. IOP Conference Series Earth and Environmental Science (2016).
- CURVATURE APPROXIMATION FROM PARABOLIC SECTORS. Image Analysis & Stereology (2017).
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