Characteristic Mapping for Ellipse Detection Acceleration.

Area of Science:

• Computer Vision
• Computational Geometry
• Algebraic Geometry

Background:

• Characterizing intrinsic geometry of high-degree algebraic curves using lower-degree approximations is computationally challenging.
• Reducing curve degree offers significant computational cost benefits for practical computer vision applications.

Purpose of the Study:

• To develop a novel characteristic mapping (CM) for recursively degenerating points on higher-order planar curves to lower-order curves.
• To enable efficient grouping of elliptical arcs while preserving intrinsic geometric properties.

Main Methods:

• A characteristic mapping (CM) is proposed to reduce 3n points on an n-th order curve to 3(n-1) points on an (n-1)-th order curve.
• An efficient arc grouping module is derived based on a necessary condition for collinearity of mapped points.
• The module is embedded into two existing arc-based ellipse detection methods.

Main Results:

• The CM enables grouping of elliptical arcs on a line, preserving geometric properties.
• The derived module efficiently identifies valid elliptical arc segments with minimal computation.
• Embedding the module reduced running times of two ellipse detection methods by 25% and 50% on average.
• The CM-embedded methods achieved faster detection with comparable or higher precision than state-of-the-art algorithms.
• Performance significantly surpassed a deep learning method across all evaluation metrics.

Conclusions:

• The characteristic mapping provides an effective method for simplifying complex curve representations.
• The proposed approach significantly enhances the efficiency and accuracy of ellipse detection algorithms.
• This method offers a promising direction for improving real-time computer vision systems.