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Scale-space behavior of planar-curve corners
Baojiang Zhong1, Kai-Kuang Ma, Wenhe Liao
1Nanjing University of Aeronautics and Astronautics, Nanjing, People's Republic of China. zhbj@nuaa.edu.cn
Summary
This study corrects a previous assumption about planar curve shrinkage in scale-space analysis. It reveals how curve shrinkage affects corner detection and provides a new measure for consistent digital curvature scale-space mapping.
Area of Science:
- Computer Vision
- Image Analysis
- Computational Geometry
Background:
- The curvature scale-space (CSS) technique is used for feature extraction from noisy object boundaries.
- Previous work on corner detection in a multiscale framework assumed no curve shrinkage during scale-space evolution.
Purpose of the Study:
- To correct the assumption of no shrinkage in planar curve evolution.
- To investigate the impact of curve shrinkage on the scale-space behavior of corners.
- To develop a robust method for corner detection in digital images.
Main Methods:
- Demonstrating nonuniform shrinkage of planar curves during scale-space evolution.
- Analyzing the properties of CSS trajectory maps considering shrinkage effects.
- Presenting a standard curvature measure for computing CSS maps of digital curves.
Main Results:
- Planar curves can shrink nonuniformly with increasing scale.
- Scale-space corner trajectories can persist, vanish, merge, or split.
- Adjacent corner trajectories exhibit attractive or repulsive behavior based on concavity.
- Digital CSS maps show consistent behavior with continuous cases.
Conclusions:
- Accounting for curve shrinkage is crucial for accurate corner detection in scale-space.
- The proposed curvature measure ensures consistent corner behavior in both continuous and digital domains.
- This research improves the reliability of the CSS technique for feature extraction.
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