A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scaling Theorems for Zero Crossings
IEEE Transactions on Pattern Analysis and Machine Intelligence
Uniqueness of the Gaussian Kernel for Scale-Space Filtering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Based Detection of Corners of Planar Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Theory of Multiscale, Curvature-Based Shape Representation for Planar Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
Iterative Smoothed Residuals: A Low-Pass Filter for Smoothing With Controlled Shrinkage
IEEE Transactions on Pattern Analysis and Machine Intelligence
Geometric heat equation and nonlinear diffusion of shapes and images
Computer Vision and Image Understanding
Optimal Local Weighted Averaging Methods in Contour Smoothing
IEEE Transactions on Pattern Analysis and Machine Intelligence
Feature Detection with Automatic Scale Selection
International Journal of Computer Vision
Edge Detection and Ridge Detection with Automatic Scale Selection
International Journal of Computer Vision
The Topological Structure of Scale-Space Images
Journal of Mathematical Imaging and Vision
Local Reproducible Smoothing Without Shrinkage
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast retrieval of isolated visual shapes
Computer Vision and Image Understanding
Curvature Scale Space Representation: Theory, Applications, and MPEG-7 Standardization
Curvature Scale Space Representation: Theory, Applications, and MPEG-7 Standardization
The Relevance of Non-Generic Events in Scale Space Models
International Journal of Computer Vision
Distinctive Image Features from Scale-Invariant Keypoints
International Journal of Computer Vision
Multi-scale curvature product for robust image corner detection in curvature scale space
Pattern Recognition Letters
Direct Curvature Scale Space: Theory and Corner Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
A new image registration scheme based on curvature scale space curve matching
The Visual Computer: International Journal of Computer Graphics
A probabilistic approach for 3D shape retrieval by characteristic views
Pattern Recognition Letters
Scale-Space Behavior of Planar-Curve Corners
IEEE Transactions on Pattern Analysis and Machine Intelligence
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
Robust player gesture spotting and recognition in low-resolution sports video
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part IV
Area and length minimizing flows for shape segmentation
IEEE Transactions on Image Processing
Matching shapes with self-intersections: application to leaf classification
IEEE Transactions on Image Processing
Foveated Visual Search for Corners
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
A multiscale representation method for nonrigid shapes with a single closed contour
IEEE Transactions on Circuits and Systems for Video Technology
Shape retrieval based on parabolically fitted curvature scale-space maps
IScIDE'12 Proceedings of the third Sino-foreign-interchange conference on Intelligent Science and Intelligent Data Engineering
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Curve smoothing has two important applications in computer vision and image processing: 1) the curvature scale-space (CSS) technique for shape analysis, and 2) the Gaussian filter for noise suppression. In this paper, we study how planar curves converge as they are smoothed with increasing scales. First, two types of convergence behavior are clarified. The coined term shrinkage refers to the reduction of arc-length of a smoothed planar curve, which describes the convergence of the curve latitudinally; and another coined term collapse refers to the movement of each point to its limiting position, which describes the convergence of the curve longitudinally. A systematic study on the shrinkage and collapse of three categories of curve models is then presented. The corner models helps to reveal how the local structures of planar curves collapse and what the smoothed curves may converge to. The sawtooth models allows us to gain insights regarding how noise is suppressed from noisy planar curves by the Gaussian filter. Our investigation on the closed curves shows that each curve collapses to a point at its center of mass. However, different curves may yield different limiting shapes at the infinity scale. Finally, based upon the derived results the performance of the CSS technique in corner detection and shape representation is analyzed, and a fast implementation method of the Gaussian filter for noise suppression is proposed.