Scale-Space Technique Based On L-Curvature

For various computer vision tasks, we need to develop computational mathematical tools toanalyze and understand digital images according to their discrete characteristics. In this sense,such problems can be viewed as an application field of computational mathematics. L-curvatureis a measure of curvature for digital curves. In this paper L-curvature scale-space (L-CSS) isproposed, including the L-CSS corner detection technique, the L-CSS shape description andrepresentation technique.Scale-space corner detection can find image features at high scales and image details at lowscales. It has therefore been considered as modern tools for detecting image corners. Multi-scalecurvature product (MSCP) can enhance curvature extreme peaks and suppress noise. Bycombining the L-curvature and MSCP corner detection algorithm, a new corner detectionalgorithm, called L-curvature multi-scale curvature corner detection (L-MSCP) algorithm isproposed in this paper. The new algorithm starts with extracting the contour from the input image,and then computes the L-curvature at various scales. Finally, the curvature product of each pointis computed, and local extremes of the curvature product are recognized as corners when the valueexceeds a threshold. The algorithm can effectively enhance curvature extreme peaks whilesuppress noise. It improves localization and is more robustness to image noise. The consistency ofcorner numbers (CCN) criteria shows that the proposed algorithm is stable under rotation, scalingand affine transforms.Multi-scale shape description based on L-curvature is also proposed and studied. With thezero-crossings or local extreme of L-curvature, L-CSS maps are constructed. Experimentalresults show that L-CSS maps are stable with respect to input parameters. Visually, L-curvaturescale-space trajectories are similar with parabolic curves. In view of this point, a shape matchingalgorithm, called L-CSS parabolic-fitting algorithm is proposed. Numerical analysis shows it isconsistent with the concept of human beings.