Scale-invariant shape representation based on the wavelet transform
Sung H. Yoon, W.E. Alexander, Jung H. Kim · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1994
Matching of occluded objects is a difficult problem. Moreover, the problem is more difficult when scale-invariant matching is needed. A scale invariant representation is essential for this application. In this paper, we propose using the wavelet transform of a boundary to obtain a scale-invariant representation. We use the cubic B-spline as a smoothing function of the wavelet transform since the B-spline is analytically well defined and simple to implement. We implement the fast continuous wavelet transform by using a dyadic wavelet decomposition and dilated B-splines. As a result of using the wavelet transform, we obtain boundaries at various scales while using a small number of data points. The existing scale-space image approaches are not effective for occluded object matching since they use a normalized x-axis and too many data points. We propose a new scale-invariant representation similar to the scale-space image. The representation is generated by locating zero-crossings of the curvature function of boundaries at only the scales where the number of zero-crossings is changing. We scale the x-axis for each scale instead of using the same normalization for all scales. The proposed representation is scale-invariant and appropriate for scale-invariant matching with occlusion.