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10 June 1994 Scale-invariant shape representation based on the wavelet transform
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Abstract
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.
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Sung H. Yoon, Winser E. Alexander, and Jung H. Kim "Scale-invariant shape representation based on the wavelet transform", Proc. SPIE 2232, Signal Processing, Sensor Fusion, and Target Recognition III, (10 June 1994); https://doi.org/10.1117/12.177738
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