Skeletonization of ribbon-like shapes based on a new wavelet function

A wavelet-based scheme to extract skeleton of Ribbon-like shape is proposed in this paper, where a novel wavelet function plays a key role in this scheme, which possesses three significant characteristics, namely, 1) the position of the local maximum moduli of the wavelet transform with respect to the Ribbon-like shape is independent of the gray-levels of the image. 2) When the appropriate scale of the wavelet transform is selected, the local maximum moduli of the wavelet transform of the Ribbon-like shape produce two new parallel contours, which are located symmetrically at two sides of the original one and have the same topological and geometric properties as that of the original shape. 3) The distance between these two parallel contours equals to the scale of the wavelet transform, which is independent of the width of the shape. This new scheme consists of two phases: 1) Generation of wavelet skeleton - based on the desirable properties of the new wavelet function, symmetry analyses of the maximum moduli of the wavelet transform is described. Midpoints of all pairs of contour elements can be connected to generate a skeleton of the shape, which is defined as wavelet skeleton. 2) Modification of the wavelet skeleton - Thereafter, a set of techniques are utilized for modifying the artifacts of the primary wavelet skeleton. The corresponding algorithm is also developed in this paper. Experimental results show that the proposed scheme is capable of extracting exactly the skeleton of the Ribbon-like shape with different width as well as different gray-levels. The skeleton representation is robust against noise and affine transformation.