AN ALGORITHM FOR MAKING A CORRESPONDENCE OF ZERO-CROSSING POINTS IN AWAVELET TRANSFORM DOMAIN WITH 2ND-ORDER DERIVATIVE PROPERTY

The multiscale wavelet transform (MWT) is the method of multiple resol ution analysis using the wavelet transform. In MWT with the property o f the second-order derivative, the position of the zero-crossing point of the transform signal corresponds to the position of the edge of th e original:signal. The edge has an important role in image information . If the correspondence of the zero-crossing points related to the edg es can be established between scanning lines or between frames by some means, the correspondence can be utilized in the sophistication of im age processing (such as motion analysis, stereo matching, interpolatio n, and noise reduction). From such a viewpoint, this paper discusses t he correspondence between the zero-crossing points in MWT, i.e., the c orrespondence of scales and the correspondence between two similar sig nals, and presents a method that provides visually plausible correspon dence as a result. Especially for the correspondence between signals, the accuracy of the correspondence of zero-crossing points is improved by introducing the cost function. Computational complexity is kept wi thin a practical range, by applying the dynamic. programming and utili zing the branch structure of the zero-crossing points among various sc ales. The idea of cross-validation is applied to the correspondence of signals between the scanning lines of the image, and a method is comp osed that evaluates visually the quality of the signal correspondence method by the naked-eye observation of this image. With this evaluatio n method, the usefulness of the proposed algorithm for the signal corr espondence and its problems are indicated. It is shown that a visually reasonable result is obtained by adjusting the weight coefficient of the multiplication factor of the cost function in the signal correspon dence process.