中華大學應用數學系

                                    演講公告

                演講人：李 子 才 博士

                國立中山大學應用數學系與資訊工程學系教授

                講題：Face Transformation by Numerical Methods

                日期：97年5月26日（星期一）

                時間 ：15：10∼17：00  

                地點：A棟演講廳           

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Abstract

The splitting-integrating method (SIM) is well suited to the inverse transformations of digital images and patterns in 2D, but it encounters some difficulties involving nonliving solutions for the forward transformations. New techniques are explored in this paper to bypass the nonlinear solution process completely, to save CPU time, and to be more flexible for general and complicated transformations T. The intensity of images under geometric transformations by the splitting-integrating method has the error bounds, O(H)+O(H/N²) by the piecewise bilinear interpolations (µ = 1) , for smooth images, where H (<<1)  is the pixel size, and N  is the division number of a 2D pixel split into N² sub-pixels. Moreover, in practical applications there often occur the images whose discontinuity intensity jump is a minor portion of the entire image, e.g., the images with piecewise continuous intensity involving intensity jump only at the interior and exterior boundary. For this kind of discontinuous intensity, the error bounds are also derived in this paper to be O(H^β)+O(H^β/N²) , 0<β≦1 as µ = 1. Compared with the error analysis in our previous reports where the image intensity is always assumed to be smooth enough, this error analysis is significant for geometric image transformations in real application.