In this paper, two control point-based image compression methods are presented. In the first method, the encoding is based on the roughness of the surface defined by the gray levels of the image. The second method utilizes a new distance transform, called the Distance Transform on Curved Space (DTOCS). The related compression ratios of both of the methods are very good. Also the computations needed are quite simple and require only a short processing time. The study includes the investigation of properties of the control point-based interpolation.
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