In this paper, a new image compression method is presented using the Distance Transform on Curved Space (DTOCS) and derivative information in finding positions for control points. In previous work it has been shown that the control points are not in exactly optimal positions. This paper presents theoretical considerations according to which the new method enhances the decompressed image quality particularly in the areas of rapid changes. The obtained results shown verify the correctness of the theoretical considerations. The reconstructed image quality is clearly better measured by error criteria. Also visually the difference is significant.