The image deformation often appears in the image processing system.So it is necessary to develop a highly efficient algorithm to get a good result of the deformation.But most of the existing deformation algorithms are based on Pixel-Fill-Method

and there are some obvious faults in these algorithms:(1) When the shape of the deformation region is complex

the efficiency of these algorithms is lower.(2) Some errors may occur when the pixels are mapped from the original image region to the destination image region since one target pixel may be relative to several source pixels.To solve these problems

a new deformation algorithm based on calculus is presented in this paper.In this algorithm a complex shape deformation region will be divided into several sub-regions firstly

and then each sub-region will be divided into many Small-Rectangles

at last a standard rectangle fill algorithm is applied to fill pixels in the corresponding rectangles.The experimental results from our algorithm show that there is a better effectof image deformation and a higher efficiency when using our algorithm.And our algorithm has been successfully applied to a human face beautifying system based on its real photo which was developed by the authors.