一种基于微分思想的图象变形算法研究与实现

Research on an Image Deformation Algorithm Based on Calculus and Its Implementation

图象变形是图象处理中的基本问题 ,不仅要求图象变形效果好 ,而且要求变形算法效率高 .目前已有的变形算法 ,大多采用基于象素点的填充方法 ,这种方法有比较明显的缺点 :(1)当变形的图象区域是一个非规则区域时 ,图象变形处理所花费的时间增加 ,即算法的时间复杂度加大 ,效率低 ;(2 )在对象素点作映射变换时 ,可能出现变形后的图象区域中一个象素点对应变形前的图象区域中多个象素点 ,因此造成取舍困难 ,甚至造成取舍错误 .为解决这一问题 ,本文提出了一种基于微分思想的图象变形算法 ,该算法先将复杂的变形区域划分为一系列子区域 ,再将每个子区域划分为多个小矩形 ,将对应的小矩形按照标准矩形填充算法进行快速填充 ,由此实现图象变形 .实验结果表明 ,该算法实现简单 ,计算速度快 ,填充效果好 ,并已成功地应用于笔者开发的基于真实照片的人脸整形与美容图象处理系统中 .

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 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 effect of image deformation and a higher efficiency when using our algorithm. And our algorithm is successfully applied to a human face beautifying system based on its real photo which was developed by the authors.