中文摘要：

图像表示是计算机图形学、计算机视觉、图像处理和模式识别等领域里的一个重要问题.文中扩展了著名的Gouraud阴影法,并通过使用矩形非对称逆布局模型（RNAM）和扩展的Gouraud阴影法,提出了一种新的灰度图像表示算法.该算法编解码部分的时间复杂度分别为O（nlogn）和O（n）,其中n为灰度图像的像素数.实验结果表明：与流行的STC和SDCT灰度图像表示算法相比,在保持图像质量的前提下,文中提出的灰度图像表示算法具有更高的压缩比和更少的块数,因而能够更有效地减少数据存储空间,是灰度图像表示的一种良好方法.这种表示方法可以应用于灰度图像表示的各个方面,在降低存储空间、加快传输速度、提高模式匹配效率等方面具有良好的理论参考意义和实际应用价值.

英文摘要：

Image representation is an important problem in computer graphics,computer vision,image processing,and pattern recognition.By extending the well-known Gouraud shading method,this paper proposes a new algorithm for the gray image representation by using the Rectangular Non-symmetry and Anti-packing Model（RNAM）and extended shading approach.The encoding and the decoding can be executed in O（n log n）and O（n）time,respectively,where n denotes the number of pixels in the gray image.By comparing the proposed algorithm with the popular STC and SDCT algorithms for the gray image representation,it is shown that the former has the higher compression ratio and the less number of blocks than the latters whereas maintaining the image quality,and therefore it can reduce the data storage much more effectively than the latters and it is a better method to represent the gray image.The proposed algorithm for the gray image representation shows a very strong promise and has good potential in theoretical research and business applications,such as reducing storage room,increasing transmission speed,improving pattern match efficiency,and so on.