Gray scale potential theory of sparse image

According to the relative position among the pixels of sparse image, we proposed the Gray Scale Potential of image. By taking the example of the binary images, this paper highlighted the definition of gray scale potential and the extraction of gray scale potential. Then we pointed out that the gray scale potential was an intrinsic feature of image. As for binary image, it reflects the relative distances of pixels to a baseline or to a reference point, and if the image is gray image, it reflects not only the distances but also the gray level feature. The gray scale potential has obvious advantage in representing the sparse image, because it can reduce the computational work and storage. Even two-dimensional image can be simplified to one-dimensional curve. Finally, some experimental data were given to illustrate the concept of gray scale potential. It shows that the gray scale potential of image is a steady feature and can be used in object recognition.