Image processing algorithms are based on the idea that all pixels of it ranked over the orderly rows, which make the algorithms easier to be implemented. Extending image processing algorithms to triangular mesh is always an important idea for triangular mesh processing. But since the topology of a triangular mesh is not as simple as an image, triangular mesh processing is relatively difficult. This paper presented a new sphere image representation of a triangular mesh, which is an image as well as a graphic, and based on it, image processing algorithms can be easily extended to a triangular mesh. Experimental results show that by simply extending the image processing algorithms the presented sphere image representation can effectively reduce difficult of segmentation and mesh editing. Moreover the sphere image representation can be used for more triangular mesh processing applications.