This paper put forward a method of image edge detection and filtration on the curve coordinate system by the use of operator on the curve coordinate system.Edge detection is a important process in image processing

currently the popular method firstly to be used is the Laplacian operator on the Cartesian coordinate system

then the zero-crossing of the Laplacian operator can be found as edge point; image filtration is the convolution result of the differential operator on the Cartesian coordinate system too. It is not fit to deal with many images painted on surfaces such as cylindrical map image

spherical map image

digital effects for motion pictures and medical regime on three dimensional scans of organs. We make use of the differential operator on the curve coordinate system for processing images on surfaces. The practical numerical experiment results showed that differential operator on the curve coordinate system is capability for processing images on surfaces.