This paper presents a new method to implement the digital image morphing based on Delaunay triangulation. Contrasting to the usually used quadrilateral meshes

the character regions are defined by triangular meshes

which can allow a more freely selection of control points and much less number of the selected control points. The two triangular meshes are determined by the corresponding control points on the two morphing images. In order to define a unique triangular mesh using a set of points on the integer grids as in digital images

three additional criterions are proposed as the complementary rule to the Delaunay triangulation. According to the large amount of computation in the coordinate transform process

a new algorithm of coordinate transform is presented based on the classical Bresenham algorithm

only addition and subtraction computation is employed

the multiplication and round computation are avoided

and then the whole process was accelerated greatly. With the new method a satisfying morphing result has been acquired.