Based on the fact that the construction of invariants for isometric deformed object is difficult to research the pattern recognition, a new construction method of moment invariants for isometric deformed object was proposed to study the isometric deformed object recognition problem. First, fast marching method on triangulate domains was employed to compute the signature matrix to store the geodesic distance of every point pair. Secondly, the invariance was guaranteed by the normalization procedure on the signature matrices. Then, the moment invariants were constructed based on the normalized s...