The triple correlation of 2D image is a complete representation of images. It has the properties of translation invariance and insensitivity to AGN. In this paper

according to the similarity among the vector triangles formed by two indepentent vectors of triple correlation function

the distributions of these two vectors are discussed

so that the triple correlation function based on the triangle form is introduced. The translation rotation scale invariant representation is established by logarithmic mapping of the scaling factor

and FFT transforming of this function.The simulation experiment illustrates the translation rotation scale invariance of invariant representation.