Bispectrum-based feature of 2D and 3D images invariant to similarity transformations

A novel feature of 2D and 3D images invariant to similarity transformations is derived from the bispectrum. The invariant feature represents the amount of the triplets of the sinusoids with the frequency components consisting of the apexes of similar triangles. An effective method of calculating the invariant feature is also presented. Computer simulation on sinusoidal patterns of different phases and texture images shows that the invariant feature is applicable to the recognition of images suffering from shift and rotation in arbitrary degree, scaling up to double, and additive noise