Shift and rotation invariant feature of 3D patterns based on the third-order correlation

The author presents a novel feature of three-dimensional (3D) patterns invariant to shift and rotation based on the third-order correlation. The invariant feature, the table of the triple product of similar triangles, represents the amount of the apexes of similar triangles in 3D image data. Computer simulation shows that three kinds of 3D lattice point patterns are well recognized under random shift and rotation by using the invariant feature.

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