A complete set of rotationally and translationally invariant features for images

We propose a new set of rotationally and translationally invariant features for image or pattern recognition and classification. The new features are cubic polynomials in the pixel intensities and have the unusual property that up to numerical error and a bandwidth limit they are complete, in the sense that they uniquely determine the original image modulo rigid transformations. Our construction is based on the generalization of the concept of bispectrum to the three-dimensional rotation group SO(3), and a projection of the image onto the sphere. Summary The generalization of the classical bispectrum to a locally compact Lie group G takes the form b(ρ1, ρ2) = C† f(ρ1) ⊗ f(ρ2) † C ρ f(ρ), (1) where ρ1 and ρ2 range over a complete set of inequivalent irreducible complex valued matrix representations of G, f(ρ) are the corresponding Fourier components, and C is the Clebsch-Gordan matrix decomposing ρ1 ⊗ ρ2 into a sum of irreducible representations here indexed by ρ. ...

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Risi Imre Kondor
• Keywords: Bispectrum, Compact Lie Groups, CORR 2007, Education, Image