Image Analysis and Reconstruction using a Wavelet Transform Constructed from a Reducible Representation of the Euclidean Motion

Abstract. Inspired by the early visual system of many mammalians we consider the construction of-and reconstruction from- an orientation score Uf : R2 ×S1 → C as a local orientation representation of an image, f : R2 → R. The mapping f → Uf is a wavelet transform Wψ corresponding to a reducible representation of the Euclidean motion group onto L2(R2 ) and oriented wavelet ψ ∈ L2(R2 ). This wavelet transform is a special case of a recently developed generalization of the standard wavelet theory and has the practical advantage over the usual wavelet approaches in image analysis (constructed by irreducible representations of the similitude group) that it allows a stable reconstruction from one (single scale) orientation score. Since our wavelet transform is a unitary mapping with stable inverse, we directly relate operations on orientation scores to operations on images in a robust manner. Furthermore, by geometrical examination of the Euclidean motion group G = R2 T, which is ...

• Type: Journal
• Year: 2007
• Where: IJCV
• Authors: Remco Duits, Michael Felsberg, Gösta H. Granlund, Bart M. ter Haar Romeny
• Keywords: Euclidean Motion Group, IJCV 2007, Orientation Scores, Wavelet