Efficient Algorithms for Invariant Discrete Wavelet Decomposition

Classical discrete wavelet packet transforms are sensitive to changes in image orientation and translation. Therefore, it is hardly possible to extract rotation invariant features from images in the transform domain. This paper proposes several algorithms for invariant discrete wavelet decomposition to produce an invariant representation for an image. The procedure can be divided into several steps. A polar transform, which employs an adaptive sampling technique, converts a rotated image into its equivalent rotation invariant row-shifted image; a row shift invariant wavelet packet decomposition is then applied to the polar image, producing the rotation invariant but over completed subbands of wavelet coefficients. Key-Words: Wavelet Transforms, Shift Invariance, Rotation Invariance, Polar Transform.