The Multiscale Local Directional Cosine Bases for Image Representation

Motivated by the fact that in textures, there is usually a presence of strongly oriented harmonics, a representation which is both well-localised in frequency and orientation is desirable to efficiently describe such oriented harmonic features. Here we introduce a family of directional trigonometric bases for a bi-variate function which is defined as !#"%$ & '( )$+* ,-&% .% /.% where the 0 is a trigonometric basis vector. Similar to the ridgelet transform, the directional trigonometric transform can be computed in the Radon domain, by applying the trigonometric transform on the projected sinograms. In practice, we use 1 ( 32%4% 65 7 !8"9$: <;>= 0 @? , commonly known as “cosine-II” vectors due to their fast convergence. We conducted denoising experiments on a Laplacian pyramid’s highpass subbands with fixed-size non-overlapping windows followed by the directional cosine transform. The results show promise of the proposed basis which almost consistently outperforms its ridgelet counterpart on natural images while the results on texture images and fingerprints are superior. Index Terms Directional representation, cosine basis, Radon transform, denoising, restoration. Z. Yao is with the Computer Science Department, University of Warwick, CV4 7AL UK. E-mail: [email protected] N. Rajpoot is with the Computer Science Department, University of Warwick, CV4 7AL UK. E-mail: [email protected] December 1, 2004 DRAFT 2