Radon and Ridgelet transforms applied to motion compensated images

Images are typically described via orthogonal, non-redundant transforms like wavelet or discrete cosine transform. The good performances of wavelets in one-dimensional domain are lost when they are applied to images using 2D separable basis since they are not able to efficiently code one-dimensional singularities. The Ridgelet transform achieves very compact representation of linear singularities in images; instrumental in the implementation of the Ridgelet is the Radon transform, which is a powerful tool to find directions where images present line features. They can offer an important contribution in order to detect and represent edges, which in natural images are very important components and especially relevant from a visual point of view. Speaking about video coding, following the classical hybrid scheme, the motion compensation procedure produces a displaced frame difference (dfd) that appears as an edge dominated image. It is intuitive that ridgelet transform can be a good tool for coding dfd, given its capacity to offer a sparse analysis of singularities. This research report investigates the application of a discrete implementation of ridgelet and Radon transform to motion compensated images. Section 2 offers a brief review of ridgelet and Radon theory, including a description of a finite, discrete algorithm. Section 3 illustrates the application of discrete ridgelets to dfd, giving some results. Section 4 proposes two new algorithms that aim to exploit the ability of Radon transform to detect straight lines. Section 5 concludes the work presenting some possible future developments of these topics.