Reversible Interpolation of Vectorial Images by an Anisotropic Diffusion-Projection PDE

In this paper, a nonlinear model for the interpolation of vector-valued images is proposed. This model is based on an anisotropic diffusion PDE and performs an interpolation that is reversible. The interpolation solution is restricted to the subspace of functions that can recover the discrete input image, after an appropriate smoothing and sampling. The proposed nonlinear diffusion flow lies on this subspace while its strength and anisotropy adapt to the local variations and geometry of image structures. The derived method effectively reconstructs the real image structures and yields a satisfactory interpolation result. Compared to classic and other existing PDE-based interpolation methods, our proposed method seems to increase the accuracy of the result and to reduce the undesirable artifacts, such as blurring, ringing, block effects and edge distortion. We present extensive experimental results that demonstrate the potential of the method as applied to graylevel and color images. The authors acknowledge the financial support of the Future and Emerging Technologies (FET) programme ‘ASPI’ within the Sixth Framework Programme for Research of the European Commission, under FET-Open contract No. 021324.