Abstract
This paper presents an image interpolation model with nonlocal p‐Laplacian regularization. The nonlocal p‐Laplacian regularization overcomes the drawback of the partial differential equation (PDE) proposed by Belahmidi and Guichard (2004) that image density diffuses in the directions pointed by local gradient. The grey values of images diffuse along image feature direction not gradient direction under the control of the proposed model, that is, minimal smoothing in the directions across the image features and maximal smoothing in the directions along the image features. The total regularizer combines the advantages of nonlocal p‐Laplacian regularization and total variation (TV) regularization (preserving discontinuities and 1D image structures). The derived model efficiently reconstructs the real image, leading to a natural interpolation, with reduced blurring and staircase artifacts. We present experimental results that prove the potential and efficacy of the method.
Highlights
Digital image interpolation is an important technology in digital photography, TV, multimedia, advertising, and printing industries, which is applied to obtain higher-resolution image with better perceptual quality
The goal of image interpolation is to solve the inverse problem 2.1, an ill-posed inverse problem. This ill-posed inverse problem is generally approached in a regularization-based framework, which would be formulated as an energy functional 9, E u Jd u, u0 λJr u, 2.2 where λ is a regularization parameter that controls the tradeoff between Jd and Jr
The diffusion process along the direction of edge curves is suppressed for small |u y, t − u x, t |p−2, and the diffusion along the orthogonal direction is enhanced for larger |u y, t − u x, t |p−2. This results in minimal smoothing in the directions across the image features preserving sharp edges and maximal smoothing in the directions along the image features reducing zigzagging artifacts and oscillatory
Summary
Digital image interpolation is an important technology in digital photography, TV, multimedia, advertising, and printing industries, which is applied to obtain higher-resolution image with better perceptual quality. The methods based on edge direction were proposed to obtain smooth edges of the resulting images 1–3. Malgouyres and Guichard 8 proposed to choose as solution of the interpolation the image that minimizes the TV This method leads to resulting images without blurring effects, as it allows discontinuities and preserves 1D fine structures. In order to enhance edge preservation, this PDE performs a diffusion with strength and orientation adapted to image structures This method balances linear zooming on homogeneous regions and anisotropic diffusion near edges, trying to combine the advantages of these two processes. We propose a new method for image interpolation based on nonlocal p-.
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