A Method for High Resolution Color Image Zooming using Curvature Interpolation

Abstract
We introduce a new zooming algorithm curvature interpolation method(CIM) based on partial differential equation, which produce high resolution(HR) color image by solving a linearized curvature equation. Partial Differential Equations (PDEs) have become an important tool for interpolation methods in image processing and analysis. CIM first evaluates the curvature of the low-resolution image, after interpolating the curvature to the high-resolution image domain, to minimize the artifacts such as image blur and the checkerboard effect. The results demonstrate that our new CIM algorithm significantly enhances the quality of the interpolated images with sharp edges over linear interpolation methods.
Keywords:Curvature interpolation method (CIM), higher resolution (HR). Image zooming, interpolation, partial differential equation (PDE).
I.Introduction
Images with high resolution and fine and shape edges are always venerable and required in many visual tasks. The major benefit of interpolation techniques is that it may cost less and the existing equipment’s can be utilized. Resampling of images is necessary for discrete image geometrical transformation. Interpolation method should be applied for resampling technique, which evaluate by two basic steps. The first one is transformation of discrete function into continuous function and second step is sampling evaluation. Image interpolation in image zooming required some basic mission such as generation, compression, and zooming [2] ,[6],[7],[13].
Interpolation techniques are classified into three methods: linear, non-linear, and variation. Linear interpolation methods are may bring up image blur or check board effect. So various non-linear methods are introduced to overcome the artifacts of linear methods. Nonlinear methods is fit the edges of images with some templates, and integrate that edges with partial differential equation (PDE). Many interpolation methods for high visual quality have been developed in image zooming process [1-3], and problems still exist. These problems are highly related to image edges, including the blurring of edges, blocking artifacts in diagonal directions and inability to generate fine details [3].
For the importance of edge-preserving in application fields, a large number of edge-directed interpolation methods have been presented [3-12]. In a new edge-directed interpolation which takes geometric duality to estimate the covariance of targeted high resolution (HR) area from that of local window pixels in low resolution (LR). a HR image with well clear edges is obtained by fourth-order linear interpolation [20]. A zooming algorithm takes as .input an RGB picture and provides as output a picture of greater size maintaining the information of the original image as much as conceivable. Unfortunately, the methods mentioned in the passage above, can preserve the low frequency content of the source image well, but are not equally well to enhance high frequencies in order to produce an image whose visual sharpness matches the quality of the original one.
The CIM based on PDE method can produce zoomed image, which have the same curvature profile as in the original image in lower resolution then can be formed in high resolution. Edge forming schemes for the image zooming of color images by general magnification factors. The basic outline of our paper is as follows. Section II shows us linear interpolation methods and edge-forming method. In section III CIM method for color image zooming is discuss with its three steps. In section IV the numerical examples and peak signal to noise ratio(PSNR) analysis are given. Section V concludes our paper and its effectiveness.