# A Method for High Resolution Color Image Zooming using Curvature Interpolation

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**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.

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