Objective

2

Image interpolation has become an active area of research in image processing

which can be easily extended to diverse applications ranging from medical imaging

remote sensing

aviation

animation production

and multimedia entertainment industries. A large number of image interpolation methods have been proposed by researchers. Generally

the interpolation methods can be divided into discrete and continuous methods. The adaptive interpolation methods based on discrete ideas can preserve the image structure of the edge. However

its performance in maintaining image details is less than satisfactory. The image cannot be amplified at any multiple by using discrete methods. And such methods are considerably time consuming. The interpolation methods based on continuous ideas can obtain rich image detail information but cannot maintain the image edge structure well. A new method of rational function image interpolation based on gradient optimization that has the advantages of the discrete and continuous methods is proposed.

Method

2

First

a novel bivariate rational interpolation function is constructed. With varying shape parameters

the function has different forms of expression

i.e.

an organic unity of polynomial and rational models. The constructed

$${{\rm{C}}^2}$$

continuous rational function interpolation model has the advantages of the continuous method

in which the appearance of the jagged edge is reduced to some extent and becomes smooth. Second

according to the regional characteristics

the image is divided into the texture and smooth regions automatically using the isoline method. If the interpolation unit has at least an isoline

then the unit belongs to the texture region. If the interpolation unit does not have isolines

then the unit belongs to the smooth region. The smooth region is interpolated by the polynomial model

and the texture region is interpolated by the rational model. Finally

according to the isotropic Sobel operator

the image gradient of the interpolation unit is calculated and the direction of the texture region is determined. According to the image gradient and texture direction

the weight of the influencing factor of every interpolation unit is obtained. Then

the center of the image patch with different directions is optimized by convoluting with the weight matrix.

Result

2

A rational function image interpolation algorithm based on gradient optimization is proposed. The proposed algorithm is tested in three different aspects

namely

objective data

visual effect

and time complexity. Compared with the state-of-the-art interpolation algorithms

the average peak signal-to-noise ratio of the proposed method is 1.5

0.36

0.14

0.28

1.11

and 0.95 dB higher than that of the bicubic

RSAI

DFDF

NARM

NEDI

and Lee's algorithms

respectively. The average structural similarity of the proposed method is 0.0968

0.007 2

0.007 6

0.005 2

0.014 1

and 0.023 7 higher than that of the bicubic

RSAI

DFDF

NARM

NEDI

and Lee's algorithms

respectively. The image reconstructed by the proposed method has richer texture detail and sharper edge structure than that by the bicubic

RSAI

DFDF

NARM

NEDI

and Lee's algorithms. The average runtime of the proposed method is 7 s

which is 3.28

5.26

53.28

43.53

and 418.54 times faster than that of DFDF

NEDI

RSAI

Lee's

and NARM algorithms. For texture images such as Baboon

Barbara

and Metal

the proposed method is highly competitive not only in objective data but also in visual effect.

Conclusion

2

We construct a bivariate rational interpolation function in this study. On the basis of this model

an image interpolation algorithm based on gradient optimization is presented

which is not only able to scale the reconstructed image indefinitely but also has a low time complexity. Experimental results show that the proposed algorithm preserves the image details and structures of the edge effectively and generates a high-quality interpolation image.