﻿ 自适应立方卷积图像插值算法
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Adaptive cubic convolution based image interpolation approach
Li Chunlong, Pan Haixia, Wang Huafeng
School of Software, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Abstract:Image interpolation is an important technique of image processing, which can be used in many image process areas. In recent years, it is often used to zoom in or zoom out images. A novel effective image interpolation mechanism to enhance the enlarged image edges was proposed for the visual artifacts problem in traditional magnification algorithms and the high computational cost in some adaptive image interpolation algorithms. The proposed algorithm combines the edge-directed gradient with the cubic convolution interpolation algorithm to obtain the higher quality of an image both in the edges and smooth areas. The result shows that the proposed algorithm gets a better visual effect and effectively removes the jaggy and blur at the edge. The proposed algorithm is less complex with running time reduced by 3.19 s on average, compared with the edge-adaptive interpolation algorithm, and has higher quality with the peak signal-to-noise ratio (PSNR) raised by 0.89 dB on average, compared with the cubic algorithm.
Key words: image interpolation     edge direction     cubic convolution     gradient     peak signal-to-noise ratio (PSNR)

Keys[2]的三次插值基函数表达式为

 图 1 待插值点示意图 Fig. 1 Diagram of integration point

 图 2 本文图像插值流程图 Fig. 2 Flowchart of proposed algorithm

 图 3 插值示意图 Fig. 3 Diagrams of integration
2.1 边缘检测

135°对角线方向梯度计算公式为

 图 4 对角线梯度示意图 Fig. 4 Diagram of diagonal gradient
 图 5 水平与垂直梯度示意图 Fig. 5 Diagrams of horizontal and vertical gradient

1) 初始化:将n×n的低分辨率图像IL放大为(2n-1)×(2n-1)的高分辨率图像IH,两图像对应关系为IH(2x-1,2y-1)=IL(x,y),其中x,y=1,2,…,n.

2) 第1轮插值,对图 3a中的白色方块IH(2x,2y),x,y=1,2,…,n进行插值,根据立方卷积计算每一待插值点的45°对角线方向和135°对角线方向的像素p1p2,根据式(13)确定该点的像素值:

3) 第2轮插值,此时方块点为已知像素,对图 3b中的灰色圆点IH(2x-1,2y)和白色圆点IH(2x-1,2y-1)，x,y=1,2,…,n进行插值,根据立方卷积计算每一待插值点水平方向和垂直方向的像素p1p2,根据式(13)确定该点的像素值. 3) 第2轮插值,此时方块点为已知像素,对图 3b中的灰色圆点IH(2x-1,2y)和白色圆点IH(2x-1,2y-1)，x,y=1,2,…,n进行插值,根据立方卷积计算每一待插值点水平方向和垂直方向的像素p1p2,根据式(13)确定该点的像素值. 2.3 阈值T与指数k的确定

 图 6 信噪比变化图 Fig. 6 Curves of PSNR
 图 7 各算法插值结果图 Fig. 7 A set of result images

PSNR值和平均计算时间如表 1所示.

 s 图像单位 立方卷积 基于边缘特征 本文算法 Airplane 29.47 30.39 30.68 Bike 26.02 26.10 26.39 Einstein 30.99 31.07 31.40 Flinstones 26.78 27.50 27.79 Flower 31.98 32.41 32.54 Gripen 31.89 32.02 32.23 Lena 32.87 33.30 34.40 Monarch 29.99 30.76 31.30 Parrot 32.99 33.89 34.26 Rings 53.28 53.34 54.11 计算时间 2.55 5.87 2.68

1) 边缘定向平滑,具有较高的视觉质量,成功消除了传统插值算法存在的边缘锯齿现象;

2) 与传统立方卷积插值算法相比,信噪比增加了0.89dB;

3) 与基于特征的插值算法相比,本文所提算法的平均运行时间降低了3.19s.

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#### 文章信息

Li Chunlong, Pan Haixia, Wang Huafeng

Adaptive cubic convolution based image interpolation approach

Journal of Beijing University of Aeronautics and Astronsutics, 2014, 40(10): 1463-1468.
http://dx.doi.org/10.13700/j.bh.1001-5965.2013.0621