特征约束的有理多项式图像放大  

Rational Polynomial Image Magnification Constrained by Feature

作　　者：张帆 周浩 王桦 姜新波 张彩明 Zhang Fan;Zhou Hao;Wang Hua;Jiang Xinbo;Zhang Caiming(School of Computer Science and Technology,Shandong Technology and Business University,Yantai 264005;Shandong Future Intelligent Financial Engineering Laboratory,Yantai 264005;School of Information and Electrical Engineering,Ludong University,Yantai 264011;School of Software,Shandong University,Jinan 250101)

机构地区：[1]山东工商学院计算机科学与技术学院,烟台264005 [2]山东省未来智能金融工程实验室,烟台264005 [3]鲁东大学信息与电气工程学院,烟台264011 [4]山东大学软件学院,济南250101

出　　处：《计算机辅助设计与图形学学报》2022年第7期1047-1057,共11页Journal of Computer-Aided Design & Computer Graphics

基　　金：山东省高等学校青创科技计划(2019KJN042);国家自然科学基金(62007017,61602277,61907025).

摘　　要：图像边缘的质量对图像的视觉效果起着至关重要的作用,而现有图像放大方法保持图像边缘的作用不明显.因此,提出一种构造有理多项式曲面对图像拟合的图像放大方法.首先,对每个像素,以图像边缘为约束,构造能较好保持图像边缘特征的局部拟合二次多项式曲面片.然后,根据每个曲面片对邻近图像的逼近精度构造有理权函数,每个正方形网格上由4张二次多项式曲面片加权组合生成有理多项式曲面片,所有有理多项式曲面片拼合起来形成整体曲面.整体曲面在图像边缘处的误差较大,因此构造误差曲面对整体曲面进行修正,以提高整体曲面的精度和保边缘特征能力.文中方法与其他7种方法相比的实验结果表明,对于4组常用的比较图像集,其生成的放大图像在set5,set14和Urban100图像集的平均PSNR和SSIM值是最高的,而在BSD100图像集的平均PSNR和SSIM值是次高的;对用于比较边缘保持效果的3幅图像,其边缘保持能力都最好,因此视觉效果最好;另外,该方法的复杂度和速度和Bicubic属于相同的数量级,适用于实时图像放大处理,比其余6种方法的速度明显更快.The quality of the image edge plays a crucial role in the visual effect of the image,and the existing image magnification methods keep the edge of the image insignificant.To this end,an image magnification method is proposed to construct a rational polynomial surface to fit the image.First,for each pixel,taking the edge of the image as the constraint,a local fitting quadratic polynomial surface patch which can better preserve the edge features of the image is constructed.Then,according to the approximation accuracy of each surface patch to adjacent images,a rational weight function is constructed.On each square grid,the weighted combination of four quadratic polynomial surfaces generates a rational polynomial surface patch,and all rational polynomial surface patches are combined to form an overall surface.The error of the overall surface at the edge of the image is relatively large,so the error surface is constructed.The overall surface is corrected to improve the accuracy of the overall surface and the ability to preserve edge features.The ex-perimental results compared with the other seven methods show that,for the four commonly used compari-son image sets,the average PSNR and SSIM values of the magnified images generated by this method are the highest in set5,set14 and Urban100,and are the second highest in BSD100.For the three images used to compare the effect of edge preservation,proposed method has the best edge preservation ability,so the vis-ual effect is the best.In addition,the complexity and algorithm speed of proposed method belong to the same order of magnitude as Bicubic,which is suitable for real-time image magnification processing,and is sig-nificantly faster than the other six methods.

关 键 词：有理多项式曲面 边缘特征 图像放大 逼近精度 修正曲面 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]