基于边缘和距离约束的有理多项式图像放大  

Rational polynomial image magnification based on edge and distance constraints

作　　者：张帆 王桦 范辉[1] 张彩明 Fan ZHANG;Hua WANG;Hui FAN;Caiming ZHANG(School of Computer Science and Technology,Shandong Technology and Business University,Yantai 264005,China;School of Information and Electrical Engineering,Ludong University,Yantai 264025,China;Shandong Provincial Key Laboratory of Digital Media Technology,Shandong University of Finance and Economics,Jinan 250014,China)

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]鲁东大学信息与电气工程学院,烟台264025 [3]山东财经大学山东省数字媒体技术重点实验室,济南250014

出　　处：《中国科学：信息科学》2021年第8期1270-1286,共17页Scientia Sinica(Informationis)

基　　金：山东省高等学校青创科技支持计划(批准号:2019KJN042);国家自然科学基金(批准号:U1609218,62007017)资助项目。

摘　　要：曲面拟合是最有效的图像放大方法之一,其关键是构造对图像拟合的曲面.图像细节和边缘等特征对图像的视觉效果起着关键作用,因此,构造拟合曲面的关键之一是保持图像细节和边缘.基于样条和多项式方法构造的拟合曲面不能有效地保持图像的边缘信息,从而使放大图像在边缘处锯齿状明显.本文提出了以边缘和距离为特征约束的图像放大新算法.算法以边缘和距离为约束,在每个像素的邻近区域上构造一张对邻域上像素点拟合的二次多项式曲面片,并在每个四边形网格上构造一张二次多项式中间曲面片.在每个四边形网格上由五张曲面片加权平均生成有理多项式曲面片.该曲面片具有二次多项式逼近精度,产生的图像具有较好的视觉效果.通过构造误差曲面片对二次多项式曲面片进行修正,提高了放大图像的精度和视觉效果.新算法把二次多项式的常数项、一次和二次项采用不同方法分别计算,为构造带约束的多项式函数提供了新技术.实验结果表明,相比于其他算法,本文算法不仅有较高的逼近精度,而且放大图像的视觉效果也较好.Surface fitting is one of the most effective methods in image magnification. The key is to construct the surface fitting the image. Image details and edges play a key role in the visual effect of the image. Therefore,one of the keys to constructing the fitting surface is to preserve the image details and edges. The surface fitting methods based on spline and polynomial cannot effectively preserve the edge information of the image, so that the magnified image has obvious jagged edges. In this paper, a new image magnification algorithm based on edge and distance constraints is proposed. The algorithm constructs a quadratic polynomial surface patch on the adjacent region of each pixel, which fits the pixels in the neighborhood, and a quadratic polynomial median surface patch is constructed on each quadrilateral mesh. The rational polynomial patch is generated from the weighted average of five patches on each quadrilateral mesh. The patch has the accuracy of the quadratic polynomial approximation,and the resulting image has a better visual effect. The accuracy and visual effects of the magnified image are improved by constructing error patches. The new algorithm calculates the constant term, the first term and the second term of the quadratic polynomial by different methods, which provides a new technique for constructing the polynomial function with constraints. The experimental results show that compared with other algorithms, the proposed algorithm not only has higher approximation accuracy but also has better visual effect of the magnified image.

关 键 词：二次多项式 边缘和距离约束 逼近曲面 逼近精度 图像放大 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]