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## 留言板

 引用本文: 李晶晶, 许建楼, 熊静, 张选德. 基于方向场正则化的线描画生成算法. 自动化学报, 2021, 47(3): 685−694
Li Jing-Jing, Xu Jian-Lou, Xiong Jing, Zhang Xuan-De. Line drawing generation algorithm based on direction field regularization. Acta Automatica Sinica, 2021, 47(3): 685−694 doi: 10.16383/j.aas.c190393
 Citation: Li Jing-Jing, Xu Jian-Lou, Xiong Jing, Zhang Xuan-De. Line drawing generation algorithm based on direction field regularization. Acta Automatica Sinica, 2021, 47(3): 685−694

## Line Drawing Generation Algorithm Based on Direction Field Regularization

Funds: Supported by National Natural Science Foundation of China (61871260, 61603234)
###### Author Bio: LI Jing-Jing　Master student at the School of Electronic Information and Artificial Intelligence, Shaanxi University of Science and Technology. She received her bachelor degree in internet of things engineering from Xi＇ an Innovation College of Yan ＇ an University in 2017. Her research interest covers image processing and image style transfer XU Jian-Lou　Associate professor at the School of Mathematics and Statistics, Henan University of Science and Technology. He received his Ph.D. degree in applied mathematics from Xidian University in 2013. His research interest covers image processing variational method and sparse optimization XIONG Jing　Lecturer at the School of Electronic Information and Artificial Intelligence, Shaanxi University of Science and Technology. She received her Ph.D. degree in computer application from Xidian University in 2016. Her research interest covers video image processing, moving target detection and tracking ZHANG Xuan-De　Professor at the School of Electronic Information and Artificial Intelligence, Shaanxi University of Science and Technology. He received his Ph.D. degree in applied mathematics from Xidian University in 2013. His research interest covers image restoration, image quality evaluation, sparse representation, and low rank approximation theory. Corresponding author of this paper
• 摘要:

图像风格转化在计算机视觉领域广受关注, 其研究目标在于将输入图像利用计算机转化为具有某种特定艺术风格的图像. 线描画作为一种古老的画种, 它通过简单的线条勾勒物体的轮廓, 具有简约、抽象的风格. 本文提出一种基于方向场正则化的线描画生成算法, 该算法由4部分构成: 1)采用非局部平均滤波对输入图像进行预处理; 2)计算输入图像的方向场, 并基于自表示的思想对方向场进行Tikhonov正则化, 为了提高运算速度, 采用Sherman-Morrison-Woodbury公式来对正则化算法进行加速; 3)以正则方向场作为引导, 对预处理图像作高斯差分滤波; 4)根据人类视觉系统的非线性特点, 设计感知阈值(Perceptual thresholding)算法来对高斯差分滤波的结果进行阈值处理, 得到二值化的线描画图像. 仿真实验表明, 该算法可将输入图像转化为线条流畅且能有效表达输入图像主要信息的线描画图像.

• 图  1  线描画图

Fig.  1  Line drawing

图  2  几种边缘检测算子采用的模板

Fig.  2  Templates for several edge detection operators

图  3  几种边缘检测算子和本文算法在Baboon上的效果对比

Fig.  3  Comparison of several edge detection operators and the algorithm of this paper on Baboon

图  4  几种边缘检测算子和本文算法在Lena上的效果对比

Fig.  4  Comparison of several edge detection operators and the algorithm of this paper on Lena

图  5  基于方向场正则化的线描画生成算法框图

(注: 为了使正则化的效果可视, 对方向场进行降维处理且只在Lena局部区域上显示)

Fig.  5  Block diagram of line drawing generation algorithm based on direction field regularization

(Note: In order to make the regularization effect visible, the direction field is dimension-reduced and displayed only on the local area of Lena)

图  6  计算方向导数采用的模板

Fig.  6  Template for calculating directional derivatives

图  7  方向场正则化效果图

(注: 为了使正则化的效果可视, 对方向场进行降维处理且只在Lena局部区域上显示)

Fig.  7  Directional field regularization effect map

(Note: In order to make the regularization effect visible, the direction field is dimension-reduced and displayed only on the local area of Lena)

图  8  RDF-DoG滤波操作示意图

Fig.  8  RDF-DoG filtering operation diagram

图  9  HVS对于灰度变化的感知过程

Fig.  9  HVS perception process of grayscale changes

图  10  客观灰度变化与感知到的变化之间的关系

Fig.  10  The relationship between objective grayscale changes and perceived changes

图  11  Lena图像在不同参数$\tau$时的线描画

Fig.  11  Line drawing of Lena images at different parameters $\tau$

图  13  线描画图

Fig.  13  Line drawing

图  12  测试图像

Fig.  12  Test image

•  [1] Pandey R K, Karmakar S, Ramakrishnan A G. Computationally efficient approaches for image style transfer. arXiv preprint. arXiv: 1807.05927, 2018. [2] Decaudin P. Cartoon-looking rendering of 3D-scenes. INRIA, 1996. [3] DeCarlo D, Santella A. Stylization and abstraction of photographs. In: Proceedings of the 29th Annual Conference on Computer Graphics and Interactive Techniques. New York, USA: TOG, 2002, 21(3): 769−776 [4] Santella A, DeCarlo D. Visual interest and npr: an evaluation and manifesto. In: Proceedings of the 3rd International Symposium on Non-Photorealistic Animation and Rendering. New York, USA: ACM Press, 2004. 71−78 [5] Kyprianidis J E, Döllner J. Image abstraction by structure adaptive filtering. In: Proceedings of the 6th Theory and Practice of Computer Graphics Conference. Manchester, UK: TPCG, 2008. 51−58 [6] Kang H, Lee S, Chui C K. Flow-based image abstraction. IEEE Transactions on Visualization Computer Graphics, 2009, 15(1): 62−76 [7] Qian W H, Xu D, Yue K, Guan Z. Image abstraction painting of flow-like stylization. Tehnicki Vjesnik, 2015, 22(4): 837−844 doi: 10.17559/TV [8] Gatys L A, Ecker A S, Bethge M. Image style transfer using convolutional neural networks. In: Proceedings of the 2016 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Las Vegas, USA: IEEE, 2016. 2414−2423 [9] Johnson J, Alahi A, Li F F. Perceptual losses for real-time style transfer and super-resolution. In: Proceedings of the 14th European Conference on Computer Vision. Amsterdam, Netherlands: Springer, 2016. 694−711 [10] Ulyanov D, Lebedev V, Vedaldi A, Lempitsky V. Texture networks: feed-forward synthesis of textures and stylized images. In: Proceedings of the 33rd International Conference on Machine Learning. New York, USA. 2016. 1(2): 4 [11] Elad M, Milanfar P. Style-transfer via texture-synthesis. IEEE Transactions on Image Processing, 2017, 26(5): 2338−2351 [12] Kwatra V, Essa I, Bobick A. Texture optimization for example-based synthesis. ACM Transactions on Graphics (ToG), ACM, 2005, 24(3): 795−802 doi: 10.1145/1073204 [13] Buades A, Coll B, Morel J M. A non-local algorithm for image denoising. In: Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. San Diego, USA: IEEE, 2005. 60−65 [14] Horn R A and Johnson C R. Matrix Analysis. New York: Cambridge University Press, 2012. [15] Marr D, Hildreth E. Theory of edge detection. Proceedings of the Royal Society B: Biological Sciences, 1980, 207(1167): 187−217 [16] Winnemöller H, Olsen S C, Gooch B. Real-time video abstraction. In: Proceedings of the 2006 ACM Siggraph Papers. New York, USA: TOG, 2006. 25(3): 1221−1226

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##### 出版历程
• 收稿日期:  2019-05-20
• 录用日期:  2019-06-27
• 刊出日期:  2021-04-02

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