零相位滤波与最小二乘拟合下的聚焦形貌恢复
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摘要
为提升形貌恢复精度,提出一种高精度的聚焦形貌恢复算法。该方法从序列图像的预处理以及深度值连续化处理角度入手,将零相位滤波与最小二乘拟合法相结合。自行设计了基于巴特沃斯低通的零相位滤波器用以聚焦评价函数曲线的滤波处理,在消除噪声干扰的同时,保持各空间数据点位置不变;根据聚焦评价函数曲线特性,利用基于高斯函数的最小二乘拟合峰值法获取窗口序列的聚焦位置,进一步提高了峰值定位精度;为得到更为连续化的被测物深度信息,采用三次B样条曲面对各个像素点的初始深度值进行插值。实验表明,方法兼具形貌恢复的平滑性及高精度性。
In order to improve shape recovery precision,this paper introduces a high accuracy of 3 D shape recovery algorithm which took cue from reducing the effect of noise and refining the initial depth map and combined zero-phase filer with least squares fitting. To filter the evaluation function of window sequence image,a new Zero-phase Filter is designed based on Butterworth low pass filter,it can remain the position of each dimensional data point constant while eliminating noise,so as to get a more accurate focusing position. According to the properties of focus measure curve,the peak value position of the evaluation function is got by computing the extreme of the least square quadratic curve based on Gaussian function. At last using the cubic surface interpolation,all the more continuous depth of the measurement object is obtained. The experiment shows that the method of this paper both flatness and higher accuracy of shape recovery.
In order to improve shape recovery precision,this paper introduces a high accuracy of 3 D shape recovery algorithm which took cue from reducing the effect of noise and refining the initial depth map and combined zero-phase filer with least squares fitting. To filter the evaluation function of window sequence image,a new Zero-phase Filter is designed based on Butterworth low pass filter,it can remain the position of each dimensional data point constant while eliminating noise,so as to get a more accurate focusing position. According to the properties of focus measure curve,the peak value position of the evaluation function is got by computing the extreme of the least square quadratic curve based on Gaussian function. At last using the cubic surface interpolation,all the more continuous depth of the measurement object is obtained. The experiment shows that the method of this paper both flatness and higher accuracy of shape recovery.
引文
[1]Nayar S K,Nakagawa Y.Shape from focus[J].Pattern analysis and machine intelligence,IEEE Transactions on,1994,16(8):824-831.
[2]姜志国,史文华,韩冬兵.基于聚焦合成的显微三维成像系统[J].CT理论与应用研究,2004,13(4):9-15.(Jiang Zhi-guo,Shi Wen-hua,Han Dong-bing.Study on auto focusing algorithm for automatic microscope[J].Journal of Image and Graphics,2004,9(4):396-401.)
[3]Nourbakhsh I R,Andre D,Tomasi C.Mobile robot obstacle avoidance via depth from focus[J].Robotics and Autonomous Systems,1997,22(2):151-158.
[4]朱爱斌,胡浩强,何大勇.采用频域融合方法的砂轮刀具磨损三维重构技术[J].西安交通大学学报,2015,49(5):82-86.(Zhu Ai-bin,Hu Hao-qiang,He Da-yong.Three-dimensional reconstruction of tool wear area for grinding wheel using frequency-domain fusion method[J].Journal of Xi’an Jiaotong University,2015,49(5):82-86.)
[5]Darrell T,Wohn K.Pyramid based depth from focus[C]//Computer Vision and Pattern Recognition,1988.Proceedings CVPR'88.Computer Society Conference on.IEEE,1988:504-509.
[6]Nayar S K,Nakagawa Y.Shape from focus:An effective approach for rough surfaces[C]//Robotics and Automation,1990.Proceedings.,1990IEEE International Conference on.IEEE,1990:218-225.
[7]Subbarao M,Choi T.Accurate recovery of three-dimensional shape from image focus[J].Pattern analysis and machine intelligence,IEEE Transactions on,1995,17(3):266-274.
[8]Shim S O,Malik A S,Choi T S.Noise reduction using mean shift algorithm for estimating 3D shape[J].The Imaging Science Journal,2011,59(5):267-273.
[9]杨维,范勇,陈念年.基于灰色关联度的聚焦形貌恢复[J].计算机应用研究,2015,32(2):613-618.(Yang Wei,Fan Yong,Chen Nian-nian.Shape from focus using relative degree of grey incidence[J].Application Research of Computers,2015,32(2):613-618.)
[10]Lee I H,Shim S O,Choi T S.Improving focus measurement via variable window shape on surface radiance distribution for 3D shape reconstruction[J].Optics and Lasers in Engineering,2013,51(5):520-526.
[11]Mahmood M T,Choi T S.3D shape recovery from image focus using kernel regression in eigenspace[J].Image and Vision Computing,2010,28(4):634-643.
[12]Mahmood M T,Majid A,Choi T S.Optimal depth estimation by combining focus measures using genetic programming[J].Information Sciences,2011,181(7):1249-1263.
[13]Mahmood M T,Shim S O,Alshomrani S.Depth from image focus methods for micro-manufacturing[J].The International Journal of Advanced Manufacturing Technology,2013,67(5-8):1701-1709.
[14]胡涛,刘国栋,浦昭邦.基于零相位滤波的聚焦形貌恢复技术[J].光电工程,2011,38(12):145-150.(Hu Tao,Liu Guo-dong,Pu Zhao-bang.Depth from focus based on zerophase filter[J].Opto-Electronic Engineering,2011,38(12):145-150.)
[15]孙即祥.图像分析[M].北京:科学出版社,2005.(Sun Xie-xiang.Image Analysis[M].Beijing:Science Press,2005.)
[16]王能超.数值分析简明教程[M].武汉:华中科技大学出版社,2002.(Wang Neng-chao.A Concise Course of Numerical Analysis[M].Wuhan:Huazhong University of Science and Technology Press,2002.)
[2]姜志国,史文华,韩冬兵.基于聚焦合成的显微三维成像系统[J].CT理论与应用研究,2004,13(4):9-15.(Jiang Zhi-guo,Shi Wen-hua,Han Dong-bing.Study on auto focusing algorithm for automatic microscope[J].Journal of Image and Graphics,2004,9(4):396-401.)
[3]Nourbakhsh I R,Andre D,Tomasi C.Mobile robot obstacle avoidance via depth from focus[J].Robotics and Autonomous Systems,1997,22(2):151-158.
[4]朱爱斌,胡浩强,何大勇.采用频域融合方法的砂轮刀具磨损三维重构技术[J].西安交通大学学报,2015,49(5):82-86.(Zhu Ai-bin,Hu Hao-qiang,He Da-yong.Three-dimensional reconstruction of tool wear area for grinding wheel using frequency-domain fusion method[J].Journal of Xi’an Jiaotong University,2015,49(5):82-86.)
[5]Darrell T,Wohn K.Pyramid based depth from focus[C]//Computer Vision and Pattern Recognition,1988.Proceedings CVPR'88.Computer Society Conference on.IEEE,1988:504-509.
[6]Nayar S K,Nakagawa Y.Shape from focus:An effective approach for rough surfaces[C]//Robotics and Automation,1990.Proceedings.,1990IEEE International Conference on.IEEE,1990:218-225.
[7]Subbarao M,Choi T.Accurate recovery of three-dimensional shape from image focus[J].Pattern analysis and machine intelligence,IEEE Transactions on,1995,17(3):266-274.
[8]Shim S O,Malik A S,Choi T S.Noise reduction using mean shift algorithm for estimating 3D shape[J].The Imaging Science Journal,2011,59(5):267-273.
[9]杨维,范勇,陈念年.基于灰色关联度的聚焦形貌恢复[J].计算机应用研究,2015,32(2):613-618.(Yang Wei,Fan Yong,Chen Nian-nian.Shape from focus using relative degree of grey incidence[J].Application Research of Computers,2015,32(2):613-618.)
[10]Lee I H,Shim S O,Choi T S.Improving focus measurement via variable window shape on surface radiance distribution for 3D shape reconstruction[J].Optics and Lasers in Engineering,2013,51(5):520-526.
[11]Mahmood M T,Choi T S.3D shape recovery from image focus using kernel regression in eigenspace[J].Image and Vision Computing,2010,28(4):634-643.
[12]Mahmood M T,Majid A,Choi T S.Optimal depth estimation by combining focus measures using genetic programming[J].Information Sciences,2011,181(7):1249-1263.
[13]Mahmood M T,Shim S O,Alshomrani S.Depth from image focus methods for micro-manufacturing[J].The International Journal of Advanced Manufacturing Technology,2013,67(5-8):1701-1709.
[14]胡涛,刘国栋,浦昭邦.基于零相位滤波的聚焦形貌恢复技术[J].光电工程,2011,38(12):145-150.(Hu Tao,Liu Guo-dong,Pu Zhao-bang.Depth from focus based on zerophase filter[J].Opto-Electronic Engineering,2011,38(12):145-150.)
[15]孙即祥.图像分析[M].北京:科学出版社,2005.(Sun Xie-xiang.Image Analysis[M].Beijing:Science Press,2005.)
[16]王能超.数值分析简明教程[M].武汉:华中科技大学出版社,2002.(Wang Neng-chao.A Concise Course of Numerical Analysis[M].Wuhan:Huazhong University of Science and Technology Press,2002.)