基于三次B样条小波变换和Franklin矩亚像素级图像边缘检测算法

李锦鹏; 熊显名; 曾启林; 胡怡威; 丁子婷

基于三次B样条小波变换和Franklin矩亚像素级图像边缘检测算法

李锦鹏^{1, 2,},
熊显名^{1, 2, ,},
曾启林^{1, 2},
胡怡威¹,
丁子婷¹

1.
桂林电子科技大学电子工程与自动化学院, 广西桂林 541004
2.
广西高校光电信息处理重点实验室, 广西桂林 541004

基金项目:

国家科技重大专项课题 2017ZX02101007-003

详细信息

作者简介:
李锦鹏（1995-），男，硕士研究生，主要研究方向为机器视觉。E-mail：503482546@qq.com

通讯作者:
熊显名（1964-），男，研究员，主要研究方向为光电测量，机器视觉。E-mail：XXM5864@163.com

中图分类号: TP391.4
计量
- 文章访问数: 140
- HTML全文浏览量: 44
- PDF下载量: 25
- 被引次数: 0
出版历程
- 收稿日期: 2020-07-05
- 修回日期: 2020-08-19
- 刊出日期: 2022-03-20

Sub-pixel Level Image Edge Detection Algorithm Based on Cubic B-spline Wavelet Transform and Franklin Moment

LI Jinpeng^{1, 2
,},
XIONG Xianming^{1, 2
, ,},
ZENG Qilin^{1, 2},
HU Yiwei¹,
DING Ziting¹

1.
Institute of Electrical Engineering and Automation, Guilin University of Electronic Technology, Guilin 541004, China
2.
Key Laboratory of Optoelectronic Information Processing in Guangxi Universities, Guilin 541004, China

摘要

摘要: 为了满足精密测量和红外与可见光图像配准对图像边缘定位的高精确度和高抗噪性的要求，提出一种基于三次B样条小波变换和Franklin矩结合的亚像素级图像边缘检测算法。首先，利用三次B样条小波窗函数对图像边缘多层分解，根据小波模极大值原理对各层检测得到初始边缘信息，随后将其边缘点与多尺度范围下3×3邻域内的点进行比较，将模值和幅角相近的点保留，建立新的边缘图像。然后，建立亚像素边缘模型，根据Franklin矩旋转不变性原理，分析图像边缘旋转至一定角度之后各级Franklin矩之间的关系，得到计算亚像素边缘点的模板关键参数，将模板在小波变换得到的新边缘图像上移动并与其覆盖下的子图进行卷积运算，进而得到图像的亚像素级边缘点。实验结果表明，并与当下表现较优的3种算法进行对比，本文提出的基于三次B样条小波变换和Franklin矩结合的算法精确度更高且抗噪性更强，能够更好地满足对于红外与可见光图像配准稳定可靠及高精度测量的要求。
- 边缘检测 /
- 三次B样条小波 /
- Franklin矩 /
- 亚像素 /
- 图像配准
Abstract: To meet the requirements of high accuracy and strong anti-noise performance of image edge positioning for infrared and visible image registration and precision measurement, a sub-pixel image edge detection algorithm based on the cubic B-spline wavelet transform and Franklin moment is proposed. First, the image edge was decomposed using a cubic B-spline wavelet window function. Under the premise of setting the threshold, according to the principle of wavelet modulus maxima, the initial edge information is detected for each layer, and then the edge points are compared with the points in the 3 × 3 neighborhood in the multi-scale range. Points with similar moduli and amplitudes were reserved to establish a new edge image. Subsequently, a subpixel edge model is established. According to the principle of Franklin moment rotation invariance, the relationship between Franklin moments at all levels after the image edge is rotated to a certain angle is analyzed and the key parameters of the template for calculating the sub-pixel edge points are obtained. The template is moved on the new edge image obtained by wavelet transform and convoluted with the sub-image covered by it, and then the sub-image of the image is obtained from the edge points of the prime level. The experimental results show that, compared with the three algorithms with the current best performance, the algorithm based on the combination of the cubic B-spline wavelet transform and Franklin moments proposed in this paper has higher accuracy and stronger noise resistance. It can better meet the requirements for stable, reliable, and high-precision measurements of infrared and visible image registration.
- edge detection /
- cubic B-spline wavelet /
- Franklin moment /
- sub-pixel /
- image registration

HTML全文

图 1 亚像素边缘检测模型

Figure 1. Sub-pixel edge detection model

下载: 全尺寸图片幻灯片

图 2 自适应阈值化图像

Figure 2. Adaptive thresholding image

下载: 全尺寸图片幻灯片

图 3 二值图像

Figure 3. Binary image

下载: 全尺寸图片幻灯片

图 4 Lena图像及4种算法的边缘检测结果

Figure 4. Lena image and the edge detection results for 4 different algorithms

下载: 全尺寸图片幻灯片

表 1 Franklin径向多项式R_nm

Table 1. Franklin radial polynomials R_nm

m/n	0	1	2	3	4
0	1	Non-existent	2r²−1	Non-existent	6r⁴−6r²+1
1	Non-existent	r	Non-existent	3r³−2r	Non-existent

下载: 导出CSV

表 2 Franklin矩的复数域多项式V_nm

Table 2. Complex domain polynomial of Franklin moment V_nm

n/m	0	1
0	1	Non-existent
1	Non-existent	x+yi
2	2x²+2y²−1	Non-existent
3	Non-existent	(3x³+3xy²−2x)+(3y³+3x²y−2y)i
4	6x⁴+6y⁴+12x²y²−6x²−6y²+1	不存在

下载: 导出CSV

表 3 检测的亚像素坐标

Table 3. The detected sub-pixel coordinates

Coordinate of actual pixel	Coordinate of our algorithm	Error
(64, 114)	(64.09, 114.07)	(0.09, 0.07)
(64, 14)	(64.10, 14.11)	(0.10, 0.11)
(114, 64)	(114.09, 63.92)	(0.09, 0.08)
(14, 64)	(14.11, 64.07)	(0.11, 0.07)
(103.37, 94.24)	(103.4676, 94.3183)	(0.0976, 0.0783)
(103.37, 33.76)	(103.5185, 33.9097)	(0.1485, 0.1497)
(24.63, 94.24)	(24.7282, 94.3364)	(0.0982, 0.0964)
(24.63, 33.76)	(24.7442, 33.8883)	(0.1142, 0.1283)
(92.63, 104.52)	(92.7297, 104.6079)	(0.0997, 0.0879)
(92.63, 23.48)	(92.7538, 23.6226)	(0.1238, 0.1426)

下载: 导出CSV

表 4 四种算法运行时间

Table 4. The running time of four algorithm

Algorithm	Zernike moment	Franklin moment	Roberts operator+Zernike moment	Ours
Running time/s	0.3853	0.314 2	0.8256	0.3313

下载: 导出CSV

表 5 四种算法峰值信噪比

Table 5. PSNR for four algorithms

Algorithm	Zernike moment	Franklin moment	Roberts operator+Zernike moment	Ours
PSNR	31.8625	40.5871	36.6297	46.782

下载: 导出CSV

参考文献(13)

[1]	金光远. 图像测量技术与系统[D]. 长春: 吉林大学, 2008. JIN G Y. The Design and Realization for the Measuring System Based on Image Processing[D]. Changchun: Jilin University, 2008.
[2]	戴宪策, 刘昌锦. 快速亚像素图像配准算法研究[J]. 红外技术, 2015, 37(7): 579-581. http://hwjs.nvir.cn/article/id/0034469b-9aca-4927-8c01-0790b9e344c4 DAI Xiance, LIU Changjin. Research on fast sub-pixel image registration algorithm[J]. Infrared Technology, 2015, 37(7): 579-581. http://hwjs.nvir.cn/article/id/0034469b-9aca-4927-8c01-0790b9e344c4
[3]	Ghosal S, Mehrotra R. Orthogonal moment operators for subpixel edge detection[J]. Pattern Recognition, 1993, 26(2): 295-306. doi: 10.1016/0031-3203(93)90038-X
[4]	李金泉, 王建伟, 陈善本, 等. 一种改进的Zernike正交矩亚像素边缘检测算法[J]. 光学技术, 2003, 29(4): 500-503. doi: 10.3321/j.issn:1002-1582.2003.04.036 LI J Q, WANG J W, CHEN SH B, et al. An improved Zernike orthogonal moment sub-pixel edge detection algorithm[J]. Optical Technology, 2003, 29(4): 500-503. doi: 10.3321/j.issn:1002-1582.2003.04.036
[5]	高世一, 赵明扬, 张雷, 等. 基于Zernike正交矩的图像亚像素边缘检测算法改进[J]. 自动化学报, 2008, 34(9) : 1163-1168. https://www.cnki.com.cn/Article/CJFDTOTAL-MOTO200809019.htm GAO S Y, ZHAO M Y, ZHANG L, et al. Improvement of image sub-pixel edge detection algorithm based on Zernike orthogonal moments[J]. Journal of Automation, 2008, 34(9): 1163-1168. https://www.cnki.com.cn/Article/CJFDTOTAL-MOTO200809019.htm
[6]	吴一全, 龙云淋, 周杨. 基于Arimoto熵和Zernike矩的刀具图像亚像素边缘检测[J]. 华南理工大学学报: 自然科学版, 2017, 45(12): 50-56. doi: 10.3969/j.issn.1000-565X.2017.12.008 WU Y Q, LONG Y L, ZHOU Y. Sub-pixel edge detection of tool image based on Arimoto entropy and Zernike moment[J]. Journal of South China University of Technology: Natural Science Edition, 2017, 45(12): 50-56. doi: 10.3969/j.issn.1000-565X.2017.12.008
[7]	魏本征, 赵志敏, 华晋. 基于改进形态学梯度和Zernike矩的亚像素边缘检测算法[J]. 仪器仪表学报, 2010, 31(4): 838-844. https://www.cnki.com.cn/Article/CJFDTOTAL-YQXB201004020.htm WEI B Z, ZHAO Z M, HUA J. Sub-pixel edge detection algorithm based on improved morphological gradient and Zernike moment[J]. Chinese Journal of Scientific Instrument, 2010, 31(4): 838-844. https://www.cnki.com.cn/Article/CJFDTOTAL-YQXB201004020.htm
[8]	吴一全, 邹宇, 刘忠林. 基于Franklin矩的亚像素级图像边缘检测算法[J]. 仪器仪表学报, 2019, 29(5): 221-229. https://www.cnki.com.cn/Article/CJFDTOTAL-YQXB201905026.htm WU Y Q, ZOU Y, LIU Z l. Sub-pixel image edge detection algorithm based on Franklin moment[J]. Chinese Journal of Scientific Instrument, 2019, 29(5): 221-229. https://www.cnki.com.cn/Article/CJFDTOTAL-YQXB201905026.htm
[9]	杨小娜, 黄欢, 徐晓煜, 等. 基于小波模极大值多尺度的图像边缘提取[J]. 贵州大学学报: 自然版, 2013, 30(1): 91-93. doi: 10.3969/j.issn.1000-5269.2013.01.020 YANG X N, HUANG H, XU X Y, et al. Multi scale image edge extraction based on wavelet modulus maxima[J]. Journal of Guizhou University: Natrual Edition, 2013, 30(1): 91-93. doi: 10.3969/j.issn.1000-5269.2013.01.020
[10]	Franklin P. A set of continuous orthogonal functions[J]. Mathematische Annalen, 1928, 100(1): 522-529. doi: 10.1007/BF01448860
[11]	DA F, ZHANG H. Sub-pixel edge detection based on an improved moment[J]. Image & Vision Computing, 2010, 28(12): 1645-1658. https://www.sciencedirect.com/science/article/pii/S0262885610000788
[12]	朱文斌, 雷秉山, 雷志勇. 基于小波变换的红外探测系统信号去噪[J]. 红外技术, 2018, 40(11): 1047-1051. http://hwjs.nvir.cn/article/id/59ccddf6-ee9a-43da-983b-35ee872dd707 ZHU W B, LEI B S, LEI ZY. Signal denoising of infrared detection system based on wavelet transform[J]. Infrared Technology, 2018, 40(11): 1047-1051. http://hwjs.nvir.cn/article/id/59ccddf6-ee9a-43da-983b-35ee872dd707
[13]	刘小豫, 韩丽娜, 赵蔷. 基于B样条小波的图像边缘检测算法[J]. 电子设计工程, 2013, 21(14): 178-180. doi: 10.3969/j.issn.1674-6236.2013.14.055 LIU X Y, HAN L, ZHAO Q. Image edge detection algorithm based on B -spline wavelet[J]. Electronic Design Engineering, 2013, 21(14): 178-180. doi: 10.3969/j.issn.1674-6236.2013.14.055