An improved algorithm for monocular camera edge spectrum based ranging by defocused images
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摘要:
为了实现基于单目相机的弱或无表面纹理特征目标精确测距，提出了一种基于保留边缘频谱信息的改进散焦图像测距算法。通过对比以傅立叶变换和拉普拉斯变换为计算核心的两种经典散焦测距理论，构建相应的清晰度评价函数，根据灵敏度更好的频谱清晰度函数选择基于频谱的散焦测距法，并根据频谱清晰度函数在保留目标边缘信息的基础上选择频域计算范围，从而进行测距。为验证算法的可行性，本文采用6组不同的鸭蛋样本，获取不同光圈、不同距离的散焦图像，利用该改进算法求解鸭蛋到相机镜头的距离。实验结果表明，基于边缘频谱保留的散焦图像测距改进算法具有良好的测距效果，相关系数为0.986，均方根误差为11.39 mm，并发现对于斜放拍摄的鸭蛋图像进行图像旋转处理后，可有效地提升测距能力，均方根误差从11.39 mm下降至8.76 mm，平均相对误差从2.85%下降至2.28%，相关系数提升至0.99。基本满足了弱或无表面纹理特征目标测距的稳定、精度等要求。
Abstract:In order to achieve accurate target ranging of weak or non surface texture features using a monocular camera, an improved defocused image ranging algorithm based on preserving edge spectral information is presented. By comparing two classical defocal ranging theories with Fourier transform and Laplace transform as the foundational principals of calculation, a corresponding definition evaluation function is constructed. We select the method based on the spectrum definition function with better sensitivity, and select the calculation range of the frequency domain by retaining the information on the target edge. To verify the feasibility of the algorithm, 6 sets of different duck egg samples are used to obtain scattered focus images of different apertures and distances, and the improved algorithm was used to solve the distance of the duck eggs from the camera lens. The experimental results show that the improved algorithm based on the edge spectrum preservation has a good ranging effect with a correlation coefficient of 0.986 and Root Mean Square Error (RMSE) of 11.39 mm. It is found that the range ability can be effectively improved after the image rotation processing of the duck egg image taken at an oblique angle, with the RMSE is reduced from 11.39 mm to 8.76 mm, the average relative error is reduced from 2.85% to 2.28% and the correlation coefficient reaches 0.99. The proposed algorithm fundamentally meets the requirements of stability and high accuracy in ranging targets with weak or non surface texture features.
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图 4（a）基于拉普拉斯算子及（b）基于频谱的清晰度变化
Figure 4.Sharpness changes based on (a) the Laplacian operator and (b) spectrum
图 5（a）与（e）为鸭蛋图像，（b）与（f）为原频谱图，（c）与（g）为边缘保留频率截取图，（d）与（h）为频率截取后的频谱图像对应的时域图像
Figure 5.(a) and (e) are egg images, (b) and (f) are original spectral images, (c) and (g) are frequency-intercepted spectral images, (d) and (h) are time-domain images corresponding to the spectral images after frequency interception
图 6（a）频率截取后的清晰度变化图；（b）原清晰度变化图
Figure 6.(a) The definition change curve after the frequency interception; (b) the change of original definition
图 7基于边缘保留散焦图像测距算法流程图
Figure 7.The flow chart of ranging algorithm based on edge retaining defocus image
图 8实际距离与计算距离相关系数图
Figure 8.The correlations between observed distance and calculated distance
图 9图像旋转示意图。（a）原图；（b）旋转后图像
Figure 9.The process of image rotation. (a) Original image; (b) rotated image
图 10斜放鸭蛋经旋转处理后实际距离与计算距离相关系数图
Figure 10.The correlation between observed distance and calculated distance for oblique duck eggs after rotation treatment
图 124号鸭蛋取自然对数清晰度与物距关系图
Figure 12.Relationship between natural logarithmic clarity and object distance of egg No. 4
图 13拟合模型计算物距的相对误差
Figure 13.The relative error of the object distance from fitting model
表 1实际距离与计算距离实验结果
Table 1.The results of observed distance and calculated distance
序号 鸭蛋特征 最大误差
（mm）均方根误差
（mm）平均相对
误差（%）1 绿壳、竖放 10.90 6.59 1.63 2 白壳、竖放 16.60 10.22 2.87 3 白壳、竖放 16.99 10.65 2.98 4 白壳、横放 13.92 8.30 2.24 5 白壳、斜放 29.44 16.93 4.31 6 绿壳、斜放 24.75 12.73 3.08 总计 29.44 11.39 2.85 
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表 2图像旋转前后测距结果对比
Table 2.The ranging results before and after image rotating
序号 处理方式 最大误差
（mm）均方根误差
（mm）平均相对
误差（%）5 原始图像 29.44 16.93 4.31 图像旋转后 13.55 8.72 2.25 6 原始图像 24.75 12.73 3.08 图像旋转后 14.82 5.93 1.73 总计 原始图像 29.44 11.39 2.85 图像旋转后 16.99 8.76 2.28 下载:
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表 3拟合模型所得结果
Table 3.The results of fitting model
序号 实际距离/mm 计算距离/mm 误差/mm 相对误差/% 1 250 246.82 −3.18 −1.27 2 270 273.41 3.41 1.26 3 290 285.12 −4.88 −1.68 4 310 310.62 0.62 0.20 5 330 332.27 2.27 0.69 6 350 354.30 4.30 1.23 7 370 372.32 2.32 0.63 8 390 390.98 0.98 0.25 9 410 409.52 −0.48 −0.12 10 430 424.64 −5.36 −1.25 下载:
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表 4拟合模型参数表
Table 4.Parameters of fitting model
α β SSE R2 RMSE −91.97 (−96.21,−87.74) 1349 (1302,1395) 104.9 0.9968 3.62 下载:
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