Epipolar Rectification Based on Singular Value Decomposition of Camera Translation Matrix
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摘要: 极线校正是一种针对双目相机原始图像对的投影变换方法, 使校正后图像对应的极线位于同一水平线上，消除垂直视差，将立体匹配优化为一维搜索问题。针对现今极线校正的不足，本文提出一种基于双目相机平移矩阵的极线校正方法：首先利用奇异值分解（singular value decomposition, SVD）平移矩阵，求得校正后的新旋转矩阵；其次通过校正前后的图像关系确立一个新相机内参矩阵，完成极线校正。运用本文方法对SYNTIM数据库的不同场景多组双目图像进行验证，实验结果表明平均校正误差在0.6像素内，图像几乎不产生畸变，平均偏斜在2.4°左右，平均运行时间为0.2302 s，该方法具有应用价值，完全满足极线校正的需求，解决了双目相机在立体匹配过程中由于相机的机械偏差而产生的误差和繁琐的计算过程。Abstract: Epipolar rectification is a projection transformation method for the original image pair of a binocular camera such that the corresponding polar lines of the corrected image are on the same horizontal line, no vertical parallax occurs, and stereo-matching is optimized as a one-dimensional search problem. A polar correction method based on a binocular camera translation matrix is proposed to address the shortcomings of current polar correction methods. First, the new corrected rotation matrix is derived using the translation matrix of singular value decomposition. Second, a new camera internal reference matrix is established based on the image relationship before and after correction to complete the polar correction. The proposed method was used to verify multiple groups of binocular images in different scenes in the SYNTIM database. The experimental results show that the average correction error is within 0.6 pixels. The image produces minimal distortion, and the average deviation is approximately 2.4°. The average operation time is 0.2302 s. With its application value, this method fully satisfies polar correction requirements, solves the error, and improves the tedious calculation process caused by the mechanical deviation of the camera during the stereo matching of binocular cameras.
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Keywords:
- binocular vision /
- epipolar rectification /
- machine vision /
- depth camera
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图 3 20对图像使用不同方法的误差(a)、畸变(b)、偏斜(c)、运行时间(d)
Figure 3. Rectification error(a), scale variance(b), skewness(c)and runtime(d) of different methods for 20 images
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图 4 画出极线的Rubik图像及极线斜率(a) 原始图像（斜率=1.23×10-2）(b) Bouguet方法（斜率=3.82×10-7）(c) Fusiello方法（斜率=2.71×10-7）(d) Hartley方法（斜率=3.95×10-5）(e) Mallon方法（斜率=3.19×10-7）(f) Wu方法（斜率=1.48×10-6）(g) 本文推荐方法（斜率=2.39×10-7）
Figure 4. Rubik image with polar line drawn and polar line slope (a) Original image(Slope=1.23×10-2); (b) Bouguet's method (Slope=3.82×10-7); (c) Fusiello's method(Slope=2.71×10-7); (d) Hartley's method(Slope=3.95×10-5); (e) Mallon's method(Slope=3.19×10-7); (f) Wu's method(Slope=1.48×10-6); (g) Proposed rectification method (Slope=2.39×10-7)
表 1 平均误差、畸变、偏斜、运行时间
Table 1 Average error, scale, variance, skewness and runtime
Methods Bouguet Fusiello Hartley Mallon Wu Proposed Error in pixels 0.6495 0.6268 0.8467 0.6361 0.7028 0.5940 Scale variance 1.2275 1.2261 1.1270 1.1243 1.1900 1.0062 Skewness/(°) 2.3369 2.4472 2.5156 3.2096 3.0419 2.3941 Runtime/s 0.2349 0.2294 0.8473 1.305 0.2412 0.2302 
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