Exact bias correction and covariance estimation for stereo vision
Exact bias correction and covariance estimation for stereo vision
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立体视觉的精确偏差校正和协方差估计
DOI：
10.1109/cvpr.2015.7298950
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Philippos Mordohai
中科院分区：
文献类型：
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作者：
Charles Freundlich;M. Zavlanos;Philippos Mordohai
我们提出了一种方法，用于纠正由校准的立体声钻机成像的3D重建点的偏差。我们的分析基于以下观察结果：由于量化误差，由三角测量重建的3D点基本上代表了整个空间中的整个区域。产生三角剖分点的世界点的真实位置可能在该地区的任何地方。我们认为，如果要在没有偏见的空间中代表该区域的重建点，则应位于该地区的质心上，这不是文献中所做的。我们在空间中得出了这些区域的确切几何形状，我们称之为3D单元，并展示了它们如何被视为一对相应像素的可能的前图像的均匀分布。通过假设3D中的点均匀分布，而不是图像上这些3D点的投影的均匀分布，我们得出了每个单元中三角测量偏置的快速准确计算。此外，我们得出了3D细胞的确切协方差矩阵。我们在各种模拟中验证我们的方法，从3D重建到相机定位和相对运动估计。在所有情况下，我们都可以证明与小小观值的常规技术相比，偏见很大，所需的校正很大。
We present an approach for correcting the bias in 3D reconstruction of points imaged by a calibrated stereo rig. Our analysis is based on the observation that, due to quantization error, a 3D point reconstructed by triangulation essentially represents an entire region in space. The true location of the world point that generated the triangulated point could be anywhere in this region. We argue that the reconstructed point, if it is to represent this region in space without bias, should be located at the centroid of this region, which is not what has been done in the literature. We derive the exact geometry of these regions in space, which we call 3D cells, and we show how they can be viewed as uniform distributions of possible pre-images of the pair of corresponding pixels. By assuming a uniform distribution of points in 3D, as opposed to a uniform distribution of the projections of these 3D points on the images, we arrive at a fast and exact computation of the triangulation bias in each cell. In addition, we derive the exact covariance matrices of the 3D cells. We validate our approach in a variety of simulations ranging from 3D reconstruction to camera localization and relative motion estimation. In all cases, we are able to demonstrate a marked improvement compared to conventional techniques for small disparity values, for which bias is significant and the required corrections are large.