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摘要: 提出一种利用运动目标三维轨迹重建的视频时域同步算法.待同步的视频序列由不同相机在同一场景中同时拍摄得到，对场景及相机运动不做限制性约束.假设每帧图像的相机投影矩阵已知，首先基于离散余弦变换基重建运动目标的三维轨迹.然后提出一种基于轨迹基系数矩阵的秩约束，用于衡量不同序列子段间的空间时间对准程度.最后构建代价矩阵，并利用基于图的方法实现视频间的非线性时域同步.我们不依赖已知的点对应关系，不同视频中的跟踪点甚至可以对应不同的三维点，只要它们之间满足以下假设：观测序列中跟踪点对应的三维点，其空间位置可以用参考序列中所有跟踪点对应的三维点集的子集的线性组合描述，且该线性关系维持不变.与多数现有方法要求特征点跟踪持续整个图像序列不同，本文方法可以利用长短不一的图像点轨迹.本文在仿真数据和真实数据集上验证了提出方法的鲁棒性和性能.Abstract: We present an algorithm for synchronization of an arbitrary number of videos captured by cameras independently moving in a dynamic 3D scene. Assuming the 3D spatial poses of the cameras are known for each frame, we first reconstruct the 3D trajectory of a moving point using the trajectory basis-based method. The trajectory coefficients are computed for each sequence separately. Point correspondences across sequences are not required, or even it is possible to track different points in different sequences, only if every 3D point tracked in the second sequence is a linear combination of subsets of the 3D points tracked in the first sequence. Then we propose use a robust rank constraint of the coefficient matrices to measure the spatio-temporal alignment quality for every feasible pair of video fragments. Finally, the optimal temporal mapping is found using a graph-based approach. Our algorithm can use both short and long feature trajectories, and it is robust to mild outliers. We verify the robustness and performance of the proposed approach on synthetic data as well as on challenging real video sequences.1) 本文责任编委 黄庆明
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图 2 测试序列对同步和不同步时基系数矩阵$\overline{M}$的奇异值
Fig. 2 An example of the singular values of $\overline{ M}$ in synchronized case and non-synchronized cases
图 5 仿真数据重建结果(黑)和真实值(灰)
Fig. 5 Reconstruction (black) and ground truth (gray) of simulated data
图 6 跟踪误差、数据丢失和图像点数量对同步结果的影响
Fig. 6 Comparisons of robustness with regard to tracking error, missing data and point number
图 7 仿真数据集上各算法在不同跟踪误差下的实验结果对比以及估算的代价矩阵示例
Fig. 7 Comparisons of alignment accuracy using different methods regarding tracking noise level and representative cost matrices with estimated optimal paths superimposed
图 8 三维重建结果(从左到右对应场景依次为:积木, 健身毯, 篮球#1, 篮球#2和玩具火车)
Fig. 8 The 3D reconstruction results (From left to right: block building, exercise mat, basketball (#1), basketball (#2) and toy train.)
图 9 积木场景中各算法的时域对准结果对比(从左到右依次为:参考序列中的图像帧、本文算法、PDM、BPM、ECM、MFM和SMM找到的第二个序列中的对应帧(上)及第三个序列中的对应帧(下))
Fig. 9 Synchronization results on the blocks scene (From left to right: sample frames from the reference sequence, corresponding frames from the second sequence (top) and the third sequence (bottom) by our method, PDM, BPM, ECM, MFM and SMM, respectively.)
图 11 篮球#1场景中各算法的时域对准结果对比(从左到右依次为:参考序列中的图像帧、本文算法、PDM、BPM、ECM、MFM和SMM找到的第二个序列中的对应帧)
Fig. 11 Synchronization results on the basketball scene (#1) (From left to right: sample frames from the reference sequence, corresponding frames from the second sequence by our method, PDM, BPM, ECM, MFM and SMM, respectively.)
图 14 不同有效秩对同步结果的影响及不同有效秩对应的代价矩阵
Fig. 14 Comparisons of alignment accuracy with different λ values for efficient rank and cost matrices computed with different λ values
图 15 不同帧率比对同步结果的影响及观测序列帧率为46 fps、40 fps和24 fps时的代价矩阵
Fig. 15 Comparisons of alignment accuracy with different frame rate ratios and cost matrices computed when the frame rate of the observed sequence is 46, 40 and 24, respectively
表 1 真实数据集上各算法的归一化时域对准误差对比(帧)
Table 1 Quantitative comparisons of alignment error on real scenes (frame)
积木#1 积木#2 健身毯#1 健身毯#2 篮球#1 篮球#2 玩具火车 BPM (手动标记点轨迹) 39.61 9.16 12.05 15.63 16.81 12.42 56.80 ECM (手动标记点轨迹) 25.15 32.37 57.48 62.60 50.44 29.83 24.86 MFM (自动跟踪点轨迹) 11.81 21.70 22.17 9.44 17.68 22.78 70.04 SMM (SIFT) 155.75 196.56 132.08 202.50 9.71 31.74 130.83 PDM (手动标记点轨迹) 0.85 2.53 2.96 4.60 4.29 1.49 1.28 本文算法(手动标记点轨迹) 0.45 1.27 2.52 2.76 3.07 1.12 1.33 本文算法(自动跟踪点轨迹) 0.52 1.74 1.35 1.48 2.84 1.54 3.18 本文算法(手动标记和自动跟踪) 0.56 1.40 2.07 1.99 3.75 0.92 2.01 
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