秩约束多帧特征对应算法

Rank Constraint Based Multi-Frame Correspondence Estimation Algorithm

由于在一个关于刚体场景的长的图像序列中可能出现遮挡现象,使得度量矩阵中存在丢失数据项,为此提出一种在线多帧特征对应算法.由于图像度量值加权的偏移矩阵和轨迹矩阵均位于一个低维的线性子空间中,将偏移矩阵中的完整子矩阵秩约束后重组织成轨迹矩阵,对轨迹矩阵秩约束后求得相应的基矩阵和系数矩阵;为了解决光流的孔径问题,由基矩阵和系数矩阵估计相应的偏移分量并回填至多帧偏移矩阵;随着后继帧数据的输入,使用增量奇异值分解将新数据融合到多帧特征对应框架中;当处理完所有后继帧数据后,对于依然存在的丢失数据项使用非线性算法进行最后的处理.通过数学形式的推导证明了该算法的可行性;与Irani特征对应算法比较,对于不同的有效数据项比率和噪声水平,文中算法在误差控制和所用时间上的性能更优.

Occlusions existing in long image sequences of a rigid scene cause missing entries in the measure matrix. A novel online multi-frame correspondence estimation algorithm is proposed in this paper to recover missing frames. The trajectory matrix and displacement matrix, which is weighted by image gradient statistics, reside in a low-dimensional linear subspace. Firstly, a complete sub-matrix selected from the displacement matrix is constrained by the rank of the low-dimensional linear subspaces and reorganized into a corresponding trajectory matrix. The trajectory matrix is then constrained by the corresponding rank and decomposed into a base matrix and a coefficient matrix. Secondly, to solve the aperture problem, the displacement components are estimated from the base and coefficient matrix and then backfilled into multi-frame displacement matrix. Thirdly, as subsequent frames acquired, the new data are integrated into the multi-frame correspondence estimation by using incremental SVD. Lastly, after processed all of the frames, the remaining missing entries are processed with the nonlinear optimization algorithm. We mathematically proved the feasibility of the algorithm. Compared with Irani＇s correspondence estimation algorithm, our experimental results show that the proposed algorithm is faster and more effective in error-control and under different valid entry ratios and error levels.