@article {12661,
	title = {Bayesian algorithms for simultaneous structure from motion estimation of multiple independently moving objects},
	journal = {Image Processing, IEEE Transactions on},
	volume = {14},
	year = {2005},
	month = {2005/01//},
	pages = {94 - 109},
	abstract = {The problem of simultaneous structure from motion estimation for multiple independently moving objects from a monocular image sequence is addressed. Two Bayesian algorithms are presented for solving this problem using the sequential importance sampling (SIS) technique. The empirical posterior distribution of object motion and feature separation parameters is approximated by weighted samples. The first algorithm addresses the problem when only two moving objects are present. A singular value decomposition (SVD)-based sample clustering algorithm is shown to be capable of separating samples related to different objects. A pair of SIS procedures is used to track the posterior distribution of the motion parameters. In the second algorithm, a balancing step is added into the SIS procedure to preserve samples of low weights so that all objects have enough samples to propagate empirical motion distributions. By using the proposed algorithms, the relative motions of all the moving objects with respect to the camera can be simultaneously estimated. Both algorithms have been tested on synthetic and real- image sequences. Improved results have been achieved.},
	keywords = {Automated;Reproducibility of Results;Sensitivity and Specificity;Signal Processing, Bayesian algorithm;clustering algorithm;empirical posterior distribution;feature separation parameter;monocular image sequence;motion estimation;multiple independently moving object;object motion;real-image sequence;sequential importance sampling techniqu, Biological;Models, Computer-Assisted;Imaging, Computer-Assisted;Pattern Recognition, Computer-Assisted;Subtraction Technique;Video Recording;Walking;, Statistical;Movement;Numerical Analysis, Three-Dimensional;Information Storage and Retrieval;Models},
	isbn = {1057-7149},
	doi = {10.1109/TIP.2004.837551},
	author = {Qian,Gang and Chellapa, Rama and Qinfen Zheng}
}
@article {12654,
	title = {Statistical bias in 3-D reconstruction from a monocular video},
	journal = {Image Processing, IEEE Transactions on},
	volume = {14},
	year = {2005},
	month = {2005/08//},
	pages = {1057 - 1062},
	abstract = {The present state-of-the-art in computing the error statistics in three-dimensional (3-D) reconstruction from video concentrates on estimating the error covariance. A different source of error which has not received much attention is the fact that the reconstruction estimates are often significantly statistically biased. In this paper, we derive a precise expression for the bias in the depth estimate, based on the continuous (differentiable) version of structure from motion (SfM). Many SfM algorithms, or certain portions of them, can be posed in a linear least-squares (LS) framework Ax=b. Examples include initialization procedures for bundle adjustment or algorithms that alternately estimate depth and camera motion. It is a well-known fact that the LS estimate is biased if the system matrix A is noisy. In SfM, the matrix A contains point correspondences, which are always difficult to obtain precisely; thus, it is expected that the structure and motion estimates in such a formulation of the problem would be biased. Existing results on the minimum achievable variance of the SfM estimator are extended by deriving a generalized Cramer-Rao lower bound. A detailed analysis of the effect of various camera motion parameters on the bias is presented. We conclude by presenting the effect of bias compensation on reconstructing 3-D face models from rendered images.},
	keywords = {3D face models, 3D video reconstruction, algorithms, artifacts, Artificial intelligence, Automated;Signal Processing, bias compensation, bundle adjustment, camera motion estimation, Computer simulation, Computer-Assisted;Imaging, Computer-Assisted;Subtraction Technique;Video Recording;, depth estimate, error covariance estimation, error statistics, generalized Cramer-Rao lower bound, Image Enhancement, Image Interpretation, Image reconstruction, initialization procedures, least squares approximations, linear least-squares framework, monocular video, motion compensation, Motion estimation, statistical bias, Statistical;Pattern Recognition, structure from motion algorithms, Three-Dimensional;Information Storage and Retrieval;Models, video signal processing},
	isbn = {1057-7149},
	doi = {10.1109/TIP.2005.849775},
	author = {Roy-Chowdhury, A.K. and Chellapa, Rama}
}
