@article {12475,
	title = {Robust Height Estimation of Moving Objects From Uncalibrated Videos},
	journal = {IEEE Transactions on Image Processing},
	volume = {19},
	year = {2010},
	month = {2010/08//},
	pages = {2221 - 2232},
	abstract = {This paper presents an approach for video metrology. From videos acquired by an uncalibrated stationary camera, we first recover the vanishing line and the vertical point of the scene based upon tracking moving objects that primarily lie on a ground plane. Using geometric properties of moving objects, a probabilistic model is constructed for simultaneously grouping trajectories and estimating vanishing points. Then we apply a single view mensuration algorithm to each of the frames to obtain height measurements. We finally fuse the multiframe measurements using the least median of squares (LMedS) as a robust cost function and the Robbins-Monro stochastic approximation (RMSA) technique. This method enables less human supervision, more flexibility and improved robustness. From the uncertainty analysis, we conclude that the method with auto-calibration is robust in practice. Results are shown based upon realistic tracking data from a variety of scenes.},
	keywords = {algorithms, Biometry, Calibration, EM algorithm, geometric properties, Geometry, Image Enhancement, Image Interpretation, Computer-Assisted, Imaging, Three-Dimensional, least median of squares, least squares approximations, MOTION, motion information, multiframe measurements, Pattern Recognition, Automated, Reproducibility of results, Robbins-Monro stochastic approximation, robust height estimation, Sensitivity and Specificity, Signal Processing, Computer-Assisted, stochastic approximation, Subtraction Technique, tracking data, uncalibrated stationary camera, uncalibrated videos, uncertainty analysis, vanishing point, video metrology, Video Recording, video signal processing},
	isbn = {1057-7149},
	doi = {10.1109/TIP.2010.2046368},
	author = {Jie Shao and Zhou,S. K and Chellapa, Rama}
}
@article {19662,
	title = {MCMC Data Association and Sparse Factorization Updating for Real Time Multitarget Tracking with Merged and Multiple Measurements},
	journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
	volume = {28},
	year = {2006},
	month = {2006/12//},
	pages = {1960 - 1972},
	abstract = {In several multitarget tracking applications, a target may return more than one measurement per target and interacting targets may return multiple merged measurements between targets. Existing algorithms for tracking and data association, initially applied to radar tracking, do not adequately address these types of measurements. Here, we introduce a probabilistic model for interacting targets that addresses both types of measurements simultaneously. We provide an algorithm for approximate inference in this model using a Markov chain Monte Carlo (MCMC)-based auxiliary variable particle filter. We Rao-Blackwellize the Markov chain to eliminate sampling over the continuous state space of the targets. A major contribution of this work is the use of sparse least squares updating and downdating techniques, which significantly reduce the computational cost per iteration of the Markov chain. Also, when combined with a simple heuristic, they enable the algorithm to correctly focus computation on interacting targets. We include experimental results on a challenging simulation sequence. We test the accuracy of the algorithm using two sensor modalities, video, and laser range data. We also show the algorithm exhibits real time performance on a conventional PC},
	keywords = {algorithms, approximate inference, Artificial intelligence, auxiliary variable particle filter, Computational efficiency, continuous state space, downdating, Image Enhancement, Image Interpretation, Computer-Assisted, Inference algorithms, Information Storage and Retrieval, laser range scanner, laser range scanner., Least squares approximation, least squares approximations, Least squares methods, linear least squares, Markov chain Monte Carlo, Markov processes, MCMC data association, merged measurements, Monte Carlo methods, Movement, multiple merged measurements, multitarget tracking, particle filter, particle filtering (numerical methods), Particle filters, Pattern Recognition, Automated, probabilistic model, QR factorization, Radar tracking, Rao-Blackwellized, real time multitarget tracking, Reproducibility of results, Sampling methods, Sensitivity and Specificity, sensor fusion, sparse factorization updating, sparse least squares, State-space methods, Subtraction Technique, target tracking, updating},
	isbn = {0162-8828},
	author = {Zia Khan and Balch, T. and Dellaert, F.}
}
@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}
}
@conference {14267,
	title = {The statistics of optical flow: implications for the process of correspondence in vision},
	booktitle = {15th International Conference on Pattern Recognition, 2000. Proceedings},
	volume = {1},
	year = {2000},
	month = {2000///},
	pages = {119-126 vol.1 - 119-126 vol.1},
	publisher = {IEEE},
	organization = {IEEE},
	abstract = {This paper studies the three major categories of flow estimation methods: gradient-based, energy-based, and correlation methods; it analyzes different ways of compounding 1D motion estimates (image gradients, spatio-temporal frequency triplets, local correlation estimates) into 2D velocity estimates, including linear and nonlinear methods. Correcting for the bias would require knowledge of the noise parameters. In many situations, however, these are difficult to estimate accurately, as they change with the dynamic imagery in unpredictable and complex ways. Thus, the bias really is a problem inherent to optical flow estimation. We argue that the bias is also integral to the human visual system. It is the cause of the illusory perception of motion in the Ouchi pattern and also explains various psychophysical studies of the perception of moving plaids. Finally, the implication of the analysis is that flow or correspondence can be estimated very accurately only when feedback is utilized},
	keywords = {Bias, Computer vision, correlation, correlation methods, energy-based method, flow estimation, Frequency estimation, gradient method, gradient methods, Image analysis, Image motion analysis, Image sequences, least squares, least squares approximations, Motion estimation, Nonlinear optics, Optical feedback, optical flow, Optical harmonic generation, Optical noise, Statistics, Visual perception},
	isbn = {0-7695-0750-6},
	doi = {10.1109/ICPR.2000.905288},
	author = {Ferm{\"u}ller, Cornelia and Aloimonos, J.}
}
