We describe an end-to-end framework for learning parameters of min-cost flow multi-target tracking problem with quadratic trajectory interactions including suppression of overlapping tracks and contextual cues about co-occurrence of different objects. Our approach utilizes structured prediction with a tracking-specific loss function to learn the complete set of model parameters. In this learning framework, we evaluate two different approaches to finding an optimal set of tracks under a quadratic model objective, one based on an linear program (LP) relaxation and the other based on novel greedy variants of dynamic programming that handle pairwise interactions. We find the greedy algorithms achieve almost equivalent accuracy to the LP relaxation while being up to 10 @math ? faster than a commercial LP solver. We evaluate trained models on three challenging benchmarks. Surprisingly, we find that with proper parameter learning, our simple data association model without explicit appearance motion reasoning is able to achieve comparable or better accuracy than many state-of-the-art methods that use far more complex motion features or appearance affinity metric learning.
@cite_2 attempt to solve both data association and trajectory smoothing problem simultaneously, which results in a problem with varying dimensionality and difficult approximate inference. @cite_25 avoid this varying dimensionality problem by integrating out trajectory-related variables and using Markov Chain Monte Carlo sampling to estimate the marginal likelihoods for data association and trajectory estimation. @cite_5 propose yet another way to avoid varying dimensionality: instead of explicitly enumerating number of tracks, they assign a latent variable for each real detection track and conduct data association on these latent variables.
@cite_5 @cite_25 @cite_2
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We propose a framework for general multiple target tracking, where the input is a set of candidate regions in each frame, as obtained from a state of the art background learning, and the goal is to recover trajectories of targets over time from noisy observations. Due to occlusions by targets and static objects, noisy segmentation and false alarms, one foreground region may not correspond to one target faithfully. Therefore the one-to-one assumption used in most data association algorithm is not always satisfied. Our method overcomes the one-to-one assumption by formulating the visual tracking problem in terms of finding the best spatial and temporal association of observations, which maximizes the consistency of both motion and appearance of trajectories. To avoid enumerating all possible solutions, we take a data driven Markov chain Monte Carlo (DD-MCMC) approach to sample the solution space efficiently. The sampling is driven by an informed proposal scheme controlled by a joint probability model combining motion and appearance. To make sure the Markov chain to converge to a desired distribution, we propose an automatic approach to determine the parameters in the target distribution. Comparative experiments with quantitative evaluations are provided. This paper provides methods for carrying out likelihood based inference for diffusion driven models, for example discretely observed multivariate diffusions, continuous time stochastic volatility models and counting process models. The diffusions can potentially be non-stationary. Although our methods are sampling based, making use of Markov chain Monte Carlo methods to sample the posterior distribution of the relevant unknowns, our general strategies and details are different from previous work along these lines. The methods we develop are simple to implement and simulation efficient. Importantly, unlike previous methods, the performance of our technique is not worsened, in fact it improves, as the degree of latent augmentation is increased to reduce the bias of the Euler approximation. In addition, our method is not subject to a degeneracy that afflicts previous techniques when the degree of latent augmentation is increased. We also discuss issues of model choice, model checking and filtering. The techniques and ideas are applied to both simulated and real data. We develop a Bayesian modeling approach for tracking people in 3D from monocular video with unknown cameras. Modeling in 3D provides natural explanations for occlusions and smoothness discontinuities that result from projection, and allows priors on velocity and smoothness to be grounded in physical quantities: meters and seconds vs. pixels and frames. We pose the problem in the context of data association, in which observations are assigned to tracks. A correct application of Bayesian inference to multi-target tracking must address the fact that the model's dimension changes as tracks are added or removed, and thus, posterior densities of different hypotheses are not comparable. We address this by marginalizing out the trajectory parameters so the resulting posterior over data associations has constant dimension. This is made tractable by using (a) Gaussian process priors for smooth trajectories and (b) approximately Gaussian likelihood functions. Our approach provides a principled method for incorporating multiple sources of evidence, we present results using both optical flow and object detector outputs. Results are comparable to recent work on 3D tracking and, unlike others, our method requires no pre-calibrated cameras. In this paper, we study the problem of sampling from a given probability density function that is known to be smooth and strongly log-concave. We analyze several methods of approximate sampling based on discretizations of the (highly overdamped) Langevin diffusion and establish guarantees on its error measured in the Wasserstein-2 distance. Our guarantees improve or extend the state-of-the-art results in three directions. First, we provide an upper bound on the error of the first-order Langevin Monte Carlo (LMC) algorithm with optimized varying step-size. This result has the advantage of being horizon free (we do not need to know in advance the target precision) and to improve by a logarithmic factor the corresponding result for the constant step-size. Second, we study the case where accurate evaluations of the gradient of the log-density are unavailable, but one can have access to approximations of the aforementioned gradient. In such a situation, we consider both deterministic and stochastic approximations of the gradient and provide an upper bound on the sampling error of the first-order LMC that quantifies the impact of the gradient evaluation inaccuracies. Third, we establish upper bounds for two versions of the second-order LMC, which leverage the Hessian of the log-density. We nonasymptotic guarantees on the sampling error of these second-order LMCs. These guarantees reveal that the second-order LMC algorithms improve on the first-order LMC in ill-conditioned settings.