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 multitarget 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.

We develop a novel probabilistic model for multi-part shapes based on Gaussian processes, which we apply to model rosette leaves of Arabidopsis plants. Our model incorporates domain knowledge of Arabidopsis leaves in two ways. First, leaves are modeled using two anatomical parts: a blade and a petiole. We model the two regions with separate Gaussian processes, with a smoothness constraint at the boundary. Second, we constrain all leaf petioles to initiate at the rosette center, which is also modeled. This Bayesian prior is combined with a simple likelihood function over foreground pixels to perform image segmentation by optimizing a posterior distribution. A simple datadriven approach is used to over-segment the image, then excess leaves are pruned using a Bayesian model selection criterion. We show that our approach is effective, even with minimal training data.

We propose a robust method for estimating dynamic 3D curvilinear branching structure from monocular images. While 3D reconstruction from images has been widely studied, estimating thin structure has received less attention. This problem becomes more challenging in the presence of camera error, scene motion, and a constraint that curves are attached in a branching structure. We propose a new generalpurpose prior, a branching Gaussian processes (BGP), that models spatial smoothness and temporal dynamics of curves while enforcing attachment between them. We apply this prior to fit 3D trees directly to image data, using an efficient scheme for approximate inference based on expectation propagation. The BGP prior's Gaussian form allows us to approximately marginalize over 3D trees with a given model structure, enabling principled comparison between tree models with varying complexity. We test our approach on a novel multi-view dataset depicting plants with known 3D structures and topologies undergoing small nonrigid motion. Our method outperforms a state-of-the-art 3D reconstruction method designed for non-moving thin structure. We evaluate under several common measures, and we propose a new measure for reconstructions of branching multi-part 3D scenes under motion.

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