The interest in 3D dynamical tracking is growing in fields such as robotics, biology and fluid dynamics. Recently, a major source of progress in 3D tracking has been the study of collective behaviour in biological systems, where the trajectories of individual animals moving within large and dense groups need to be reconstructed to understand the behavioural interaction rules. Experimental data in this field are generally noisy and at low spatial resolution, so that individuals appear as small featureless objects and trajectories must be retrieved by making use of epipolar information only. Moreover, optical occlusions often occur: in a multi-camera system one or more objects become indistinguishable in one view, potentially jeopardizing the conservation of identity over long-time trajectories. The most advanced 3D tracking algorithms overcome optical occlusions making use of set-cover techniques, which however have to solve NP-hard optimization problems. Moreover, current methods are not able to cope with occlusions arising from actual physical proximity of objects in 3D space. Here, we present a new method designed to work directly in 3D space and time, creating (3D+1) clouds of points representing the full spatio-temporal evolution of the moving targets. We can then use a simple connected components labeling routine, which is linear in time, to solve optical occlusions, hence lowering from NP to P the complexity of the problem. Finally, we use normalized cut spectral clustering to tackle 3D physical proximity.
The first @math tracking algorithms dealing with featureless objects were developed in the field of fluid dynamics, where the motion of passive tracer particles is studied to investigate turbulent fluid flows. The most successful algorithm in this field is the one presented in @cite_16 , which solves occlusion-related ambiguities locally in time, potentially producing fragmented trajectories. However, in the study of turbulence one can actually tune the density of tracers, so decreasing the optical density to a point where this is no longer critical. Clearly, this cannot be done in biological systems.
@cite_16
2096404799 2081455211 2155191357 2164720308
We introduce an algorithm for tracking deformable objects from a sequence of point clouds. The proposed tracking algorithm is based on a probabilistic generative model that incorporates observations of the point cloud and the physical properties of the tracked object and its environment. We propose a modified expectation maximization algorithm to perform maximum a posteriori estimation to update the state estimate at each time step. Our modification makes it practical to perform the inference through calls to a physics simulation engine. This is significant because (i) it allows for the use of highly optimized physics simulation engines for the core computations of our tracking algorithm, and (ii) it makes it possible to naturally, and efficiently, account for physical constraints imposed by collisions, grasping actions, and material properties in the observation updates. Even in the presence of the relatively large occlusions that occur during manipulation tasks, our algorithm is able to robustly track a variety of types of deformable objects, including ones that are one-dimensional, such as ropes; two-dimensional, such as cloth; and three-dimensional, such as sponges. Our implementation can track these objects in real time. Methods to extract information from the tracking of mobile objects particles have broad interest in biological and physical sciences. Techniques based on simple criteria of proximity in time-consecutive snapshots are useful to identify the trajectories of the particles. However, they become problematic as the motility and or the density of the particles increases due to uncertainties on the trajectories that particles followed during the images’ acquisition time. Here, we report an efficient method for learning parameters of the dynamics of the particles from their positions in time-consecutive images. Our algorithm belongs to the class of message-passing algorithms, known in computer science, information theory, and statistical physics as belief propagation (BP). The algorithm is distributed, thus allowing parallel implementation suitable for computations on multiple machines without significant intermachine overhead. We test our method on the model example of particle tracking in turbulent flows, which is particularly challenging due to the strong transport that those flows produce. Our numerical experiments show that the BP algorithm compares in quality with exact Markov Chain Monte Carlo algorithms, yet BP is far superior in speed. We also suggest and analyze a random distance model that provides theoretical justification for BP accuracy. Methods developed here systematically formulate the problem of particle tracking and provide fast and reliable tools for the model’s extensive range of applications. We present an algorithm for identifying and tracking independently moving rigid objects from optical flow. Some previous attempts at segmentation via optical flow have focused on finding discontinuities in the flow field. While discontinuities do indicate a change in scene depth, they do not in general signal a boundary between two separate objects. The proposed method uses the fact that each independently moving object has a unique epipolar constraint associated with its motion. Thus motion discontinuities based on self-occlusion can be distinguished from those due to separate objects. The use of epipolar geometry allows for the determination of individual motion parameters for each object as well as the recovery of relative depth for each point on the object. The algorithm assumes an affine camera where perspective effects are limited to changes in overall scale. No camera calibration parameters are required. A Kalman filter based approach is used for tracking motion parameters with time. A spatiotemporal saliency algorithm based on a center-surround framework is proposed. The algorithm is inspired by biological mechanisms of motion-based perceptual grouping and extends a discriminant formulation of center-surround saliency previously proposed for static imagery. Under this formulation, the saliency of a location is equated to the power of a predefined set of features to discriminate between the visual stimuli in a center and a surround window, centered at that location. The features are spatiotemporal video patches and are modeled as dynamic textures, to achieve a principled joint characterization of the spatial and temporal components of saliency. The combination of discriminant center-surround saliency with the modeling power of dynamic textures yields a robust, versatile, and fully unsupervised spatiotemporal saliency algorithm, applicable to scenes with highly dynamic backgrounds and moving cameras. The related problem of background subtraction is treated as the complement of saliency detection, by classifying nonsalient (with respect to appearance and motion dynamics) points in the visual field as background. The algorithm is tested for background subtraction on challenging sequences, and shown to substantially outperform various state-of-the-art techniques. Quantitatively, its average error rate is almost half that of the closest competitor.