Antonio Zea

Intelligent sensor-scheduling for multi-kinect-tracking

This paper describes a method to intelligently schedule a network of multiple RGBD sensors in a Bayesian object tracking scenario, with special focus on Microsoft KinectTM devices. These setups have issues such as the large amount of raw data generated by the sensors and interference caused by overlapping fields of view. The proposed algorithm addresses these issues by selecting and exclusively activating the sensor that yields the best measurement, as defined by a novel stochastic model that also considers hardware constraints and intrinsic parameters. In addition, as existing solutions to toggle the sensors were found to be insufficient, the development of a hardware module, especially designed for quick toggling and synchronization with the depth stream, is also discussed. The algorithm then is evaluated within the scope of a multi-Kinect object tracking scenario and compared to other scheduling strategies.

Bayesian estimation of line segments

A popular approach when tracking extended objects with elongated shapes, such as ships or airplanes, is to approximate them as a line segment. Despite its simple shape, the distribution of measurement sources on a line segment can be characterized in many radically different ways. The spectrum ranges from Spatial Distribution Models that assume a distinct probability for each individual source, to Greedy Association Models as used in curve fitting, which do not assume any distribution at all. In between these border cases, Random Hypersurface Models assume a distribution over subsets of all sources. In this paper, we compare Bayesian estimators based on these different models. We point out their advantages and disadvantages and evaluate their performance by means of illustrative examples with synthetic and real data using a Linear Regression Kalman Filter.

Recursive Bayesian pose and shape estimation of 3D objects using transformed plane curves

We consider the task of recursively estimating the pose and shape parameters of 3D objects based on noisy point cloud measurements from their surface. We focus on objects whose surface can be constructed by transforming a plane curve, such as a cylinder that is constructed by extruding a circle. However, designing estimators for such objects is challenging, as the straightforward distance-minimizing approach cannot observe all parameters, and additionally is subject to bias in the presence of noise. In this article, we first discuss these issues and then develop probabilistic models for cylinder, torus, cone, and an extruded curve by adapting related approaches including Random Hypersurface Models, partial likelihood, and symmetric shape models. In experiments with simulated data, we show that these models yield unbiased estimators for all parameters even in the presence of high noise.

A closed-form likelihood for Particle Filters to track extended objects with star-convex RHMs

Modeling 2D extended targets with star-convex Random Hypersurface Models (RHMs) allows for accurate object pose and shape estimation. A star-convex RHM models the shape of an object with the aid of a radial function that describes the distance from the object center to any point on its boundary. However, up to now only linear estimators, i.e., Kalman Filters, are used due to the lack of a explicit likelihood function. In this paper, we propose a closed-form and easy to implement likelihood function for tracking extended targets with star-convex RHMs. This makes it possible to apply nonlinear estimators such as Particle Filters to estimate a detailed shape of a target.We compared the proposed likelihood against the usual Kalman filter approaches with tracking pose and shape of an airplane in 2D. The evaluations showed that the combination of the Progressive Gaussian Filter (PGF) and the new likelihood function delivers the best estimation performance and can outperform the usually employed Kalman Filters.

Depth sensor calibration by tracking an extended object

In this paper, we propose a novel algorithm for automatically calibrating a network of depth sensors, based on a moving calibration object. The sensors may have non-overlapping fields of view in order to avoid interference. Two major challenges are discussed. First, depending on where the object is located relative to the sensor, the number and quality of the measurements strongly varies. Second, a single depth sensor observes the calibration object only from one side. Dealing with these challenges requires a simple calibration object as well as an algorithm that can deal with under-determined measurements of varying quality. A recursive Bayesian estimator is developed that determines the extrinsic parameters by measuring the surface of a moving cube with known pose. Our approach does not restrict the configuration of the network and requires no manual initialization or interaction. Ambiguities that are induced by the rotational cube symmetries are resolved by applying a multiple model approach. Besides synthetic evaluation we perform real data experiments and compare to state-of-the-art calibration.

Exploiting negative measurements for tracking star-convex extended objects

In this paper, we propose a novel approach to track extended objects by incorporating negative information. While traditional techniques to track extended targets use only positive measurements, assumed to stem from the target, the proposed estimator is also capable of incorporating negative measurements, which tell us where the target cannot be. To achieve this, we introduce a simple, robust, and easy-to-implement recursive Bayesian estimator which employs ideas from the field of curve fitting. As an application of this idea, we develop a measurement equation to estimate star-convex shapes which can be used in standard non-linear Kalman filters. Finally, we evaluate the proposed estimator using synthetic data and demonstrate its robustness in scenarios with clutter and low measurement quality.

Semi-analytic progressive Gaussian filtering

As an alternative to Kalman filters and particle filters, recently the progressive Gaussian filter (PGF) was proposed for estimating the state of discrete-time stochastic nonlinear dynamic systems. Like Kalman filters, the estimate of the PGF is a Gaussian distribution, but like particle filters, its measurement update works directly with the likelihood function in order to avoid the inherent linearization of the Kalman filters. However, compared to particle filters, the PGF allows for much faster state estimation and circumvents the severe problem of particle degeneracy by gradually transforming its prior Gaussian distribution into a posterior one. In this paper, we further enhance the estimation quality and runtime of the PGF by proposing a semi-analytic measurement update applicable to likelihood functions that only depend on a subspace of the system state. In fact, the proposed semi-analytic measurement update is not limited to the PGF and can be used by any nonlinear state estimator as long as its state estimate is Gaussian, e.g., the Gaussian particle filter.

Level-set random hypersurface models for tracking nonconvex extended objects

This paper presents a novel approach to track a non-convex shape approximation of an extended target based on noisy point measurements. For this purpose, a novel type of Random Hypersurface Model (RHM), called Level-Set RHM is introduced that models the interior of a shape with level-sets of an implicit function. Based on the Level-Set RHM, a nonlinear measurement equation can be derived that allows to employ a standard Gaussian state estimator for tracking an extended object even in scenarios with high measurement noise. In this paper, shapes are described using polygons and shape regularization is applied using ideas from active contour models.

Shape tracking using Partial Information Models

One of the challenges in shape tracking is how to deal with associating measurements to sources in the shape, while also taking to account parameters such as shape curvature and noise characteristics. Partial Information Models (PIMs) introduce a new approach that addresses this issue. The idea is to reparametrize each measurement into two components, one which depends on the position of its source on the shape, and another which depends on how well it fits in the shape. This allows for the derivation of a partial likelihood which combines the strengths of probabilistic approaches and distance minimization techniques. We propose an implementation of PIMs using level-sets, which allow for a close approximation of the distribution of distances we expect for a given shape. In turn, this can be used to develop estimators that are highly robust against high noise and occlusions.

Tracking simplified shapes using a stochastic boundary

When tracking extended objects, it is often the case that the shape of the target cannot be fully observed due to issues of visibility, artifacts, or high noise, which can change with time. In these situations, it is a common approach to model targets as simpler shapes instead, such as ellipsoids or cylinders. However, these simplifications cause information loss from the original shape, which could be used to improve the estimation results. In this paper, we propose a way to recover information from these lost details in the form of a stochastic boundary, whose parameters can be dynamically estimated from received measurements. The benefits of this approach are evaluated by tracking an object using noisy, real-life RGBD data.