Tobias Kluth

An evidential approach to SLAM, path planning, and active exploration

Probability theory has become the standard framework in the field of mobile robotics because of the inherent uncertainty associated with sensing and acting. In this paper, we show that the theory of belief functions with its ability to distinguish between different types of uncertainty is able to provide significant advantages over probabilistic approaches in the context of robotics. We do so by presenting solutions to the essential problems of simultaneous localization and mapping (SLAM) and planning based on belief functions. For SLAM, we show how the joint belief function over the map and the robots poses can be factored and efficiently approximated using a Rao-Blackwellized particle filter, resulting in a generalization of the popular probabilistic FastSLAM algorithm. Our SLAM algorithm produces occupancy grid maps where belief functions explicitly represent additional information about missing and conflicting measurements compared to probabilistic grid maps. The basis for this SLAM algorithm are forward and inverse sensor models, and we present general evidential models for range sensors like sonar and laser scanners. Using the generated evidential grid maps, we show how optimal decisions can be made for path planning and active exploration. To demonstrate the effectiveness of our evidential approach, we apply it to two real-world datasets where a mobile robot has to explore unknown environments and solve different planning problems. Finally, we provide a quantitative evaluation and show that the evidential approach outperforms a probabilistic one both in terms of map quality and navigation performance. A belief-function-based approach to SLAM for mobile robots is presented.Different types of uncertainty are explicitly represented in evidential grid maps.Optimal navigation and exploration based on evidential grid maps is shown.Evidential forward and inverse models for range sensors are provided.The approach is evaluated using real-world datasets recorded by a mobile robot.

Sparse 3D reconstructions in electrical Impedance Tomography using real data

Abstract We present a 3D reconstruction algorithm with sparsity constraints for electrical impedance tomography (EIT). EIT is the inverse problem of determining the distribution of conductivity in the interior of an object from simultaneous measurements of currents and voltages on its boundary. The feasibility of the sparsity reconstruction approach is tested with real data obtained from a new planar EIT device developed at the Institut für Physik, Johannes Gutenberg Universität, Mainz, Germany. The complete electrode model is adapted for the given device to handle incomplete measurements and the inhomogeneities of the conductivity are a priori assumed to be sparse with respect to a certain basis. This prior information is incorporated into a Tikhonov-type functional by including a sparsity-promoting -regularization term. The functional is minimized with an iterative soft shrinkage-type algorithm.

Numerosity as a topological invariant

The ability to quickly recognize the number of objects in our environment is a fundamental cognitive function. However, it is far from clear which computations and which actual neural processing mechanisms are used to provide us with such a skill. Here we try to provide a detailed and comprehensive analysis of this issue, which comprises both the basic mathematical foundations and the peculiarities imposed by the structure of the visual system and by the neural computations provided by the visual cortex. We suggest that numerosity should be considered as a mathematical invariant. Making use of concepts from mathematical topology--like connectedness, Betti numbers, and the Gauss-Bonnet theorem--we derive the basic computations suited for the computation of this invariant. We show that the computation of numerosity is possible in a neurophysiologically plausible fashion using only computational elements which are known to exist in the visual cortex. We further show that a fundamental feature of numerosity perception, its Weber property, arises naturally, assuming noise in the basic neural operations. The model is tested on an extended data set (made publicly available). It is hoped that our results can provide a general framework for future research on the invariance properties of the numerosity system.

Active Sensorimotor Object Recognition in Three-Dimensional Space

Spatial interaction of biological agents with their environment is based on the cognitive processing of sensory as well as motor information. There are many models for sole sensory processing but only a few for integrating sensory and motor information into a unifying sensorimotor approach. Additionally, neither the relations shaping the integration are yet clear nor how the integrated information can be used in an underlying representation. Therefore, we propose a probabilistic model for integrated processing of sensory and motor information by combining bottom-up feature extraction and top-down action selection embedded in a Bayesian inference approach. The integration of sensory perceptions and motor information brings about two main advantages: (i) Their statistical dependencies can be exploited by representing the spatial relationships of the sensor information in the underlying joint probability distribution and (ii) a top-down process can compute the next most informative region according to an information gain strategy. We evaluated our system in two different object recognition tasks. We found that the integration of sensory and motor information significantly improves active object recognition, in particular when these movements have been chosen by an information gain strategy.

Adaptive Information Selection in Images: Efficient Naive Bayes Nearest Neighbor Classification

We propose different methods for adaptively selecting information in images during object recognition. In contrast to standard feature selection, we consider this problem in a Bayesian framework where features are sequentially selected based on the current belief distribution over object classes. We define three different selection criteria and provide efficient Monte Carlo algorithms for the selection. In particular, we extend the successful Naive Bayes Nearest Neighbor (NBNN) classification approach, which is very costly to compute in its original form. We show that the proposed information selection methods result in a significant speed-up because only a small number of features needs to be extracted for accurate classification. In addition to adaptive methods based on the current belief distribution, we also consider image-based selection methods and we evaluate the performance of the different methods on a standard object recognition data set.

Spatial Numerosity: A Computational Model Based on a Topological Invariant

The estimation of the cardinality of objects in a spatial environment requires a high degree of invariance. Numerous experiments showed the immense abstraction ability of the numerical cognition system in humans and other species. It eliminates almost all structures of the objects and determines the number of objects in a scene. Based on concepts and quantities like connectedness and Gaussian curvature, we provide a general solution to this problem and apply it to the numerosity estimation from visual stimuli.

Affordance-Based Object Recognition Using Interactions Obtained from a Utility Maximization Principle

The interaction of biological agents within the real world is based on their abilities and the affordances of the environment. By contrast, the classical view of perception considers only sensory features, as do most object recognition models. Only a few models make use of the information provided by the integration of sensory information as well as possible or executed actions. Neither the relations shaping such an integration nor the methods for using this integrated information in appropriate representations are yet entirely clear. We propose a probabilistic model integrating the two information sources in one system. The recognition process is equipped with an utility maximization principle to obtain optimal interactions with the environment

On the degree of ill-posedness of multi-dimensional magnetic particle imaging

Magnetic particle imaging is an imaging modality of relatively recent origin, and it exploits the nonlinear magnetization response for reconstructing the concentration of nanoparticles. Since first invented in 2005, it has received much interest in the literature. In this work, we study one prototypical mathematical model in multi-dimension, i.e., the equilibrium model, which formulates the problem as a linear Fredholm integral equation of the first kind. We analyze the degree of ill-posedness of the associated linear integral operator by means of the singular value decay estimate for Sobolev smooth bivariate functions, and discuss the influence of various experimental parameters. In particular, applied magnetic fields with a field free point and a field free line are distinguished. The study is complemented with extensive numerical experiments.