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Black-box variational inference (BBVI) is a technique to approximate the posterior of Bayesian models by optimization. Similar to MCMC, the user only needs to specify the model; then, the inference procedure is done automatically. In contrast to MCMC, BBVI scales to many observations, is faster for some applications, and can take advantage of highly optimized deep learning frameworks since it can be formulated as a minimization task. In the case of complex posteriors, however, other state-of-the-art BBVI approaches often yield unsatisfactory posterior approximations. This paper presents Bernstein flow variational inference (BF-VI), a robust and easy-to-use method flexible enough to approximate complex multivariate posteriors. BF-VI combines ideas from normalizing flows and Bernstein polynomial-based transformation models. In benchmark experiments, we compare BF-VI solutions with exact posteriors, MCMC solutions, and state-of-the-art BBVI methods, including normalizing flow-based BBVI. We show for low-dimensional models that BF-VI accurately approximates the true posterior; in higher-dimensional models, BF-VI compares favorably against other BBVI methods. Further, using BF-VI, we develop a Bayesian model for the semi-structured melanoma challenge data, combining a CNN model part for image data with an interpretable model part for tabular data, and demonstrate, for the first time, the use of BBVI in semi-structured models.
Random matrices are used to filter the center of gravity (CoG) and the covariance matrix of measurements. However, these quantities do not always correspond directly to the position and the extent of the object, e.g. when a lidar sensor is used.In this paper, we propose a Gaussian processes regression model (GPRM) to predict the position and extension of the object from the filtered CoG and covariance matrix of the measurements. Training data for the GPRM are generated by a sampling method and a virtual measurement model (VMM). The VMM is a function that generates artificial measurements using ray tracing and allows us to obtain the CoG and covariance matrix that any object would cause. This enables the GPRM to be trained without real data but still be applied to real data due to the precise modeling in the VMM. The results show an accurate extension estimation as long as the reality behaves like the modeling and e.g. lidar measurements only occur on the side facing the sensor.
Motion estimation is an essential element for autonomous vessels. It is used e.g. for lidar motion compensation as well as mapping and detection tasks in a maritime environment. Because the use of gyroscopes is not reliable and a high performance inertial measurement unit is quite expensive, we present an approach for visual pitch and roll estimation that utilizes a convolutional neural network for water segmentation, a stereo system for reconstruction and simple geometry to estimate pitch and roll. The algorithm is validated on a novel, publicly available dataset recorded at Lake Constance. Our experiments show that the pitch and roll estimator provides accurate results in comparison to an Xsens IMU sensor. We can further improve the pitch and roll estimation by sensor fusion with a gyroscope. The algorithm is available in its implementation as a ROS node.
Targetless Lidar-camera registration is a repeating task in many computer vision and robotics applications and requires computing the extrinsic pose of a point cloud with respect to a camera or vice-versa. Existing methods based on learning or optimization lack either generalization capabilities or accuracy. Here, we propose a combination of pre-training and optimization using a neural network-based mutual information estimation technique (MINE [1]). This construction allows back-propagating the gradient to the calibration parameters and enables stochastic gradient descent. To ensure orthogonality constraints with respect to the rotation matrix we incorporate Lie-group techniques. Furthermore, instead of optimizing on entire images, we operate on local patches that are extracted from the temporally synchronized projected Lidar points and camera frames. Our experiments show that this technique not only improves over existing techniques in terms of accuracy, but also shows considerable generalization capabilities towards new Lidar-camera configurations.