Teleoperation can enable human intervention to help handle instances of failure in autonomy thus allowing for much safer deployment of autonomous vehicle technology. Successful teleoperation requires recreating the environment around the remote vehicle using camera data received over wireless communication channels. This paper develops a new predictive display system to tackle the significant time delays encountered in receiving camera data over wireless networks. First, a new high gain observer is developed for estimating the position and orientation of the ego vehicle. The novel observer is shown to perform accurate state estimation using only GNSS and gyroscope sensor readings. A vector field method which fuses the delayed camera and Lidar data is then presented. This method uses sparse 3D points obtained from Lidar and transforms them using the state estimates from the high gain observer to generate a sparse vector field for the camera image. Polynomial based interpolation is then performed to obtain the vector field for the complete image which is then remapped to synthesize images for accurate predictive display. The method is evaluated on real-world experimental data from the nuScenes and KITTI datasets. The performance of the high gain observer is also evaluated and compared with that of the EKF. The synthesized images using the vector field based predictive display are compared with ground truth images using various image metrics and offer vastly improved performance compared to delayed images.

Abstract Teleoperation can enable human intervention to help handle instances of failure in autonomy thus allowing for much safer deployment of autonomous vehicle technology. Successful teleoperation requires recreating the environment around the remote vehicle using camera data received over wireless communication channels. This paper develops a new predictive display system to tackle the significant time delays encountered in receiving camera data over wireless networks. First, a new high gain observer is developed for estimating the position and orientation of the ego vehicle. The novel observer is shown to perform accurate state estimation using only GNSS and gyroscope sensor readings. A vector field method which fuses the delayed camera and Lidar data is then presented. This method uses sparse 3D points obtained from Lidar and transforms them using the state estimates from the high gain observer to generate a sparse vector field for the camera image. Polynomial based interpolation is then performed to obtain the vector field for the complete image which is then remapped to synthesize images for accurate predictive display. The method is evaluated on real-world experimental data from the nuScenes and KITTI datasets. The performance of the high gain observer is also evaluated and compared with that of the EKF. The synthesized images using the vector field based predictive display are compared with ground truth images using various image metrics and offer vastly improved performance compared to delayed images.

The advent of diverse frequency bands in 5G networks has promoted measurement studies focused on 5G signal propagation, aiming to understand its pathloss, coverage, and channel quality characteristics. Nonetheless, conducting a thorough 5G measurement campaign is markedly laborious given the large number of samples that must be collected. To alleviate this burden, the present contribution leverages principled active learning (AL) methods to prudently select only a few, yet most informative locations to collect samples. The core idea is to rely on a Gaussian Process (GP) model to efficiently extrapolate measurements throughout the coverage area. Specifically, an ensemble (E) of GP models is adopted that not only provides a rich learning function space, but also quantifies uncertainty, and can offer accurate predictions. Building on this EGP model, a suite of acquisition functions (AFs) are advocated to query new locations on-the-fly. To account for realistic scenaria, the proposed AFs are augmented with a novel distance-based AL rule that selects informative samples, while penalizing queries at long distances. Numerical tests on 5G data generated by the Sionna simulator and on real urban and suburban datasets, showcase the merits of the novel EGP-AL approaches.

Shortest path graph distances are widely used in data science and machine learning, since they can approximate the underlying geodesic distance on the data manifold. However, the shortest path distance is highly sensitive to the addition of corrupted edges in the graph, either through noise or an adversarial perturbation. In this paper we study a family of Hamilton-Jacobi equations on graphs that we call the $p$-eikonal equation. We show that the $p$-eikonal equation with $p=1$ is a provably robust distance-type function on a graph, and the $p\to \infty$ limit recovers shortest path distances. While the $p$-eikonal equation does not correspond to a shortest-path graph distance, we nonetheless show that the continuum limit of the $p$-eikonal equation on a random geometric graph recovers a geodesic density weighted distance in the continuum. We consider applications of the $p$-eikonal equation to data depth and semi-supervised learning, and use the continuum limit to prove asymptotic consistency results for both applications. Finally, we show the results of experiments with data depth and semi-supervised learning on real image datasets, including MNIST, FashionMNIST and CIFAR-10, which show that the $p$-eikonal equation offers significantly better results compared to shortest path distances.

We propose a new framework, called Poisson learning, for graph based semi-supervised learning at very low label rates. Poisson learning is motivated by the need to address the degeneracy of Laplacian semi-supervised learning in this regime. The method replaces the assignment of label values at training points with the placement of sources and sinks, and solves the resulting Poisson equation on the graph. The outcomes are provably more stable and informative than those of Laplacian learning. Poisson learning is efficient and simple to implement, and we present numerical experiments showing the method is superior to other recent approaches to semi-supervised learning at low label rates on MNIST, FashionMNIST, and Cifar-10. We also propose a graph-cut enhancement of Poisson learning, called Poisson MBO, that gives higher accuracy and can incorporate prior knowledge of relative class sizes.

We show how to compute the circular area invariant of planar curves, and the spherical volume invariant of surfaces, in terms of line and surface integrals, respectively. We use the divergence theorem to express the area and volume integrals as line and surface integrals, respectively, against particular kernels; our results also extend to higher-dimensional hypersurfaces. The resulting surface integrals are computable analytically on a triangulated mesh. This gives a simple computational algorithm for computing the spherical volume invariant for triangulated surfaces that does not involve discretizing the ambient space. We discuss potential applications to feature detection on broken bone fragments of interest in anthropology.

We consider the problem of identifying patterns in a data set that exhibits anomalous behavior, often referred to as anomaly detection. Similarity-based anomaly detection algorithms detect abnormally large amounts of similarity or dissimilarity, e.g., as measured by the nearest neighbor Euclidean distances between a test sample and the training samples. In many application domains, there may not exist a single dissimilarity measure that captures all possible anomalous patterns. In such cases, multiple dissimilarity measures can be defined, including nonmetric measures, and one can test for anomalies by scalarizing using a nonnegative linear combination of them. If the relative importance of the different dissimilarity measures are not known in advance, as in many anomaly detection applications, the anomaly detection algorithm may need to be executed multiple times with different choices of weights in the linear combination. In this paper, we propose a method for similarity-based anomaly detection using a novel multicriteria dissimilarity measure, the Pareto depth. The proposed Pareto depth analysis (PDA) anomaly detection algorithm uses the concept of Pareto optimality to detect anomalies under multiple criteria without having to run an algorithm multiple times with different choices of weights. The proposed PDA approach is provably better than using linear combinations of the criteria, and shows superior performance on experiments with synthetic and real data sets.

Most content-based image retrieval systems consider either one single query, or multiple queries that include the same object or represent the same semantic information. In this paper, we consider the content-based image retrieval problem for multiple query images corresponding to different image semantics. We propose a novel multiple-query information retrieval algorithm that combines the Pareto front method with efficient manifold ranking. We show that our proposed algorithm outperforms state of the art multiple-query retrieval algorithms on real-world image databases. We attribute this performance improvement to concavity properties of the Pareto fronts, and prove a theoretical result that characterizes the asymptotic concavity of the fronts.

We consider the problem of identifying patterns in a data set that exhibit anomalous behavior, often referred to as anomaly detection. In most anomaly detection algorithms, the dissimilarity between data samples is calculated by a single criterion, such as Euclidean distance. However, in many cases there may not exist a single dissimilarity measure that captures all possible anomalous patterns. In such a case, multiple criteria can be defined, and one can test for anomalies by scalarizing the multiple criteria by taking some linear combination of them. If the importance of the different criteria are not known in advance, the algorithm may need to be executed multiple times with different choices of weights in the linear combination. In this paper, we introduce a novel non-parametric multi-criteria anomaly detection method using Pareto depth analysis (PDA). PDA uses the concept of Pareto optimality to detect anomalies under multiple criteria without having to run an algorithm multiple times with different choices of weights. The proposed PDA approach scales linearly in the number of criteria and is provably better than linear combinations of the criteria.

The representation of curves by integral invariant signatures is an important step in shape recognition and classification. Integral invariants are preferred over their differential counterparts due to their robustness with respect to noise. However, in contrast to differential invariants of curves, it is currently unknown whether integral signatures offer unique representations of curves. In this article, we prove some results on the uniqueness of the circular area signature. In particular, we study the case for graphs of periodic functions. We show that the circular area signature is unique if taken with respect to parametrization by the $x$-axis. Furthermore, we prove that the true circular area signature (parametrized by arclength) is unique in a neighborhood of constant functions. Finally, we show uniqueness in the special case that the functions of interest agree on an interval of width $2r$.

Motivated by some recent work in active contour applications, we study the use of Sobolev gradients for PDE-based image diffusion and sharpening. We begin by studying, for the case of isotropic diffusion, the gradient descent/ascent equation obtained by modifying the usual metric on the space of images, which is the $L^2$ metric, to a Sobolev metric. We present existence and uniqueness results for the Sobolev isotropic diffusion, derive a number of maximum principles, and show that the differential equations are stable and well-posed both in the forward and backward directions. This allows us to apply the Sobolev flow in the backward direction for sharpening. Favorable comparisons to the well-known shock filter for sharpening are demonstrated. Finally, we continue to exploit this same well-posed behavior both forward and backward in order to formulate new constrained gradient flows on higher order energy functionals which preserve the first order energy of the original image for interesting combined smoothing and sharpening effects.