Related papers: Fast Methods for Eikonal Equations: an Experimenta…

Human motion prediction is essential for the safe and smooth operation of mobile service robots and intelligent vehicles around people. Commonly used neural network-based approaches often require large amounts of complete trajectories to…

In this work we describe a fast and stable algorithm for the computation of the orthogonal moments of an image. Indeed, orthogonal moments are characterized by a high discriminative power, but some of their possible formulations are…

We survey key techniques and results from approximation theory in the context of uniform approximations to real functions such as e^{-x}, 1/x, and x^k. We then present a selection of results demonstrating how such approximations can be used…

Fast sweeping methods have become a useful tool for computing the solutions of static Hamilton-Jacobi equations. By adapting the main idea behind these methods, we describe a new approach for computing steady state solutions to systems of…

Autonomous agents face the challenge of coordinating multiple tasks (perception, motion planning, controller) which are computationally expensive on a single onboard computer. To utilize the onboard processing capacity optimally, it is…

FastMap was first introduced in the Data Mining community for generating Euclidean embeddings of complex objects. In this dissertation, we first present FastMap to generate Euclidean embeddings of graphs in near-linear time: The pairwise…

Neural networks are increasingly used in robotics as policies, state transition models, state estimation models, or all of the above. With these components being learned from data, it is important to be able to analyze what behaviors were…

We provide a simple method and relevant theoretical analysis for efficiently estimating higher-order lp distances. While the analysis mainly focuses on l4, our methodology extends naturally to p = 6,8,10..., (i.e., when p is even).…

Trajectory optimization methods for motion planning attempt to generate trajectories that minimize a suitable objective function. Such methods efficiently find solutions even for high degree-of-freedom robots. However, a globally optimal…

Estimating the diagonal entries of a matrix, that is not directly accessible but only available as a linear operator in the form of a computer routine, is a common necessity in many computational applications, especially in image…

Discrete Hahn polynomials (DHPs) and their moments are considered to be one of the efficient orthogonal moments and they are applied in various scientific areas such as image processing and feature extraction. Commonly, DHPs are used as…

The computation time required by standard finite difference methods with fixed timesteps for solving fractional diffusion equations is usually very large because the number of operations required to find the solution scales as the square of…

The method of alternation projections (MAP) is an iterative procedure for finding the projection of a point on the intersection of closed subspaces of an Hilbert space. The convergence of this method is usually slow, and several methods for…

The k Nearest Neighbors (kNN) method has received much attention in the past decades, where some theoretical bounds on its performance were identified and where practical optimizations were proposed for making it work fairly well in high…

The increased availability of interactive maps on the Internet and on personal mobile devices has created new challenges in computational cartography and, in particular, for label placement in maps. Operations like rotation, zoom, and…

This paper proposes a fast and accurate surface normal estimation method which can be directly used on depth maps (organized point clouds). The surface normal estimation process is formulated as a closed-form expression. In order to reduce…

The minimum distance of a code is an important concept in information theory. Hence, computing the minimum distance of a code with a minimum computational cost is a crucial process to many problems in this area. In this paper, we present…

Safe path planning is a crucial component in autonomous robotics. The many approaches to find a collision free path can be categorically divided into trajectory optimisers and sampling-based methods. When planning using occupancy maps, the…

Numerical methods for the optimal transport problem is an active area of research. Recent work of Kitagawa and Abedin shows that the solution of a time-dependent equation converges exponentially fast as time goes to infinity to the solution…

The dynamic time scan forecasting method relies on the premise that the most important pattern in a time series precedes the forecasting window, i.e., the last observed values. Thus, a scan procedure is applied to identify similar patterns,…