Related papers: An Elliptic Curve Based Solution to the Perspectiv…
The goal of this paper is to reconstruct spatially distributed dielectric constants from complex-valued scattered wave field by solving a 3D coefficient inverse problem for the Helmholtz equation at multi-frequencies. The data are generated…
We formulate a simple algorithm for computing global exact symmetries of closed discrete curves in plane. The method is based on a suitable trigonometric interpolation of vertices of the given polyline and consequent computation of the…
Reconstructing 3D geometry and appearance from a sparse set of fixed cameras is a foundational task with broad applications, yet it remains fundamentally constrained by the limited viewpoints. We show that this bound can be broken by…
An elliptic curve-based signcryption scheme is introduced in this paper that effectively combines the functionalities of digital signature and encryption, and decreases the computational costs and communication overheads in comparison with…
Self-supervised pre-training has achieved remarkable success in NLP and 2D vision. However, these advances have yet to translate to 3D data. Techniques like masked reconstruction face inherent challenges on unstructured point clouds, while…
Sensors producing 3D point clouds such as 3D laser scanners and RGB-D cameras are widely used in robotics, be it for autonomous driving or manipulation. Aligning point clouds produced by these sensors is a vital component in such…
An accurate and rapid-response perception system is fundamental for autonomous vehicles to operate safely. 3D object detection methods handle point clouds given by LiDAR sensors to provide accurate depth and position information for each…
We present a non-conforming least squares method for approximating solutions of second order elliptic problems with discontinuous coefficients. The method is based on a general Saddle Point Least Squares (SPLS) method introduced in previous…
Evolutionary methods are effective tools for obtaining high-quality results when solving hard practical problems. Linkage learning may increase their effectiveness. One of the state-of-the-art methods that employ linkage learning is the…
Computing the epipolar geometry from feature points between cameras with very different viewpoints is often error prone, as an object's appearance can vary greatly between images. For such cases, it has been shown that using motion…
This paper presents a reachability-based approach to finite-time transition problem of nonlinear systems between two stationary points (i.e., the point-to-point steering problem). When the target state is reachable, we prove that a solution…
This paper consists of a formal analysis and one solid solution to the knot finding problem given a source polyline and a parametric curve (e.g. circular arc, ellipse or biarc). We solve the problem using both a greedy algorithm to collect…
After characterizing the integrable discrete analogue of the Euler's elastica, we focus our attention on the problem of approximating a given discrete planar curve by an appropriate discrete Euler's elastica. We carry out the fairing…
In this work, we present a novel iterative deep Ritz method (IDRM) for solving a general class of elliptic problems. It is inspired by the iterative procedure for minimizing the loss during the training of the neural network, but at each…
By combining tools from different areas of mathematics, we obtain 3D visualizations of elliptic curves over different fields that faithfully capture the underlying algebra and geometry.
We consider the problem of reorienting a rigid object with arbitrary known shape on a table using a two-finger pinch gripper. Reorienting problem is challenging because of its non-smoothness and high dimensionality. In this work, we focus…
A method for detecting and approximating fault lines or surfaces, respectively, or decision curves in two and three dimensions with guaranteed accuracy is presented. Reformulated as a classification problem, our method starts from a set of…
The ellipsoid method is an algorithm that solves the (weak) feasibility and linear optimization problems for convex sets by making oracle calls to their (weak) separation problem. We observe that the previously known method for showing that…
We introduce a highly efficient method for panoptic segmentation of large 3D point clouds by redefining this task as a scalable graph clustering problem. This approach can be trained using only local auxiliary tasks, thereby eliminating the…
In this paper we consider the unconstrained minimization problem of a smooth function in ${\mathbb{R}}^n$ in a setting where only function evaluations are possible. We design a novel randomized derivative-free algorithm --- the stochastic…