Related papers: Robust Fitting of Ellipses and Spheroids
Contrastive Language-Image Pre-Training (CLIP) is highly instrumental in machine learning applications within a large variety of domains. We investigate the geometry of this embedding, which is still not well understood. We examine the raw…
We consider geometric multigrid methods for the solution of linear systems arising from isogeometric discretizations of elliptic partial differential equations. For classical finite elements, such methods are well known to be fast solvers…
Path planning has long been one of the major research areas in robotics, with PRM and RRT being two of the most effective classes of planners. Though generally very efficient, these sampling-based planners can become computationally…
Algorithms for the computation of the forward and inverse geodesic problems for an ellipsoid of revolution are derived. These are accurate to better than 15 nm when applied to the terrestrial ellipsoids. The solutions of other problems…
The paper aims at proposing the first shape identification and classification algorithm in echolocation. The approach is based on first extracting geometric features from the reflected waves and then matching them with precomputed ones…
When determining the parameters of a parametric planar shape based on a single low-resolution image, common estimation paradigms lead to inaccurate parameter estimates. The reason behind poor estimation results is that standard estimation…
We focus on the analysis of planar shapes and solid objects having thin features and propose a new mathematical model to characterize them. Based on our model, that we call an epsilon-shape, we show how thin parts can be effectively and…
We give a deterministic 2^{O(n)} algorithm for computing an M-ellipsoid of a convex body, matching a known lower bound. This has several interesting consequences including improved deterministic algorithms for volume estimation of convex…
Semi-implicit time-stepping schemes for atmosphere and ocean models require elliptic solvers that work efficiently on modern supercomputers. This paper reports our study of the potential computational savings when using mixed precision…
Weak gravitational lensing analyses are fundamentally limited by the intrinsic, non-Gaussian distribution of galaxy shapes. We explore alternative statistics for samples of ellipticity measurements that are unbiased, efficient, and robust.…
Efficiently estimating properties of large and strongly coupled quantum systems is a central focus in many-body physics and quantum information theory. While quantum computers promise speedups for many such tasks, near-term devices are…
We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…
We propose a multiscale approach for an elliptic multiscale setting with general unstructured diffusion coefficients that is able to achieve high-order convergence rates with respect to the mesh parameter and the polynomial degree. The…
Polyhedral estimate is a generic efficiently computable nonlinear in observations routine for recovering unknown signal belonging to a given convex compact set from noisy observation of signal's linear image. Risk analysis and optimal…
We consider finite element approximations of ill-posed elliptic problems with conditional stability. The notion of {\emph{optimal error estimates}} is defined including both convergence with respect to mesh parameter and perturbations in…
This paper describes a 2-D graphics algorithm that uses shifts and adds to precisely plot a series of points on an ellipse of any shape and orientation. The algorithm can also plot an elliptic arc that starts and ends at arbitrary angles.…
Differentially private computation often begins with a bound on some $d$-dimensional statistic's $\ell_p$ sensitivity. For pure differential privacy, the $K$-norm mechanism can improve on this approach using a norm tailored to the…
In this work, we investigate data fitting problems with random noises. A randomized progressive iterative regularization method is proposed. It works well for large-scale matrix computations and converges in expectation to the least-squares…
Most existing distance metric learning methods assume perfect side information that is usually given in pairwise or triplet constraints. Instead, in many real-world applications, the constraints are derived from side information, such as…
A method is proposed to generate an optimal fit of a number of connected linear trend segments onto time-series data. To be able to efficiently handle many lines, the method employs a stochastic search procedure to determine optimal…