相关论文: Interactive $G^1$ and $G^2$ Hermite Interpolation …

The geometric iterative method (GIM) is widely used in data interpolation/fitting, but its slow convergence affects the computational efficiency. Recently, much work was done to guarantee the acceleration of GIM in the literature. In this…

Numerical integration methods are central to the study of self-gravitating systems, particularly those comprised of many bodies or otherwise beyond the reach of analytical methods. Predictor-corrector schemes, both multi-step methods and…

A new modification of the Hermite cubic rectangular patch is proposed: the S-Patch, which is based on the requirement that diagonal curves must be of degree 3 instead of degree 6 as it is in the case of the Hermite patch. Theoretical…

We propose a randomized first order optimization algorithm Gradient Projection Iterative Sketch (GPIS) and an accelerated variant for efficiently solving large scale constrained Least Squares (LS). We provide theoretical convergence…

In this paper we propose a high-order accurate scheme for image segmentation based on the level-set method. In this approach, the curve evolution is described as the 0-level set of a representation function but we modify the velocity that…

We propose a novel Hermite-Taylor correction function method to handle embedded boundary and interface conditions for Maxwell's equations. The Hermite-Taylor method evolves the electromagnetic fields and their derivatives through order $m$…

Regional facial image synthesis conditioned on semantic mask has achieved great success using generative adversarial networks. However, the appearance of different regions may be inconsistent with each other when conducting regional image…

Semantic segmentation is a fundamental problem in computer vision and it requires high-resolution feature maps for dense prediction. Current coordinate-guided low-resolution feature interpolation methods, e.g., bilinear interpolation,…

Cubic spline interpolation on Euclidean space is a standard topic in numerical analysis, with countless applications in science and technology. In several emerging fields, for example computer vision and quantum control, there is a growing…

Each elliptic curve can be embedded uniquely in the projective plane, up to projective equivalence. The hessian curve of the embedding is generically a new elliptic curve, whose isomorphism type depends only on that of the initial elliptic…

We propose a new method for smoothly interpolating probability measures using the geometry of optimal transport. To that end, we reduce this problem to the classical Euclidean setting, allowing us to directly leverage the extensive toolbox…

We consider families of smooth projective curves of genus 2 with a single point removed and study their integral points. We show that in many such families there is a dense set of fibres for which the integral points can be effectively…

The goal of interactive image segmentation is to delineate specific regions within an image via visual or language prompts. Low-latency and high-quality interactive segmentation with diverse prompts remain challenging for existing…

In this paper, we combine the $m$th-order Taylor expansion of the objective function with cubic Hermite interpolation conditions. Then, we derive a series of modified secant equations with higher accuracy in approximation of the Hessian…

Iterative Hessian sketch (IHS) is an effective sketching method for modeling large-scale data. It was originally proposed by Pilanci and Wainwright (2016; JMLR) based on randomized sketching matrices. However, it is computationally…

Interactive image segmentation is a topic of many studies in image processing. In a conventional approach, a user marks some pixels of the object(s) of interest and background, and an algorithm propagates these labels to the rest of the…

The blown up complex projective plane in the twelve triple points of the dual Hesse arrangement has an infinite number of irreducible rational curves of self-intersection $-1$, for short, $(-1)$-curves. In the preprint version of [Dumnicki,…

An accurate implicit description of geometries is enabled by the level-set method. Level-set data is given at the nodes of a higher-order background mesh and the interpolated zero-level sets imply boundaries of the domain or interfaces…

The goal of interactive segmentation is to assist users in producing segmentation masks as fast and as accurately as possible. Interactions have to be simple and intuitive and the number of interactions required to produce a satisfactory…

A great number of theoretical results are known about log Gromov-Witten invariants, but few calculations are worked out. In this paper we restrict to surfaces and to genus 0 stable log maps of maximal tangency. We ask how various natural…