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Surface reconstruction and novel view rendering from sparse-view images are challenging. Signed Distance Function (SDF)-based methods struggle with fine details, while 3D Gaussian Splatting (3DGS)-based approaches lack global geometry…
In this paper we introduce a new class of diffeomorphic smoothers based on general spline smoothing techniques and on the use of some tools that have been recently developed in the context of image warping to compute smooth diffeomorphisms.…
We propose Differentiable Surface Splatting (DSS), a high-fidelity differentiable renderer for point clouds. Gradients for point locations and normals are carefully designed to handle discontinuities of the rendering function.…
This paper addresses the problems of spline interpolation on smooth Riemannian manifolds, with or without the inclusion of least-squares fitting. Our unified approach utilizes gradient flows for successively connected curves or networks,…
It is vital to infer a signed distance function (SDF) in multi-view based surface reconstruction. 3D Gaussian splatting (3DGS) provides a novel perspective for volume rendering, and shows advantages in rendering efficiency and quality.…
A common numerical task is to represent functions which are highly spatially anisotropic, and to solve differential equations related to these functions. One way such anisotropy arises is that information transfer along one spatial…
Real-time semantic segmentation of LiDAR data is crucial for autonomously driving vehicles, which are usually equipped with an embedded platform and have limited computational resources. Approaches that operate directly on the point cloud…
We consider overlap splines that are defined by connecting the patches of piecewise functions via common values at given finite sets of nodes, without using any partitions of the computational domain. It is shown that some classical finite…
Differentiable real function reproducing primes up to a given number and having a differentiable inverse function is constructed. This inverse function is compared with the Riemann-Von Mangoldt exact expression for the number of primes not…
Modeling data using manifold values is a powerful concept with numerous advantages, particularly in addressing nonlinear phenomena. This approach captures the intrinsic geometric structure of the data, leading to more accurate descriptors…
We formulate hydrodynamic equations and spectrally accurate numerical methods for investigating the role of geometry in flows within two-dimensional fluid interfaces. To achieve numerical approximations having high precision and level of…
Accurate and fast 3D imaging of specular surfaces still poses major challenges for state-of-the-art optical measurement principles. Frequently used methods, such as phase-measuring deflectometry (PMD) or shape-from-polarization (SfP), rely…
Monte Carlo integration is a commonly used technique to compute intractable integrals and is typically thought to perform poorly for very high-dimensional integrals. To show that this is not always the case, we examine Monte Carlo…
In Functional Data Analysis, data are commonly assumed to be smooth functions on a fixed interval of the real line. In this work, we introduce a comprehensive framework for the analysis of functional data, whose domain is a two-dimensional…
In this article, a new method for segmentation and restoration of images on two-dimensional surfaces is given. Active contour models for image segmentation are extended to images on surfaces. The evolving curves on the surfaces are…
Generalizing tensor-product splines to smooth functions whose control nets outline topological polyhedra, bi-cubic polyhedral splines form a piecewise polynomial, first-order differentiable space that associates one function with each…
Stripe patterns are ubiquitous in nature and everyday life. While the synthesis of these patterns has been thoroughly studied in the literature, their potential to control the mechanics of structured materials remains largely unexplored. In…
This paper reviews a class of univariate piecewise polynomial functions known as discrete splines, which share properties analogous to the better-known class of spline functions, but where continuity in derivatives is replaced by (a…
We use a discrete multiscale analysis to study the asymptotic integrability of differential-difference equations. In particular, we show that multiscale perturbation techniques provide an analytic tool to derive necessary integrability…
One of the challenges in using numerical methods to address many-body problems is the multi-dimensional integration over poles. More often that not, one needs such integrations to be evaluated as a function of an external variable. An…