相关论文: A Differential Invariant for Zooming

The exact determination of ground states of small systems is used in a scaling study of the random-field Ising model. While three variants of the model are found to be in the same universality class in 3 dimensions, the Gaussian and bimodal…

The purpose of this article is to delve into the properties of invariants. The properties, explained in [2], reveal new ways to develop algorithms that allow us to test the primality of a number. In this article, some of these are shown,…

The invariant is one of central topics in science, technology and engineering. The differential invariant is essential in understanding or describing some important phenomena or procedures in mathematics, physics, chemistry, biology or…

Moving object detection (MOD) is a significant problem in computer vision that has many real world applications. Different categories of methods have been proposed to solve MOD. One of the challenges is to separate moving objects from…

We give an algorithm to write down all conformally invariant differential operators acting between scalar functions on Minkowski space. All operators of order k are nonlinear and are functions on a finite family of functionally independent…

Accounting for all the relativistic effects, we have developed the fully nonlinear gauge-invariant formalism for describing the cosmological observables and presented the second-order perturbative expressions associated with light…

This paper focuses on visual motion-based invariants that result in a representation of 3D points in which the stationary environment remains invariant, ensuring shape constancy. This is achieved even as the images undergo constant change…

In this paper we study closed subspaces of ultradifferentiable functions which are invariant under the differentiation operator. We propose a version of spectral synthesis which takes into account the presence of non-trivial differentiation…

In this paper, we propose a global method for estimating the motion of a camera which films a static scene. Our approach is direct, fast and robust, and deals with adjacent frames of a sequence. It is based on a quadratic approximation of…

This paper is devoted to the study of generalized differentiation properties of the infimal convolution. This class of functions covers a large spectrum of nonsmooth functions well known in the literature. The subdifferential formulas…

In this note, we propose a variational framework in which the minimization of the acceleration on the group of diffeomorphisms endowed with a right-invariant metric is well-posed. It relies on constraining the acceleration to belong to a…

Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudo-stable…

Because physical phenomena on Earth's surface occur on many different length scales, it makes sense when seeking an efficient approximation to start with a crude global approximation, and then make a sequence of corrections on finer and…

A variational method is discussed, extending the Gaussian effective potential to higher orders. The single variational parameter is replaced by trial unknown two-point functions, with infinite variational parameters to be optimized by the…

Gaussian Splatting has recently become one of the most popular frameworks for photorealistic 3D scene reconstruction and rendering. While current rasterizers allow for efficient mappings of 3D Gaussian splats onto 2D camera views, this work…

This paper explores a mathematical technique for deriving dynamical invariants (i.e. constants of motion) in time-dependent gravitational potentials. The method relies on the construction of a canonical transformation that removes the…

Recent diffusion models provide a promising zero-shot solution to noisy linear inverse problems without retraining for specific inverse problems. In this paper, we reveal that recent methods can be uniformly interpreted as employing a…

The paper deals with systems of ordinary differential equations containing in the right-hand side controls which are discontinuous in phase variables. These controls cause the occurrence of sliding modes. If one uses one of the well-known…

Light detection and ranging (LiDAR) on a moving agent could suffer from motion distortion due to simultaneous rotation of the LiDAR and fast movement of the agent. An accurate piecewise linear de skewing algorithm is proposed to correct the…

Computer Vision techniques represent a class of algorithms that are highly computation and data intensive in nature. Generally, performance of these algorithms in terms of execution speed on desktop computers is far from real-time. Since…