相关论文: A Differential Invariant for Zooming

A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing…

Derivatives and integration operators are well-studied examples of linear operators that commute with scaling up to a fixed multiplicative factor; i.e., they are scale-invariant. Fractional order derivatives (integration operators) also…

We give a survey on higher invariants in noncommutative geometry and their applications to differential geometry and topology.

We propose a scene-level inverse rendering framework that uses multi-view images to decompose the scene into geometry, a SVBRDF, and 3D spatially-varying lighting. Because multi-view images provide a variety of information about the scene,…

The equivalence problem for linear differential operators of the second order, acting in vector bundles, is discussed. The field of rational invariants of symbols is described and connections, naturally accosiated with differential…

A system is invariant with respect to an input transformation if we can transform any dynamic input by this function and obtain the same output dynamics after adjusting the initial conditions appropriately. Often, the set of all such input…

We investigate the relationship between the analytical properties of the Green's function and $\mathbb{Z}_2$ topological insulators, focusing on three-dimensional inversion-symmetric systems. We show that the diagonal zeros of the Green's…

For a system of partial differential equations that has an extended Kovalevskaya form, a reduction procedure is presented that allows one to use a local (point, contact, or higher) symmetry of a system and a symmetry-invariant conservation…

This article is concerned with the representation of curves by means of integral invariants. In contrast to the classical differential invariants they have the advantage of being less sensitive with respect to noise. The integral invariant…

Invertible image representation methods (transforms) are routinely employed as low-level image processing operations based on which feature extraction and recognition algorithms are developed. Most transforms in current use (e.g. Fourier,…

The isomorphism between the reduction algebra and the invariant differential operators on G/H is sketched.

In this paper, we propose a neural network architecture for scale-invariant semantic segmentation using RGB-D images. We utilize depth information as an additional modality apart from color images only. Especially in an outdoor scene which…

Many perception systems in mobile computing, autonomous navigation, and AR/VR face strict compute constraints that are particularly challenging for high-resolution input images. Previous works propose nonuniform downsamplers that "learn to…

Simultaneously localizing camera poses and constructing Gaussian radiance fields in dynamic scenes establish a crucial bridge between 2D images and the 4D real world. Instead of removing dynamic objects as distractors and reconstructing…

In this study, a novel feature coding method that exploits invariance for transformations represented by a finite group of orthogonal matrices is proposed. We prove that the group-invariant feature vector contains sufficient discriminative…

Unlike standard object classification, where the image to be classified contains one or multiple instances of the same object, indoor scene classification is quite different since the image consists of multiple distinct objects. Further,…

To be invariant, or not to be invariant: that is the question formulated in this work about local descriptors. A limitation of current feature descriptors is the trade-off between generalization and discriminative power: more invariance…

We study the algebra of invariant differential operators on a certain homogeneous vector bundle over a Riemannian symmetric space of type $A_2$. We computed radial parts of its generators explicitly to obtain matrix-valued commuting…

Differentiable rendering aims to compute the derivative of the image rendering function with respect to the rendering parameters. This paper presents a novel algorithm for 6-DoF pose estimation through gradient-based optimization using a…

In this report, a de-hazing algorithm based on probability and multi-scale fractional order-based fusion is proposed. The proposed scheme improves on a previously implemented multiscale fraction order-based fusion by augmenting its local…