相关论文: A Differential Invariant for Zooming

Interest point detection methods have received increasing attention and are widely used in computer vision tasks such as image retrieval and 3D reconstruction. In this work, second-order anisotropic Gaussian directional derivative filters…

We propose Camera Splatting, a novel view optimization framework for novel view synthesis. Each camera is modeled as a 3D Gaussian, referred to as a camera splat, and virtual cameras, termed point cameras, are placed at 3D points sampled…

A new version of differential renormalization is presented. It is based on pulling out certain differential operators and introducing a logarithmic dependence into diagrams. It can be defined either in coordinate or momentum space, the…

In gravitational lensing, the magnification effect changes the luminosity and size of a background galaxy. If the image sizes are not small compared to the scale over which the magnification and shear vary, higher-order distortions occur…

This paper considers the intra-image color-space of an object or a scene when these are subject to a dominant single-source of variation. The source of variation can be intrinsic or extrinsic (i.e., imaging conditions) to the object. We…

We compute invariants for the two-variable M\"obius transformation. In particular we are interested in partial differential equations in two dependent and two independent variables that are kept invariant under this transformation.

Recently, variational methods were successfully applied for computing the optical flow in gray and RGB-valued image sequences. A crucial assumption in these models is that pixel-values do not change under transformations. Nowadays, modern…

This paper presents a novel 3D object detection framework that processes LiDAR data directly on its native representation: range images. Benefiting from the compactness of range images, 2D convolutions can efficiently process dense LiDAR…

In this position paper, we consider the state of computer vision research with respect to invariance to the horizontal orientation of an image -- what we term reflection invariance. We describe why we consider reflection invariance to be an…

Some model reduction techniques for multiple time-scale dynamical systems make use of the identification of low dimensional slow invariant attracting manifolds (SIAM) in order to reduce the dimensionality of the phase space by restriction…

We outline the construction of differential invariants for higher--rank tensors.

We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…

A methodology is developed to extract $d$ invariant features $W=f(X)$ that predict a response variable $Y$ without being confounded by variables $Z$ that may influence both $X$ and $Y$. The methodology's main ingredient is the penalization…

Extending the Liouville-Caputo definition of a fractional derivative to a nonlocal covariant generalization of arbitrary bound operators acting on multidimensional Riemannian spaces an appropriate approach for the 3D shape recovery of…

Typically, a salient object detection (SOD) model faces opposite requirements in processing object interiors and boundaries. The features of interiors should be invariant to strong appearance change so as to pop-out the salient object as a…

Building on an analogy with conformal invariance, local scale transformations consistent with dynamical scaling are constructed. Two types of local scale invariance are found which act as dynamical space-time symmetries of certain non-local…

In this paper, we propose a second-order dynamical system with a smoothing effect for solving paramonotone variational inequalities. Under standard assumptions, we prove that the trajectories of this dynamical system converges to a solution…

Reasoning about 3D scenes from their 2D image projections is one of the core problems in computer vision. Solutions to this inverse and ill-posed problem typically involve a search for models that best explain observed image data. Notably,…

New universal invariant operators are introduced in a class of geometries which include the quaternionic structures and their generalisations as well as 4-dimensional conformal (spin) geometries. It is shown that, in a broad sense, all…

The accuracy of many multiscale methods based on localized computations suffers from high contrast coefficients since the localization error generally depends on the contrast. We study a class of methods based on the variational multiscale…