Related papers: An Atlas for the Pinhole Camera

The purpose of this note is to give a survey of the algebraic properties of multiplier ideals, and illustrate some of their applications to classical projective geometry.

Inferring 3D structure of a generic object from a 2D image is a long-standing objective of computer vision. Conventional approaches either learn completely from CAD-generated synthetic data, which have difficulty in inference from real…

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…

The internal calibration of a pinhole camera is given by five parameters that are combined into an upper-triangular $3\times 3$ calibration matrix. If the skew parameter is zero and the aspect ratio is equal to one, then the camera is said…

To endow machines with the ability to perceive the real-world in a three dimensional representation as we do as humans is a fundamental and long-standing topic in Artificial Intelligence. Given different types of visual inputs such as…

In computer graphics, the field of view of a camera is represented by a viewing frustum and a corresponding projection matrix, the properties of which, in the absence of restrictions on rectangular shape of the near plane and its…

We study objects in triangulated categories which have a two-dimensional graded endomorphism algebra. Given such an object, we show that there is a unique maximal triangulated subcategory, in which the object is spherical. This general…

We study the 3D-aware image attribute editing problem in this paper, which has wide applications in practice. Recent methods solved the problem by training a shared encoder to map images into a 3D generator's latent space or by per-image…

Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this…

Electron tomography is becoming an increasingly important tool in materials science for studying the three-dimensional morphologies and chemical compositions of nanostructures. The image quality obtained by many current algorithms is…

Deep neural networks have reshaped modern machine learning by learning powerful latent representations that often align with the manifold hypothesis: high-dimensional data lie on lower-dimensional manifolds. In this paper, we establish a…

The photometric stereo (PS) problem consists in reconstructing the 3D-surface of an object, thanks to a set of photographs taken under different lighting directions. In this paper, we propose a multi-scale architecture for PS which,…

In computer vision, camera pose estimation from correspondences between 3D geometric entities and their projections into the image has been a widely investigated problem. Although most state-of-the-art methods exploit low-level primitives…

We give a definition of atlases for ineffective orbifolds, and prove that this definition leads to the same notion of orbifold as that defined via topological groupoids.

This extended abstract is about an effort to build a formal description of a triangulation algorithm starting with a naive description of the algorithm where triangles, edges, and triangulations are simply given as sets and the most complex…

Maps are a key component in image-based camera localization and visual SLAM systems: they are used to establish geometric constraints between images, correct drift in relative pose estimation, and relocalize cameras after lost tracking. The…

A computational anatomy atlas is a set of internal organ geometries. It is based on data of real patients and complemented with virtual cases by using a some numerical approach. Atlases are in demand in computational physiology, especially…

In this note we discuss some arithmetic and geometric questions concerning self maps of projective algebraic varieties.

This paper introduces the geodesics of triangulated image object shapes. Both rectilinear and curvilinear triangulations of shapes are considered. The triangulation of image object shapes leads to collections of what are known as nerve…

Both in the plane and in space, we invert the nonlinear Ullman transformation for 3 points and 3 orthographic cameras. While Ullman's theorem assures a unique reconstruction modulo a reflection for 3 cameras and 4 points, we find a locally…