Related papers: When is one pinhole camera image equal to some oth…

A basic problem in computer vision is to understand the structure of a real-world scene given several images of it. Here we study several theoretical aspects of the intra multi-view geometry of calibrated cameras when all that they can…

In the conventional approach to lens imaging, rays are used to map object points to image points. However, many students have a need to think of the image as a whole. To answer this need, lens imaging is reinterpreted as a superposition of…

Estimating a depth map from multiple views of a scene is a fundamental task in computer vision. As soon as more than two viewpoints are available, one faces the very basic question how to measure similarity across >2 image patches.…

This paper combines two classical theories, namely metric projective differential geometry and superintegrability. We study superintegrable systems on 2-dimensional geometries that share the same geodesics, viewed as unparametrized curves.…

The problem of image registration is finding a transformation that aligns two images, such that the corresponding points are in the same location. This paper introduces a simple, end-to-end trainable algorithm that is implementable in a few…

The essential variety is an algebraic subvariety of dimension $5$ in real projective space $\mathbb R\mathrm P^{8}$ which encodes the relative pose of two calibrated pinhole cameras. The $5$-point algorithm in computer vision computes the…

The problem of structure from motion is concerned with recovering 3-dimensional structure of an object from a set of 2-dimensional images. Generally, all information can be uniquely recovered if enough images and image points are provided,…

Calibration in a multi camera network has widely been studied for over several years starting from the earlier days of photogrammetry. Many authors have presented several calibration algorithms with their relative advantages and…

Projection matrices are necessary for a large portion of rendering computer graphics. There are primarily two different types of projection matrices -- perspective and orthographic -- which are used frequently, and are traditionally treated…

Structure from motion is the process of recovering information about cameras and 3D scene from a set of images. Generally, in a noise-free setting, all information can be uniquely recovered if enough images and image points are provided.…

We propose a new method for estimating the relative pose between two images, where we jointly learn keypoint detection, description extraction, matching and robust pose estimation. While our architecture follows the traditional pipeline for…

Light field cameras can capture both spatial and angular information of light rays, enabling 3D reconstruction by a single exposure. The geometry of 3D reconstruction is affected by intrinsic parameters of a light field camera…

A pair of planes, both projective or both affine, of the same order and on the same pointset are orthogoval if each line of one plane intersects each line of the other plane in at most two points. In this paper we prove new constructions…

We propose two minimal solutions to the problem of relative pose estimation of (i) a calibrated camera from four points in two views and (ii) a calibrated generalized camera from five points in two views. In both cases, the relative…

The inverse problem of diffraction theory in essence amounts to the reconstruction of the atomic positions of a solid from its diffraction image. From a mathematical perspective, this is a notoriously difficult problem, even in the…

A peculiar feature of quantum states is that they may embody so-called projective representations of symmetries rather than ordinary representations. Projective representations of space groups-the defining symmetry of crystals-remain…

Image registration is a classical problem in machine vision which seeks methods to align discrete images of the same scene to subpixel accuracy in general situations. As with all estimation problems, the underlying difficulty is the partial…

We present a technique for estimating the similarity between objects such as movies or foods whose proper representation depends on human perception. Our technique combines a modest number of human similarity assessments to infer a pairwise…

In this paper, we propose a topological classification of points for 2D discrete binary images. This classification is based on the values of the calculus of topological numbers. Six classes of points are proposed: isolated point, interior…

Visual question answering is the task of returning the answer to a question about an image. A challenge is that different people often provide different answers to the same visual question. To our knowledge, this is the first work that aims…