Related papers: Existence of Two View Chiral Reconstructions
Generically, one expects the images of two different point sets, in two different (projective) cameras, to be different. However, it can happen that the images are the same up to a projective transformation which is an instance of…
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,…
To reconstruct the points in three dimensional space, we need at least two images. In this paper we compared two different methods: the first uses only two images, the second one uses three. During the research we measured how camera…
The reconstruction of a scene via a stereo-camera system is a two-steps process, where at first images from different cameras are matched to identify the set of point-to-point correspondences that then will actually be reconstructed in the…
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…
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…
In our previous works we have classified real non-singular cubic hypersurfaces in the 5-dimensional projective space up to equivalence that includes both real projective transformations and continuous variations of coefficients preserving…
We give a complete deformation classification of real Zariski sextics, that is of generic apparent contours of nonsingular real cubic surfaces. As a by-product, we observe a certain "reversion" duality in the set of deformation classes of…
Correspondences between k-tuples of points are key in multiple view geometry and motion analysis. Regular transformations are posed by homographies between two projective planes that serves as structural models for images. Such…
We study a class of four-dimensional N=1 superconformal field theories obtained from the six-dimensional (1,0) theory, on M5-branes on C^2/Z_k orbifold singularity, compactified on a Riemann surface. This produces various quiver gauge…
We present evidence for renormalization group fixed points with dual magnetic descriptions in fourteen new classes of four-dimensional $N=1$ supersymmetric models. Nine of these classes are chiral and many involve two or three gauge groups.…
How can we tell whether an image has been mirrored? While we understand the geometry of mirror reflections very well, less has been said about how it affects distributions of imagery at scale, despite widespread use for data augmentation in…
This article has been written for an educational magazine whose target audience consists of students and teachers of mathematics in universities, colleges and schools. It concerns a notion of duality between rectangles. A proof is given…
The rational camera model recently introduced in [19] provides a general methodology for studying abstract nonlinear imaging systems and their multi-view geometry. This paper builds on this framework to study "physical realizations" of…
In this paper, we address the inverse problem of reconstructing a scene as well as the camera motion from the image sequence taken by an omni-directional camera. Our structure from motion results give sharp conditions under which the…
The multiview variety of an arrangement of cameras is the Zariski closure of the images of world points in the cameras. The prime vanishing ideal of this complex projective variety is called the multiview ideal. We show that the bifocal and…
This paper studies the problem of 3D volumetric reconstruction from two views of a scene with an unknown camera. While seemingly easy for humans, this problem poses many challenges for computers since it requires simultaneously…
This paper is a theoretical study of the following Non-Rigid Structure from Motion problem. What can be computed from a monocular view of a parametrically deforming set of points? We treat various variations of this problem for affine and…
We consider the problem of reconstructing binary images from their horizontal and vertical projections. We present a condition that the projections must necessarily satisfy when there exist two disjoint reconstructions from those…
In our previous works (2012, 2013), we provided a finite list of properties characterizing all potential types of quadratic birational transformations of a projective space into a factorial variety, whose base locus is smooth and…