Related papers: Existence of Two View Chiral Reconstructions
We consider the notion of finite dimensional reconstructions systems (RS's), which includes the fusion frames as projective RS's. We study erasures, some geometrical properties of these spaces, the spectral picture of the set of all dual…
Chirality plays an important role in physics, chemistry, biology, and other fields. It describes an essential symmetry in structure. However, chirality invariants are usually complicated in expression or difficult to evaluate. In this…
We study quantum field theory in six dimensions with two of them compactified on a square. A simple boundary condition is the identification of two pairs of adjacent sides of the square such that the values of a field at two identified…
In recent work, algebraic computational software was used to provide the exact algebraic conditions under which a sixtuple $\{F^{ij}\}$ of fundamental matrices, corresponding to $4$ images, will be compatible, i.e. there will exist cameras…
We present an algebraic study of the projection of plane curves and twisted cubics in space onto multiple images of pinhole cameras. The Zariski closure of the image of the projection of conics is a conic multiview varieties. Extending…
Estimating positions of world points from features observed in images is a key problem in 3D reconstruction, image mosaicking,simultaneous localization and mapping and structure from motion. We consider a special instance in which there is…
We give a non-iterative solution to a particular case of the four-point three-views pose problem when three camera centers are collinear. Using the well-known Cayley representation of orthogonal matrices, we derive from the epipolar…
This literature has proposed three fast and easy computable image features to improve computer vision by offering more human-like vision power. These features are not based on image pixels absolute or relative intensity; neither based on…
It is shown that every 2-planar graph is quasiplanar, that is, if a simple graph admits a drawing in the plane such that every edge is crossed at most twice, then it also admits a drawing in which no three edges pairwise cross. We further…
Metric auto calibration of a camera network from multiple views has been reported by several authors. Resulting 3D reconstruction recovers shape faithfully, but not scale. However, preservation of scale becomes critical in applications,…
Motivated by the embedding problem of canonical models in small codimension, we extend Severi's double point formula to the case of surfaces with rational double points, and we give more general double point formulae for varieties with…
Welschinger invariants enumerate real nodal rational curves in the plane or in another real rational surface. We analyze the existence of similar enumerative invariants that count real rational plane curves having prescribed non-nodal…
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…
Relative pose estimation using point correspondences (PC) is a widely used technique. A minimal configuration of six PCs is required for two views of generalized cameras. In this paper, we present several minimal solvers that use six PCs to…
A computation shows that there are 77 (up to scalar shifts) possible pairs of integer coefficient polynomials of degree five, having roots of unity as their roots, and satisfying the conditions of Beukers and Heckman [1], so that the…
Composed Image Retrieval (CIR) is an emerging yet challenging task that allows users to search for target images using a multimodal query, comprising a reference image and a modification text specifying the user's desired changes to the…
We study the duality of reconstruction systems, which are $g$-frames in a finite dimensional setting. These systems allow redundant linear encoding-decoding schemes implemented by the so-called dual reconstruction systems. We are…
A double-normal pair of a finite set $S$ of points from Euclidean space is a pair of points $\{p,q\}$ from $S$ such that $S$ lies in the closed strip bounded by the hyperplanes through $p$ and $q$ that are perpendicular to $pq$. A…
The fundamental issues of symmetry related to chirality are discussed and applied to simple situations relevant to liquid crystals. We show that any chiral measure of a geometric object is a pseudoscalar (invariant under proper rotations…
In 1978, Anderson and White asked whether there is a decomposition of $K_{12}$ into two graphs, one planar and one toroidal. Using theoretical arguments and a computer search of all maximal planar graphs of order 12, we show that no such…