Related papers: Projective reconstruction in algebraic vision
A set of orthonormal polynomials is proposed for image reconstruction from projection data. The relationship between the projection moments and image moments is discussed in detail, and some interesting properties are demonstrated.…
In this paper we discuss some topics related to the general theory of frames. In particular we focus our attention to the existence of different 'reconstruction formulas' for a given vector of a certain Hilbert space and to some refinement…
This paper develops the geometry of locally bounded rational functions on non-singular real algebraic varieties. First various basic geometric and algebraic results regarding these functions are established in any dimension, culminating…
We study the homotopy types of spaces of algebraic (rational) maps from real projective spaces into complex projective spaces. In a previous paper we have shown that the inclusion of the first space into the second one is a homotopy…
Creating virtual models of real spaces and objects is cumbersome and time consuming. This paper focuses on the problem of geometric reconstruction from sparse data obtained from certain image-based modeling approaches. A number of elegant…
In this survey article, we present interactions between algebraic geometry and computer vision, which have recently come under the header of algebraic vision. The subject has given new insights in multiple view geometry and its application…
A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…
We show that varieties of dimension at least 2 over infinite fields are determined as abstract schemes by their Zariski topological spaces together with the rational equivalence relation on the set of effective divisors. This gives a…
Let $L=\mathbb F_{q^n}$ be a finite field and let $F=\mathbb F_q$ be a subfield of $L$. Consider $L$ as a vector space over $F$ and the associated projective space that is isomorphic to ${\mathrm{PG}}(n-1,q)$. The properties of the…
Let $\mathcal{H}$ be a (separable) Hilbert space and $\{e_k\}_{k\geq 1}$ a fixed orthonormal basis of $\mathcal{H}$. Motivated by many papers on scaled projections, angles of subspaces and oblique projections, we define and study the notion…
Elementary Algebraic Geometry can be described as study of zeros of polynomials with integer degrees, this idea can be naturally carried over to `polynomials' with rational degree. This paper explores affine varieties, tangent space and…
In this note we discuss some arithmetic and geometric questions concerning self maps of projective algebraic varieties.
Answering a problem raised by Lazarsfeld, Hwang and Mok proved that a surjective holomorphic map from a rational homogeneous space of Picard number 1 onto projective manifold different from projective space must be a biholomorphism. THe aim…
We introduce a new formalism and a number of new results in the context of geometric computational vision. The classical scope of the research in geometric computer vision is essentially limited to static configurations of points and lines…
Here we briefly describe some topics along the lines of projective spaces and related geometric constructions connected to linear algebra, which provide fundamental examples in classical geometry and analysis.
We characterize collections of orthogonal projections for which it is possible to reconstruct a vector from the magnitudes of the corresponding projections. As a result we are able to show that in an $M$-dimensional real vector space a…
We consider cylindrical algebraic decomposition (CAD) and the key concept of delineability which underpins CAD theory. We introduce the novel concept of projective delineability which is easier to guarantee computationally. We prove results…
Motivated by applications in moduli theory, we introduce a flexible and powerful language for expressing lower bounds on relative dimension of morphisms of schemes, and more generally of algebraic stacks. We show that the theory is robust…
A geometric construction of Getzler's cohomological relation in the moduli space of 4 pointed elliptic curves is given by a push-forward of a natural rational equivalence in a space of admissible covers. In particular, Getzler's relation is…
Phylogenetic algebraic geometry is concerned with certain complex projective algebraic varieties derived from finite trees. Real positive points on these varieties represent probabilistic models of evolution. For small trees, we recover…