Related papers: Algebra and Geometry of Camera Resectioning
Vertical decomposition is a widely used general technique for decomposing the cells of arrangements of semi-algebraic sets in ${{\mathbb R}}^d$ into constant-complexity subcells. In this paper, we settle in the affirmative a few…
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…
Image segmentation is a central topic in image processing and computer vision and a key issue in many applications, e.g., in medical imaging, microscopy, document analysis and remote sensing. According to the human perception, image…
Multiview ideals arise from the geometry of image formation in pinhole cameras, and universal multiview ideals are their analogs for unknown cameras. We prove that a natural collection of polynomials form a universal Gr\"obner basis for…
Cylindrical algebraic decomposition (CAD) is an important tool for the study of real algebraic geometry with many applications both within mathematics and elsewhere. It is known to have doubly exponential complexity in the number of…
Given a finite set of closed rational points of affine space over a field, we give a Gr\"obner basis for the lexicographic ordering of the ideal of polynomials which vanish at all given points. Our method is an alternative to the…
We present algorithms for computing the reduced Gr\"{o}bner basis of the vanishing ideal of a finite set of points in a frame of ideal interpolation. Ideal interpolation is defined by a linear projector whose kernel is a polynomial ideal.…
Correspondences estimation or feature matching is a key step in the image-based 3D reconstruction problem. In this paper, we propose two algebraic properties for correspondences. The first is a rank deficient matrix construct from the…
We prove descent theorems for semiorthogonal decompositions using techniques from derived algebraic geometry. Our methods allow us to capture more general filtrations of derived categories and even marked filtrations, where one descends not…
This work introduces a multidimensional generalization of the maximum bisection problem. A mixed integer linear programming formulation is proposed with the proof of its correctness. The numerical tests, made on the randomly generated…
The multiview variety from computer vision is generalized to images by $n$ cameras of points linked by a distance constraint. The resulting five-dimensional variety lives in a product of $2n$ projective planes. We determine defining…
The principles of difference imaging outlined and the technique of Alard and Lupton (1997) is generalised to generate the best possible difference images to within the limits of measurement error. It is shown how for a large database of…
Multilevel partitioning methods that are inspired by principles of multiscaling are the most powerful practical hypergraph partitioning solvers. Hypergraph partitioning has many applications in disciplines ranging from scientific computing…
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…
This paper proposes using a Gaussian mixture model as a prior, for solving two image inverse problems, namely image deblurring and compressive imaging. We capitalize on the fact that variable splitting algorithms, like ADMM, are able to…
Computer algebra programs are presented for application in general relativity, in electrodynamics, and in gauge theories of gravity. The mathematical formalism used is the calculus of exterior differential forms, the computer algebra system…
A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…
We survey results in algebraic complexity theory, focusing on matrix multiplication. Our goals are (i.) to show how open questions in algebraic complexity theory are naturally posed as questions in geometry and representation theory, (ii.)…
Cylindrical algebraic decomposition is a classical construction in real algebraic geometry. Although there are many algorithms to compute a cylindrical algebraic decomposition, their practical performance is still very limited. In this…
We determine the algebraic degree of minimal problems for the calibrated trifocal variety in computer vision. We rely on numerical algebraic geometry and the homotopy continuation software Bertini.