Related papers: Algebra and Geometry of Camera Resectioning
This paper studies the restriction multiplicities of half-diagram modules for the partition algebra and their geometric interpretations. By specializing the Bowman-De Visscher-Orellana formula [BVC, Theorem 4.3] for restriction…
Omnidirectional cameras are widely used in such areas as robotics and virtual reality as they provide a wide field of view. Their images are often processed with classical methods, which might unfortunately lead to non-optimal solutions as…
This paper studies binary quadratic programs in which the objective is defined by a Euclidean distance matrix, subject to a general polyhedral constraint set. This class of nonconcave maximisation problems includes the capacitated,…
In this expository introductory text we discuss the multiplier ideals in algebraic geometry. We state Kawamata-Viehweg's and Nadel's vanishing theorems, give a proof (following Ein and Lazarsfeld) of Koll\'ar's bound on the maximal…
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 joint problem of reconstruction / feature extraction is a challenging task in image processing. It consists in performing, in a joint manner, the restoration of an image and the extraction of its features. In this work, we firstly…
We transpose an optimal control technique to the image segmentation problem. The idea is to consider image segmentation as a parameter estimation problem. The parameter to estimate is the color of the pixels of the image. We use the…
A strong link between information geometry and algebraic statistics is made by investigating statistical manifolds which are algebraic varieties. In particular it it shown how first and second order efficient estimators can be constructed,…
Geometric vertex decomposition and liaison are two frameworks that have been used to produce similar results about similar families of algebraic varieties. In this paper, we establish an explicit connection between these approaches. In…
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…
Resultants and Gr\"obner bases are crucial tools in studying polynomial elimination theory. We investigate relations between the variety of the resultant of two polynomials and the variety of the ideal they generate. Then we focus on the…
When imaging through a semi-reflective medium such as glass, the reflection of another scene can often be found in the captured images. It degrades the quality of the images and affects their subsequent analyses. In this paper, a novel deep…
We propose a gradient descent method for solving optimization problems arising in settings of tropical geometry - a variant of algebraic geometry that has attracted growing interest in applications such as computational biology, economics,…
We consider sequential and parallel decomposition methods for a dual problem of a general total variation minimization problem with applications in several image processing tasks, like image inpainting, estimation of optical flow and…
We propose a novel method to accurately reconstruct a set of images representing a single scene from few linear multi-view measurements. Each observed image is modeled as the sum of a background image and a foreground one. The background…
In image processing, classical methods minimize a suitable functional that balances between computational feasibility (convexity of the functional is ideal) and suitable penalties reflecting the desired image decomposition. The fact that…
We give illustrative examples of how the computer algebra system OSCAR can support research in commutative algebra and algebraic geometry. We start with a thorough introduction to Groebner basis techniques, with particular emphasis on the…
We propose a new fast algorithm for solving one of the standard formulations of image restoration and reconstruction which consists of an unconstrained optimization problem where the objective includes an $\ell_2$ data-fidelity term and a…
We consider a variational convex relaxation of a class of optimal partitioning and multiclass labeling problems, which has recently proven quite successful and can be seen as a continuous analogue of Linear Programming (LP) relaxation…
This is a computational study of bottlenecks on algebraic varieties. The bottlenecks of a smooth variety $X \subseteq \mathbb{C}^n$ are the lines in $\mathbb{C}^n$ which are normal to $X$ at two distinct points. The main result is a…