Related papers: Pictures of Combinatorial Cubes
We present a novel solution to the camera pose estimation problem, where rotation and translation of a camera between two views are estimated from matched feature points in the images. The camera pose estimation problem is traditionally…
This paper presents a novel preconditioning strategy for the classic 8-point algorithm (8-PA) for estimating an essential matrix from 360-FoV images (i.e., equirectangular images) in spherical projection. To alleviate the effect of uneven…
The fundamental matrix can be estimated from point matches. The current gold standard is to bootstrap the eight-point algorithm and two-view projective bundle adjustment. The eight-point algorithm first computes a simple linear least…
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…
3D reconstruction is a fundamental issue in many applications and the feature point matching problem is a key step while reconstructing target objects. Conventional algorithms can only find a small number of feature points from two images…
We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic…
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 propose a federated algorithm for reconstructing images using multimodal tomographic data sourced from dispersed locations, addressing the challenges of traditional unimodal approaches that are prone to noise and reduced image quality.…
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…
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…
Enumeration of all combinatorial types of point configurations and polytopes is a fundamental problem in combinatorial geometry. Although many studies have been done, most of them are for 2-dimensional and non-degenerate cases. Finschi and…
Accurate estimation of camera matrices is an important step in structure from motion algorithms. In this paper we introduce a novel rank constraint on collections of fundamental matrices in multi-view settings. We show that in general, with…
This paper addresses the problem of mirror surface reconstruction, and proposes a solution based on observing the reflections of a moving reference plane on the mirror surface. Unlike previous approaches which require tedious calibration,…
We consider frames F in a given Hilbert space, and we show that every F may be obtained in a constructive way from a reproducing kernel and an orthonormal basis in an ambient Hilbert space. The construction is operator-theoretic, building…
Maximum likelihood iteration is one of the most commonly used reconstruction algorithms in quantum tomography. The main appeal of the method is that it is easy to implement and that it converges reliably to a physically meaningful density…
The efficient computation of viewpoints under consideration of various system and process constraints is a common challenge that any robot vision system is confronted with when trying to execute a vision task. Although fundamental research…
Multi-camera systems offer rich observation capabilities for visual navigation and 3D scene reconstruction; however, the resulting feature redundancy often compromises computational efficiency. This challenge is particularly pronounced…
This paper addresses the problem of recovering projective camera matrices from collections of fundamental matrices in multiview settings. We make two main contributions. First, given ${n \choose 2}$ fundamental matrices computed for $n$…
This note contains a solution to the following problem: reconstruct the definition field and the equation of a projective cubic surface, using only combinatorial information about the set of its rational points. This information is encoded…
We establish common fixed point theorems for two pairs of weakly compatible self-mappings using an auxiliary function of two variables. Unlike classical results, our theorems do not assume continuity of the mappings and require completeness…