相关论文: Pictures of Combinatorial Cubes

The inverse problem we consider is to reconstruct the location and shape of buried obstacles in the lower half-space of an unbounded two-layered medium in two dimensions from phaseless far-field data. A main difficulty of this problem is…

This paper presents a generic 6DOF camera pose estimation method, which can be used for both the pinhole camera and the fish-eye camera. Different from existing methods, relative positions of 3D points rather than absolute coordinates in…

The fundamental matrix and trifocal tensor are convenient algebraic representations of the epipolar geometry of two and three view configurations, respectively. The estimation of these entities is central to most reconstruction algorithms,…

We show that the scenery reconstruction problem on the Boolean hypercube is in general impossible. This is done by using locally biased functions, in which every vertex has a constant fraction of neighbors colored by $1$, and locally stable…

In 3D reconstruction, the recovery of the calibration parameters of the cameras is paramount since it provides metric information about the observed scene, e.g., measures of angles and ratios of distances. Autocalibration enables the…

We investigate the combinatorial interplay between automorphisms and opposition in (primarily finite) generalised polygons. We provide restrictions on the fixed element structures of automorphisms of a generalised polygon mapping no chamber…

A unified method for three-dimensional reconstruction of objects from transmission images collected at multiple illumination directions is described. The method may be applicable to experimental conditions relevant to absorption-based,…

We consider the problem of reconstructing one-dimensional point sources from their Fourier measurements in a bounded interval $[-\Omega, \Omega]$. This problem is known to be challenging in the regime where the spacing of the sources is…

We construct an image formation theory that covers the majority of optical microscopy techniques that use diverse coherent or incoherent light-matter interactions. The theories of individual microscopy methods could not previously be…

We present To The Point (TTP), a method for reconstructing 3D objects from a single image using 2D to 3D correspondences learned from weak supervision. We recover a 3D shape from a 2D image by first regressing the 2D positions corresponding…

This note is motivated by the Question 16 of http://cubics.wikidot.com: Which configurations of 15 points in the projective 3-space arise as eigenpoints of a cubic surface? We prove that a general eigenscheme in the projective n-space is…

Motivated by topological Tverberg-type problems and by classical results about embeddings (maps without double points), we study the question whether a finite simplicial complex K can be mapped into R^d without triple, quadruple, or, more…

Determining the position and orientation of a calibrated camera from a single image with respect to a 3D model is an essential task for many applications. When 2D-3D correspondences can be obtained reliably, perspective-n-point solvers can…

Accurate camera-to-robot calibration is essential for any vision-based robotic control system and especially critical in minimally invasive surgical robots, where instruments conduct precise micro-manipulations. However, MIS robots have…

We provide criteria for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. These criteria reduce the projection problem to a certain…

This is a study of the Wittner capture construction for critically finite quadratic rational maps for which one critical point is periodic, and the second critical point is in the backward orbit of the first. This construction gives a way…

Combinatorial filters have been the subject of increasing interest from the robotics community in recent years. This paper considers automatic reduction of combinatorial filters to a given size, even if that reduction necessitates changes…

We prove that the existence of finite combinatorial objects such as affine planes, mutually orthogonal Latin squares, and resolvable balanced incomplete block designs can be reformulated as the existence of certain algorithmic reductions…

Understanding the 3D world without supervision is currently a major challenge in computer vision as the annotations required to supervise deep networks for tasks in this domain are expensive to obtain on a large scale. In this paper, we…

Flat-panel cone-beam CT (CBCT) has been applied clinically in a number of high-resolution applications. Increasing geometric magnification can potentially improve resolution, but also increases blur due to an extended x-ray focal-spot. We…