Related papers: A Computer Vision Problem in Flatland

Consider a polyhedral convex cone which is given by a finite number of linear inequalities. We investigate the problem to project this cone into a subspace and show that this problem is closely related to linear vector optimization: We…

Co-localization is the problem of localizing objects of the same class using only the set of images that contain them. This is a challenging task because the object detector must be built without negative examples that can lead to more…

3D object detection and pose estimation from a single image are two inherently ambiguous problems. Oftentimes, objects appear similar from different viewpoints due to shape symmetries, occlusion and repetitive textures. This ambiguity in…

We consider applications involving a large set of instances of projecting points to polytopes. We develop an intuition guided by theoretical and empirical analysis to show that when these instances follow certain structures, a large…

Given two rational, properly parametrized space curves ${\mathcal C}_1$ and ${\mathcal C}_2$, where $\CCC_2$ is contained in some plane $\Pi$, we provide an algorithm to check whether or not there exist perspective or parallel projections…

In this paper we analyse convergence of projected fixed-point iteration on a Riemannian manifold of matrices with fixed rank. As a retraction method we use `projector splitting scheme'. We prove that the projector splitting scheme converges…

Joint object matching, also known as multi-image matching, namely, the problem of finding consistent partial maps among all pairs of objects within a collection, is a crucial task in many areas of computer vision. This problem subsumes…

Fake projective planes are smooth complex surfaces of general type with Betti numbers equal to those of the usual projective plane. They come in complex conjugate pairs and have been classified as quotients of the two-dimensional ball by…

We determine those maps between affine or projective spaces that are linear in the abstract sense of transforming collinear points into collinear points and whose restriction to any line is constant or injective. Our results are extensions…

X-ray tomography has been studied in various fields. Although a great deal of effort has been directed at reconstructing the projection image set from a rigid-type specimen, little attention has been addressed to the reconstruction of…

We classify equivariant topological complex vector bundles over real projective plane under a compact Lie group (not necessarily effective) action. It is shown that nonequivariant Chern classes and isotropy representations at (at most)…

We study intersections of projective convex sets in the sense of Steinitz. In a projective space, an intersection of a nonempty family of convex sets splits into multiple connected components each of which is a convex set. Hence, such an…

Extracting planes from a 3D scene is useful for downstream tasks in robotics and augmented reality. In this paper we tackle the problem of estimating the planar surfaces in a scene from posed images. Our first finding is that a surprisingly…

While deep learning methods have achieved state-of-the-art performance in many challenging inverse problems like image inpainting and super-resolution, they invariably involve problem-specific training of the networks. Under this approach,…

Treating images as data has become increasingly popular in political science. While existing classifiers for images reach high levels of accuracy, it is difficult to systematically assess the visual features on which they base their…

The present work proposes a solution to the challenging problem of registering two partial point sets of the same object with very limited overlap. We leverage the fact that most objects found in man-made environments contain a plane of…

Given a network of multiple agents, the pointing consensus problem asks all agents to point toward a common target. This paper proposes a simple method to solve the pointing consensus problem in the plane. In our formulation, each agent…

We give a sufficient condition in order that $n$ closed connected subsets in the $n$-dimensional real projective space admit a common multitangent hyperplane.

Geometric embedding of graphs in a point set in the plane is a well known problem. In this paper, the complexity of a variant of this problem, where the point set is bounded by a simple polygon, is considered. Given a point set in the plane…

In this paper we address the problem of matching two images with two different resolutions: a high-resolution image and a low-resolution one. The difference in resolution between the two images is not known and without loss of generality…