Related papers: An Atlas for the Pinhole Camera
Image segmentation is the task of associating pixels in an image with their respective object class labels. It has a wide range of applications in many industries including healthcare, transportation, robotics, fashion, home improvement,…
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…
When matching parts of a surface to its whole, a fundamental question arises: Which points should be included in the matching process? The issue is intensified when using isometry to measure similarity, as it requires the validation of…
In the point set embeddability problem, we are given a plane graph $G$ with $n$ vertices and a point set $S$ with $n$ points. Now the goal is to answer the question whether there exists a straight-line drawing of $G$ such that each vertex…
Associated to any graph is a toric ideal whose generators record relations among the cuts of the graph. We study these ideals and the geometry of the corresponding toric varieties. Our theorems and conjectures relate the combinatorial…
As part of human core knowledge, the representation of objects is the building block of mental representation that supports high-level concepts and symbolic reasoning. While humans develop the ability of perceiving objects situated in 3D…
Modern computer vision has moved beyond the domain of internet photo collections and into the physical world, guiding camera-equipped robots and autonomous cars through unstructured environments. To enable these embodied agents to interact…
In this survey I should like to introduce some concepts of algebraic geometry and try to demonstrate the fruitful interaction between algebraic geometry and computer algebra and, more generally, between mathematics and computer science. One…
Clutter in photos is a distraction preventing photographers from conveying the intended emotions or stories to the audience. Photography amateurs frequently include clutter in their photos due to unconscious negligence or the lack of…
Many problems in Computer Vision can be reduced to either working around a known transform, or given a model for the transform computing the inverse problem of the transform itself. We will look at two ways of working with the matrix $A$…
Multi-view Geometry is reviewed from an Algebraic Geometry perspective and multi-focal tensors are constructed as equivariant projections of the Grassmannian. A connection to the principal minor assignment problem is made by considering…
Vanishing points and vanishing lines are classical geometrical concepts in perspective cameras that have a lineage dating back to 3 centuries. A vanishing point is a point on the image plane where parallel lines in 3D space appear to…
Recently, multiple formulations of vision problems as probabilistic inversions of generative models based on computer graphics have been proposed. However, applications to 3D perception from natural images have focused on low-dimensional…
We propose a method to learn object representations from 3D point clouds using bundles of geometrically interpretable hidden units, which we call geometric capsules. Each geometric capsule represents a visual entity, such as an object or a…
Electronically Assisted Astronomy consists in capturing deep sky images with a digital camera coupled to a telescope to display views of celestial objects that would have been invisible through direct observation. This practice generates a…
This paper presents a simple algebraic method to estimate the pose of a camera relative to a planar target from $n \geq 4$ reference points with known coordinates in the target frame and their corresponding bearing measurements in the…
This is a study of a problem in geodesy with methods from complex algebraic geometry: for a fixed number of measure points and target points at unknown position in the Euclidean plane, we study the problem of determining their relative…
For the problem of 3D object recognition, researchers using deep learning methods have developed several very different input representations, including "multi-view" snapshots taken from discrete viewpoints around an object, as well as…
In this paper, we study the problem of 3D object detection from stereo images, in which the key challenge is how to effectively utilize stereo information. Different from previous methods using pixel-level depth maps, we propose employing…
This paper propose a interactive 3D modeling method and corresponding system based on single or multiple uncalibrated images. The main feature of this method is that, according to the modeling habits of ordinary people, the 3D model of the…