Related papers: A Computer Vision Problem in Flatland
We introduce series-triangular graph embeddings and show how to partition point sets with them. This result is then used to improve the upper bound on the number of Steiner points needed to obtain compatible triangulations of point sets.…
The real projective plane has three well know isomorphic constructions: the extended euclidean plane, unit (hemi)sphere, and three dimensional vector space over the reals. In this paper we find the isomorphisms that map between these three…
In this paper we extend the notion of a Lorentz cone. We call a closed convex set isotone projection set with respect to a pointed closed convex cone if the projection onto the set is isotone (i.e., monotone) with respect to the order…
We consider the problem of mirror invisibility for plane sets. Given a circle and a finite number of unit vectors (defining the directions of invisibility) such that the angles between them are commensurable with $\pi$, for any $\varepsilon…
An oriented link projection is the image of a generic immersion of oriented circles into the 2-sphere. The circle arrangement of a link projection is a disjoint union of unoriented circles on the 2-sphere obtained by orientation-incoherent…
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,…
Given a set $P$ of $n$ points in the plane, where $n$ is even, we consider the following question: How many plane perfect matchings can be packed into $P$? We prove that at least $\lceil\log_2{n}\rceil-2$ plane perfect matchings can be…
This communication describes a representation of images as a set of edges characterized by their position and orientation. This representation allows the comparison of two images and the computation of their similarity. The first step in…
This paper poses a question about a simple localization problem. The question is if an {\em oblivious} walker on a line-segment can localize the middle point of the line-segment in {\em finite} steps observing the direction (i.e., Left or…
We propose a novel projector-camera system (ProCams) in which each pixel has both projection and capturing capabilities. Our proposed ProCams solves the difficulty of obtaining precise pixel correspondence between the projector and the…
For an interval finite quiver $Q$, we introduce a class of flat representations. We classify the indecomposable projective objects in the category $\mathrm{rep}(Q)$ of pointwise finite dimensional representations. We show that an object in…
In 1933 von Neumann proved a beautiful result that one can approximate a point in the intersection of two convex sets by alternating projections, i.e., successively projecting on one set and then the other. This algorithm assumes that one…
Recently, several clustering algorithms have been used to solve variety of problems from different discipline. This dissertation aims to address different challenging tasks in computer vision and pattern recognition by casting the problems…
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…
Let $F$ be Cayley's ruled cubic surface in a projective three-space over any commutative field $K$. We determine all collineations fixing $F$, as a set, and all cubic forms defining $F$. For both problems the cases $|K|=2,3$ turn out to be…
Random Projection is a foundational research topic that connects a bunch of machine learning algorithms under a similar mathematical basis. It is used to reduce the dimensionality of the dataset by projecting the data points efficiently to…
We provide a simple and efficient algorithm for computing the Euclidean projection of a point onto the capped simplex---a simplex with an additional uniform bound on each coordinate---together with an elementary proof. Both the MATLAB and…
Image stitching for two images without a global transformation between them is notoriously difficult. In this paper, noticing the importance of planar structure under perspective geometry, we propose a new image stitching method which…
It has always been a research hotspot to use geographic information to assist the navigation of unmanned aerial vehicles. In this paper, a road-network-based localization method is proposed. We match roads in the measurement images to the…
It is hard for us humans to recognize things in nature until we have invented them ourselves. For image-forming optics, nature has made virtually every kind of lens humans have devised. But what about lensless "imaging"? Recently, we showed…