Related papers: Tiling with Boundaries: Dense digital images have …

This note initiates an investigation of packing links into a region of Euclidean space to achieve a maximal density subject to geometric constraints. The upper bounds obtained apply only to the class of homotopically essential links and…

Filled arrays of bolometers are currently being employed for use in astronomy from the far-infrared through millimeter parts of the electromagnetic spectrum. Because of the large range of wavelengths for which such detectors are applicable,…

An irregular vertex in a tiling by polygons is a vertex of one tile and belongs to the interior of an edge of another tile. In this paper we show that for any integer $k\geq 3$, there exists a normal tiling of the Euclidean plane by convex…

In this paper, we prove that if a finite number of rectangles, every of which has at least one integer side, perfectly tile a big rectangle then there exists a strategy which reduces the number of these tiles (rectangles) without violating…

A theorem of Ding, Oporowski, Oxley, and Vertigan implies that any sufficiently large twin-free graph contains a large matching, a co-matching, or a half-graph as a semi-induced subgraph. The sizes of these unavoidable patterns are measured…

We propose a new approach to interactive image segmentation based on some properties of a family of quadratic optimization problems related to dominant sets, a well-known graph-theoretic notion of a cluster which generalizes the concept of…

In this paper we will consider an unknown binary image, of which the length of the boundary and the area of the image are given. These two values together contain some information about the general shape of the image. We will study two…

We show that a graph with $n$ vertices and vertex cover of size $k$ has at most $4^k + n$ potential maximal cliques. We also show that for each positive integer $k$, there exists a graph with vertex cover of size $k$, $O(k^2)$ vertices, and…

We establish tight lower and upper bounds on the number of edges in traceable graphs in several classes of dense graphs. A graph is traceable if it has a Hamiltonian path. We show that the bound is: - quadratic for the class of graphs of…

We show why and when optics needs thickness as well as width or area. Wave diffraction explains the fundamental need for area or diameter of a lens or aperture to achieve some resolution or number of pixels in microscopes and cameras. Now…

Superpositions of coherent light waves typically interfere. We present superpositions of up to six plane waves which defy this expectation by having a perfectly homogeneous mean square of the electric field. For many applications in optics…

We give a necessary and sufficient condition on a $d$-dimensional affine subspace of $\mathbb{R}^n$ to be characterized by a finite set of patterns which are forbidden to appear in its digitization. This can also be stated in terms of local…

In this paper, we aim at establishing accurate dense correspondences between a pair of images with overlapping field of view under challenging illumination variation, viewpoint changes, and style differences. Through an extensive ablation…

We seek a practical method for establishing dense correspondences between two images with similar content, but possibly different 3D scenes. One of the challenges in designing such a system is the local scale differences of objects…

We tackle the problem of texture synthesis in the setting where many input images are given and a large-scale output is required. We build on recent generative adversarial networks and propose two extensions in this paper. First, we propose…

Pixel binning is a technique, widely used in optical image acquisition and spectroscopy, in which adjacent detector elements of an image sensor are combined into larger pixels. This reduces the amount of data to be processed as well as the…

Photons offer the potential to carry large amounts of information in their spectral, spatial, and polarisation degrees of freedom. While state-of-the-art classical communication systems routinely aim to maximize this information-carrying…

We investigate linear resonant absorption by a dense ensemble of molecules confined to a subwavelength layer in two geometries: (i) a free-standing film in homogeneous space and (ii) the same film placed at a controlled distance from a…

We study the problems of covering or partitioning a polygon $P$ (possibly with holes) using a minimum number of small pieces, where a small piece is a connected sub-polygon contained in an axis-aligned unit square. For covering, we seek to…

The integration density of photonic integrated circuits has been limited by light coupling between waveguides. Traditional approaches to layout the waveguide with high density are based on refractive index engineering to suppress the light…