A simplicial arrangement of pseudolines is a collection of topological lines in the projective plane where each region that is formed is triangular. This paper refines and develops David Eppstein’s notion of a kaleidoscope construction for symmetric pseudoline arrangements to construct and analyze several infinite families of simplicial pseudoline arrangements with high degrees of geometric sym...

We describe a linear-time algorithm that finds a planar drawing of every graph of a simple line or pseudoline arrangement within a grid of area O(n). No known input causes our algorithm to use area Ω(n ) for any > 0; finding such an input would represent significant progress on the famous k-set problem from discrete geometry. Drawing line arrangement graphs is the main task in the Planarity puz...

Given a line arrangement A with n lines, we show that there exists a path of length n/3−O(n) in the dual graph of A formed by its faces. This bound is tight up to lower order terms. For the bicolored version, we describe an example of a line arrangement with 3k blue and 2k red lines with no alternating path longer than 14k. Further, we show that any line arrangement with n lines has a coloring ...

The realizability problem for rank 3 oriented matroids (see [1]) is equivalent to the pseudoline stretchability problem (see [4]). This paper uses an example to illustrate a new approach to this problem. The main theorem of this paper, like the trigonometric form of Ceva’s theorem, shows a non-trivial relationship amongst the angles in a specific line arrangement figure (c). We work in polar co...

In this paper, we present a method of camera-based document image retrieval for heterogeneous-content document using a multi-layer separating approach. We use Locally Likely Arrangement Hashing (LLAH) extracting text features on the layer which contains text. In addition, we employ a technique of reducing the memory required for storing the hash table. Experiment result show that our approach i...

Object identification using Scale-Invariant Feature Transform (SIFT) keypoints requires stable keypoint signatures that can be reliably reproduced across variations in lighting, viewing angle, as well as camera imaging characteristics. While reproducibility has been demonstrated under various lighting and viewing angles elsewhere, this work performs an empirical evaluation of the reproducibilit...

We present a technique for camera calibration and Euclidean reconstruction from multiple images of the same scene. Unlike standard Tsai's camera calibration from a known scene, we exploited controlled known motions of the camera to obtain its calibration and Euclidean reconstruction without any knowledge about the scene. We consider three linearly independent translations of an uncalibrated cam...

We present our efforts towards a multi-camera mouse-replacement system for computer users with severe motion impairments. We have worked with individuals with cerebral palsy or multiple sclerosis who use a publiclyavailable interface that tracks the user’s head movements with a single video camera and translates them into mouse pointer coordinates on the screen. To address the problem that the ...