Binary Adaptive Semi-Global Matching Based on Image Edges

Image-based modeling and rendering is currently one of the most challenging topics in Computer Vision and Photogrammetry. The key issue here is building a set of dense correspondence points between two images, namely dense matching or stereo matching. Among all dense matching algorithms, Semi-Global Matching (SGM) is arguably one of the most promising algorithms for real-time stereo vision. Compared with global matching algorithms, SGM aggregates matching cost from several (eight or sixteen) directions rather than only the epipolar line using Dynamic Programming (DP). Thus, SGM eliminates the classical “streaking problem” and greatly improves its accuracy and efficiency. In this paper, we aim at further improvement of SGM accuracy without increasing the computational cost. We propose setting the penalty parameters adaptively according to image edges extracted by edge detectors. We have carried out experiments on the standard Middlebury stereo dataset and evaluated the performance of our modified method with the ground truth. The results have shown a noticeable accuracy improvement compared with the results using fixed penalty parameters while the runtime computational cost was not increased

K-5 Educators\u27 Perceptions of the Role of Speech Language Pathologists

Rarely is a school-based speech language pathologist (SLP) thought of as an active contributor to the achievement of students or to the learning community in general. Researchers have found benefits for students when members of the learning community collaborate, and the SLP should be a part of this community collaboration. This qualitative case study examined elementary school teachers\u27, administrators\u27, and reading specialists\u27 perspectives related to knowledge of and the inclusion of the SLP in the learning community at a local elementary school in central Georgia. Schon\u27s theory of reflective practice and Coleman\u27s theory of social capital provided the conceptual framework. Via an open-ended questionnaire and intensive interviews, 8 educators with 3 or more years of experience in 1 of the K-5 elementary schools in this local community provided data for this study. Data were recorded, transcribed, and analyzed through inductive methods using open and axial coding with thematic analysis. The results of the study showed 4 common themes that the participants felt were important. These themes included the fact that teachers understood the SLP to be a resource, but were unsure how to access their specialty; teachers and SLPs needed allotted time to work together; teachers and SLPs needed to communicate frequently; and teachers desired more knowledge of the SLP\u27s role in the educational setting. Important implications for social change in elementary school learning communities include increasing involvement of the SLP, promoting SLP involvement in the identification of at-risk students, increasing educator awareness of the SLP\u27s benefit, and increasing collaboration between SLPs and educators promoted through a 3-day professional learning project

More Torsion in the Homology of the Matching Complex

A matching on a set $X$ is a collection of pairwise disjoint subsets of $X$ of size two. Using computers, we analyze the integral homology of the matching complex $M_n$, which is the simplicial complex of matchings on the set $\{1, >..., n\}$. The main result is the detection of elements of order $p$ in the homology for $p \in \{5,7,11,13\}$. Specifically, we show that there are elements of order 5 in the homology of $M_n$ for $n \ge 18$ and for $n \in {14,16}$. The only previously known value was $n = 14$, and in this particular case we have a new computer-free proof. Moreover, we show that there are elements of order 7 in the homology of $M_n$ for all odd $n$ between 23 and 41 and for $n=30$. In addition, there are elements of order 11 in the homology of $M_{47}$ and elements of order 13 in the homology of $M_{62}$. Finally, we compute the ranks of the Sylow 3- and 5-subgroups of the torsion part of $H_d(M_n;Z)$ for $13 \le n \le 16$; a complete description of the homology already exists for $n \le 12$. To prove the results, we use a representation-theoretic approach, examining subcomplexes of the chain complex of $M_n$ obtained by letting certain groups act on the chain complex.Comment: 35 pages, 10 figure

Schrijver graphs and projective quadrangulations

In a recent paper [J. Combin. Theory Ser. B}, 113 (2015), pp. 1-17], the authors have extended the concept of quadrangulation of a surface to higher dimension, and showed that every quadrangulation of the $n$-dimensional projective space $P^n$ is at least $(n+2)$-chromatic, unless it is bipartite. They conjectured that for any integers $k\geq 1$ and $n\geq 2k+1$, the Schrijver graph $SG(n,k)$ contains a spanning subgraph which is a quadrangulation of $P^{n-2k}$. The purpose of this paper is to prove the conjecture

Dualities in persistent (co)homology

We consider sequences of absolute and relative homology and cohomology groups that arise naturally for a filtered cell complex. We establish algebraic relationships between their persistence modules, and show that they contain equivalent information. We explain how one can use the existing algorithm for persistent homology to process any of the four modules, and relate it to a recently introduced persistent cohomology algorithm. We present experimental evidence for the practical efficiency of the latter algorithm.Comment: 16 pages, 3 figures, submitted to the Inverse Problems special issue on Topological Data Analysi

On the Expansions in Spin Foam Cosmology

We discuss the expansions used in spin foam cosmology. We point out that already at the one vertex level arbitrarily complicated amplitudes contribute, and discuss the geometric asymptotics of the five simplest ones. We discuss what type of consistency conditions would be required to control the expansion. We show that the factorisation of the amplitude originally considered is best interpreted in topological terms. We then consider the next higher term in the graph expansion. We demonstrate the tension between the truncation to small graphs and going to the homogeneous sector, and conclude that it is necessary to truncate the dynamics as well.Comment: 17 pages, 4 figures, published versio

Quantum statistics on graphs

Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph, concentrating on the simplest case of abelian statistics for two particles. In spite of the fact that graphs are locally one-dimensional, anyon statistics emerge in a generalized form. A given graph may support a family of independent anyon phases associated with topologically inequivalent exchange processes. In addition, for sufficiently complex graphs, there appear new discrete-valued phases. Our analysis is simplified by considering combinatorial rather than metric graphs -- equivalently, a many-particle tight-binding model. The results demonstrate that graphs provide an arena in which to study new manifestations of quantum statistics. Possible applications include topological quantum computing, topological insulators, the fractional quantum Hall effect, superconductivity and molecular physics.Comment: 21 pages, 6 figure

On globally non-trivial almost-commutative manifolds

Within the framework of Connes' noncommutative geometry, we define and study globally non-trivial (or topologically non-trivial) almost-commutative manifolds. In particular, we focus on those almost-commutative manifolds that lead to a description of a (classical) gauge theory on the underlying base manifold. Such an almost-commutative manifold is described in terms of a 'principal module', which we build from a principal fibre bundle and a finite spectral triple. We also define the purely algebraic notion of 'gauge modules', and show that this yields a proper subclass of the principal modules. We describe how a principal module leads to the description of a gauge theory, and we provide two basic yet illustrative examples.Comment: 34 pages, minor revision

Inverse monoids and immersions of 2-complexes

It is well known that under mild conditions on a connected topological space $\mathcal X$, connected covers of $\mathcal X$ may be classified via conjugacy classes of subgroups of the fundamental group of $\mathcal X$. In this paper, we extend these results to the study of immersions into 2-dimensional CW-complexes. An immersion $f : {\mathcal D} \rightarrow \mathcal C$ between CW-complexes is a cellular map such that each point $y \in {\mathcal D}$ has a neighborhood $U$ that is mapped homeomorphically onto $f(U)$ by $f$. In order to classify immersions into a 2-dimensional CW-complex $\mathcal C$, we need to replace the fundamental group of $\mathcal C$ by an appropriate inverse monoid. We show how conjugacy classes of the closed inverse submonoids of this inverse monoid may be used to classify connected immersions into the complex