UPGMpp: a Software Library for Contextual Object Recognition

Object recognition is a cornerstone task towards the scene understanding problem. Recent works in the field boost their perfor- mance by incorporating contextual information to the traditional use of the objects’ geometry and/or appearance. These contextual cues are usually modeled through Conditional Random Fields (CRFs), a partic- ular type of undirected Probabilistic Graphical Model (PGM), and are exploited by means of probabilistic inference methods. In this work we present the Undirected Probabilistic Graphical Models in C++ library (UPGMpp), an open source solution for representing, training, and per- forming inference over undirected PGMs in general, and CRFs in par- ticular. The UPGMpp library supposes a reliable and comprehensive workbench for recognition systems exploiting contextual information, in- cluding a variety of inference methods based on local search, graph cuts, and message passing approaches. This paper illustrates the virtues of the library, i.e. it is efficient, comprehensive, versatile, and easy to use, by presenting a use-case applied to the object recognition problem in home scenes from the challenging NYU2 dataset.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. Spanish grant program FPU-MICINN 2010 and the Spanish projects “TAROTH: New developments toward a robot at home” (Ref. DPI2011-25483) and “PROMOVE: Advances in mobile robotics for promoting independent life of elders” (Ref. DPI2014-55826-R

Auditing the Numeracy Demands of the Middle Years Curriculum

The National Numeracy Review Report recognized that numeracy development requires an across the curriculum commitment. To explore the nature of this commitment we conducted a numeracy audit of the South Australian Middle Years curriculum, using a numeracy model that incorporates mathematical knowledge, dispositions, tools, contexts, and a critical orientation. All learning areas in the published curriculum were found to have distinctive numeracy demands. The audit should encourage teachers to promote numeracy in even richer ways in the curriculum they enact with students

Vanishingly Sparse Matrices and Expander Graphs, With Application to Compressed Sensing

We revisit the probabilistic construction of sparse random matrices where each column has a fixed number of nonzeros whose row indices are drawn uniformly at random with replacement. These matrices have a one-to-one correspondence with the adjacency matrices of fixed left degree expander graphs. We present formulae for the expected cardinality of the set of neighbors for these graphs, and present tail bounds on the probability that this cardinality will be less than the expected value. Deducible from these bounds are similar bounds for the expansion of the graph which is of interest in many applications. These bounds are derived through a more detailed analysis of collisions in unions of sets. Key to this analysis is a novel {\em dyadic splitting} technique. The analysis led to the derivation of better order constants that allow for quantitative theorems on existence of lossless expander graphs and hence the sparse random matrices we consider and also quantitative compressed sensing sampling theorems when using sparse non mean-zero measurement matrices.Comment: 17 pages, 12 Postscript figure