Object Edge Contour Localisation Based on HexBinary Feature Matching

This paper addresses the issue of localising object edge contours in cluttered backgrounds to support robotics tasks such as grasping and manipulation and also to improve the potential perceptual capabilities of robot vision systems. Our approach is based on coarse-to-fine matching of a new recursively constructed hierarchical, dense, edge-localised descriptor, the HexBinary, based on the HexHog descriptor structure first proposed in [1]. Since Binary String image descriptors [2]– [5] require much lower computational resources, but provide similar or even better matching performance than Histogram of Orientated Gradient (HoG) descriptors, we have replaced the HoG base descriptor fields used in HexHog with Binary Strings generated from first and second order polar derivative approximations. The ALOI [6] dataset is used to evaluate the HexBinary descriptors which we demonstrate to achieve a superior performance to that of HexHoG [1] for pose refinement. The validation of our object contour localisation system shows promising results with correctly labelling ~86% of edgel positions and mis-labelling ~3%

Hierarchical testing designs for pattern recognition

We explore the theoretical foundations of a ``twenty questions'' approach to pattern recognition. The object of the analysis is the computational process itself rather than probability distributions (Bayesian inference) or decision boundaries (statistical learning). Our formulation is motivated by applications to scene interpretation in which there are a great many possible explanations for the data, one (``background'') is statistically dominant, and it is imperative to restrict intensive computation to genuinely ambiguous regions. The focus here is then on pattern filtering: Given a large set Y of possible patterns or explanations, narrow down the true one Y to a small (random) subset \hat Y\subsetY of ``detected'' patterns to be subjected to further, more intense, processing. To this end, we consider a family of hypothesis tests for Y\in A versus the nonspecific alternatives Y\in A^c. Each test has null type I error and the candidate sets A\subsetY are arranged in a hierarchy of nested partitions. These tests are then characterized by scope (|A|), power (or type II error) and algorithmic cost. We consider sequential testing strategies in which decisions are made iteratively, based on past outcomes, about which test to perform next and when to stop testing. The set \hat Y is then taken to be the set of patterns that have not been ruled out by the tests performed. The total cost of a strategy is the sum of the ``testing cost'' and the ``postprocessing cost'' (proportional to |\hat Y|) and the corresponding optimization problem is analyzed.Comment: Published at http://dx.doi.org/10.1214/009053605000000174 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Discrete Flavor Symmetry, Dynamical Mass Textures, and Grand Unification

Discrete flavor symmetry is explored for an intrinsic property of mass matrix forms of quarks and leptons. In this paper we investigate the S3 permutation symmetry and derive the general forms of mass matrices in various types of S3 theories. We also exhibit particular realizations of previous ansatze of mass matrices, which have often been applied in the literature to the standard model Yukawa sector. Discrete flavor symmetry is also advantageous for vanishing matrix elements being dynamically generated in the vacuum of scalar potential. This is due to the fact that group operations are discrete. While zero elements themselves do not explain mass hierarchies, we introduce an abelian flavor symmetry. A non-trivial issue is whether successful quantum numbers can be assigned so that they are compatible with other (non-abelian) flavor symmetries. We show typical examples of charge assignments which not only produce hierarchical orders of mass eigenvalues but also prohibit non-renormalizable operators which disturb the hierarchies in first-order estimation. As an explicit application, a flavor model is constructed in grand unification scheme with S3 and U(1) (or Z_N) flavor symmetries.Comment: 40 pages, references adde

Geometric deep learning: going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field

On the Construction of Safe Controllable Regions for Affine Systems with Applications to Robotics

This paper studies the problem of constructing in-block controllable (IBC) regions for affine systems. That is, we are concerned with constructing regions in the state space of affine systems such that all the states in the interior of the region are mutually accessible through the region's interior by applying uniformly bounded inputs. We first show that existing results for checking in-block controllability on given polytopic regions cannot be easily extended to address the question of constructing IBC regions. We then explore the geometry of the problem to provide a computationally efficient algorithm for constructing IBC regions. We also prove the soundness of the algorithm. We then use the proposed algorithm to construct safe speed profiles for different robotic systems, including fully-actuated robots, ground robots modeled as unicycles with acceleration limits, and unmanned aerial vehicles (UAVs). Finally, we present several experimental results on UAVs to verify the effectiveness of the proposed algorithm. For instance, we use the proposed algorithm for real-time collision avoidance for UAVs.Comment: 17 pages, 18 figures, under review for publication in Automatic