Search results for " Geometry"

Salient Spin Images: A Descriptor for 3D Object Recognition

2018

In the last decades a wide range of algorithms have been devoted to recognize 3D free-from objects under real conditions such as occlusions, clutters, rotation, scale and translation. Spin image is one of these algorithms known to be robust to rotation, translation, occlusions up to 70% and clutters up to 60%, but still suffer from scaling, resolution changes and it is time consuming. In this paper we present a novel approach based on spin images, called salient spin images (SSI). This method enhances spin images algorithm based on its limits. Particularly, it decreases significantly the complexity of the algorithm using DoG detector, it shows a higher performance due to the relevant locali…

The yttrium chloride-1,10-phenanthroline interaction: Synthesis and X-ray crystal structure of the complex [Y(OH)(H2O)2(phen)2]2Cl4·2(phen)·MeOH

1991

Abstract Investigations on the reaction between YCl3·H2O and phen (1,10-phenanthroline) led to the isolation of the title compound. The synthesis, IR and X-ray structural characterization are described. The crystal contains centrosymmetric binuclear dications [Y2(phen)4(μ-OH)2(H2O)4]4+, uncoordinated chloride anions, two clathrated phen molecules and a disordered methanol molecule. The yttrium ions are eight-coordinated with square antiprismatic geometry to the nitrogen atoms of two phen molecules, to bridging hydroxyl groups and to two water molecules. The Y ⋯ YI separation in the dimer is 3.651(2)A˚.

Elementary Deformations and the HyperKähler-Quaternionic Kähler Correspondence

2014

The hyperKahler-quaternionic Kahler correspondence constructs quaternionic Kahler metrics from hyperKahler metrics with a rotating circle symmetry. We discuss how this may be interpreted as a combination of the twist construction with the concept of elementary deformation, surveying results of our forthcoming paper. We outline how this leads to a uniqueness statement for the above correspondence and indicate how basic examples of c-map constructions may be realised in this context.

On the geometry of the characteristic class of a star product on a symplectic manifold

2001

The characteristic class of a star product on a symplectic manifold appears as the class of a deformation of a given symplectic connection, as described by Fedosov. In contrast, one usually thinks of the characteristic class of a star product as the class of a deformation of the Poisson structure (as in Kontsevich's work). In this paper, we present, in the symplectic framework, a natural procedure for constructing a star product by directly quantizing a deformation of the symplectic structure. Basically, in Fedosov's recursive formula for the star product with zero characteristic class, we replace the symplectic structure by one of its formal deformations in the parameter $\hbar$. We then s…

Spatio‐temporal classification in point patterns under the presence of clutter

2019

We consider the problem of detection of features in the presence of clutter for spatio-temporal point patterns. In previous studies, related to the spatial context, Kth nearest-neighbor distances to classify points between clutter and features. In particular, a mixture of distributions whose parameters were estimated using an expectation-maximization algorithm. This paper extends this methodology to the spatio-temporal context by considering the properties of the spatio-temporal Kth nearest-neighbor distances. For this purpose, we make use of a couple of spatio-temporal distances, which are based on the Euclidean and the maximum norms. We show close forms for the probability distributions o…

2021

Abstract We prove the existence of a smoothing for a toroidal crossing space under mild assumptions. By linking log structures with infinitesimal deformations, the result receives a very compact form for normal crossing spaces. The main approach is to study log structures that are incoherent on a subspace of codimension 2 and prove a Hodge–de Rham degeneration theorem for such log spaces that also settles a conjecture by Danilov. We show that the homotopy equivalence between Maurer–Cartan solutions and deformations combined with Batalin–Vilkovisky theory can be used to obtain smoothings. The construction of new Calabi–Yau and Fano manifolds as well as Frobenius manifold structures on moduli…

Sharp dimension free quantitative estimates for the Gaussian isoperimetric inequality

2017

We provide a full quantitative version of the Gaussian isoperimetric inequality: the difference between the Gaussian perimeter of a given set and a half-space with the same mass controls the gap between the norms of the corresponding barycenters. In particular, it controls the Gaussian measure of the symmetric difference between the set and the half-space oriented so to have the barycenter in the same direction of the set. Our estimate is independent of the dimension, sharp on the decay rate with respect to the gap and with optimal dependence on the mass.

dglars: An R Package to Estimate Sparse Generalized Linear Models

2014

dglars is a publicly available R package that implements the method proposed in Augugliaro, Mineo, and Wit (2013), developed to study the sparse structure of a generalized linear model. This method, called dgLARS, is based on a differential geometrical extension of the least angle regression method proposed in Efron, Hastie, Johnstone, and Tibshirani (2004). The core of the dglars package consists of two algorithms implemented in Fortran 90 to efficiently compute the solution curve: a predictor-corrector algorithm, proposed in Augugliaro et al. (2013), and a cyclic coordinate descent algorithm, proposed in Augugliaro, Mineo, and Wit (2012). The latter algorithm, as shown here, is significan…

Differential geometric least angle regression: a differential geometric approach to sparse generalized linear models

2013

Summary Sparsity is an essential feature of many contemporary data problems. Remote sensing, various forms of automated screening and other high throughput measurement devices collect a large amount of information, typically about few independent statistical subjects or units. In certain cases it is reasonable to assume that the underlying process generating the data is itself sparse, in the sense that only a few of the measured variables are involved in the process. We propose an explicit method of monotonically decreasing sparsity for outcomes that can be modelled by an exponential family. In our approach we generalize the equiangular condition in a generalized linear model. Although the …

A differential-geometric approach to generalized linear models with grouped predictors

2016

We propose an extension of the differential-geometric least angle regression method to perform sparse group inference in a generalized linear model. An efficient algorithm is proposed to compute the solution curve. The proposed group differential-geometric least angle regression method has important properties that distinguish it from the group lasso. First, its solution curve is based on the invariance properties of a generalized linear model. Second, it adds groups of variables based on a group equiangularity condition, which is shown to be related to score statistics. An adaptive version, which includes weights based on the Kullback-Leibler divergence, improves its variable selection fea…