Mesh Denoising via Adaptive Consistent Neighborhood

In this paper, we propose a novel guided normal filtering followed by vertex updating for mesh denoising. We introduce a two-stage scheme to construct adaptive consistent neighborhoods for guided normal filtering. In the first stage, we newly design a consistency measurement to select a coarse consistent neighborhood for each face in a patch-shift manner. In this step, the selected consistent neighborhoods may still contain some features. Then, a graph-cut based scheme is iteratively performed for constructing different adaptive neighborhoods to match the corresponding local shapes of the mesh. The constructed local neighborhoods in this step, known as the adaptive consistent neighborhoods, can avoid containing any geometric features. By using the constructed adaptive consistent neighborhoods, we compute a more accurate guide normal field to match the underlying surface, which will improve the results of the guide normal filtering. With the help of the adaptive consistent neighborhoods, our guided normal filtering can preserve geometric features well, and is robust against complex shapes of surfaces. Intensive experiments on various meshes show the superiority of our method visually and quantitatively.

Performance of F2 Rice (Oryza sativa L.) Segregants Derived from a Cross the BPT-5204 / IR-64Drt1

The present investigation was carried out with F2 plants from a cross between two parents i.e., BPT-5204 and IR-64Drt1. The selection of parents for crosses was made based on genotypes that were tolerant and susceptible to drought condition. BPT-5204 was drought susceptible and IR-64Drt1 was also tolerant to drought. In this experiment adequate amount of variability was detected for grain yield per plant and its components among 324 segregants evaluated under augmented randomized block design II in normal field condition. The analysis of variance for grain yield and its attributing characters among blocks, treatments, entries, checks and checks vs entries revealed presence of significant variation in the segregants studied. However, with respect to checks, non-significant differences were recorded for only L/B ratio. The results indicated that among 324 rice genotypes including checks, only 9 rice genotypes expressed higher yield compared to seven checks varieties under normal field condition. The segregants S-51, S-122, S-135, S-195, S-199, S-210, S-219, S-222, S-251 were top ranking genotypes with respect to all checks.

Magnetization reduction by varying normal field in stacks of composite superconductors in an electrical motor

Trapped field magnets of superconducting stacks could be an alternative to conventional magnets in electrical machine applications. A conceptual design of an electrical motor using these stacks was proposed in [1,2]. Superconducting stacks offer many advantages; however, they can be demagnetized when exposed to the varying field present in electrical motors during operation. This varying field can be generated by salient magnetic circuit or generated from the armature winding as harmonics. To study this demagnetization effect, we carried out an experiment on a superconducting stack in an electrical machine, exposing it to different levels of varying cross and normal fields. The experimental measurements recorded a demagnetization of the stack. In this work, the analyses of the reduction of magnetization of the superconducting stack by an alternating normal field and the comparison of the results with experimental measurements in the electrical motor are presented.

Robust Mesh Denoising via Triple Sparsity

Mesh denoising is to recover high quality meshes from noisy inputs scanned from the real world. It is a crucial step in geometry processing, computer vision, computer-aided design, etc. Yet, state-of-the-art denoising methods still fall short of handling meshes containing both sharp features and fine details. Besides, some of the methods usually introduce undesired staircase effects in smoothly curved regions. These issues become more severe when a mesh is corrupted by various kinds of noise, including Gaussian, impulsive, and mixed Gaussian–impulsive noise. In this paper, we present a novel optimization method for robustly denoising the mesh. The proposed method is based on a triple sparsity prior: a double sparse prior on first order and second order variations of the face normal field and a sparse prior on the residual face normal field. Numerically, we develop an efficient algorithm based on variable-splitting and augmented Lagrange method to solve the problem. The proposed method can not only effectively recover various features (including sharp features, fine details, smoothly curved regions, etc), but also be robust against different kinds of noise. We testify effectiveness of the proposed method on synthetic meshes and a broad variety of scanned data produced by the laser scanner, Kinect v1, Kinect v2, and Kinect-fusion. Intensive numerical experiments show that our method outperforms all of the compared select-of-the-art methods qualitatively and quantitatively.

Frame and direction mappings for surfaces in ℝ3

We study frames in ℝ3 and mapping from a surface M in ℝ3 to the space of frames. We consider in detail mapping frames determined by a unit tangent principal or asymptotic direction field U and the normal field N. We obtain their generic local singularities as well as the generic singularities of the direction field itself. We show, for instance, that the cross-cap singularities of the principal frame map occur precisely at the intersection points of the parabolic and subparabilic curves of different colours. We study the images of the asymptotic and principal foliations on the unit sphere by their associated unit direction fields. We show that these curves are solutions of certain first order differential equations and point out a duality in the unit sphere between some of their configurations.

A Variational Formulation for the Relativistic Klein-Gordon Equation

This article develops a variational formulation for the relativistic Klein-Gordon equation.The main results are obtained through a connection between classical and quantum mechanics. Such a connection is established through the definition of normal field and its relation with the wave function concept.

Crustal geomagnetic field and secular variation by regional and global models for Austria

Using 12-year-long series of data (2001-2012) from geomagnetic observatories and repeat stations in Austria and its neighboring countries, a regional spatial-temporal (ST) model is developed based on the polynomial expansion consisting of latitude, longitude, and time of the geomagnetic field components and total magnetic field F. Additionally, we have used three different global models (CHAOS-5, POMME-9, and EMM2015), which are built on spherical harmonics up to a maximum degree Lmax and give the core field and crustal field separately. The normal field provided by the ST model and its “model bias”, which comprise the residuals of the differences between measured and predicted values, are calculated and the respective maps are shown. The residuals are considered an estimate of the local crustal field. In the case of global models, we have applied for each of these three methods to calculate the “model bias”: residuals of the differences between observed values and predicted values of the model, residuals of the differences between observed values and core field values of the model, and the average bias for the period 2001-2012. The normal field of the region of Austria provided by each global model is also calculated. Generally, the regional and global models yield relatively similar crustal fields for the Austrian region, especially when the first method is used. The normal fields calculated by them are in good agreement with each other. Each of the global models directly provides the crustal field, and they are compared with the aeromagnetic data provided by aeromagnetic surveys over the Austrian region. The ST model is in better agreement with aeromagnetic data. We have also analyzed the secular variation over the region, which is calculated from the rate of change of normal field given by the ST and global models.

Normal Calculus on Moving Surfaces

This paper presents an extension for principles of Differential Geometry on Surfaces (re-hashed through the budding field of CMS, the Calculus of Moving Surfaces). It analyzes mostly 2D Hypersurfaces with Riemannian Geometry and proposes the construction of a 3D Static Frame combining the Surface Basis Vectors with the Orthogonal Normal Field as a 3D Orthogonal Vector Frame. The paper introduces conventions for manipulating Tensors defined using this 3D Orthogonal Vector Frame as well as Curvature Connections associated with this Vector Frame. It then finally introduces Symbols and Tensors to describe Inner Products and Variance within the 3D Vector Frame and then extends all the above concepts to a surface which is Dynamic utilizing principles from CMS. This formulation has potential to extend identities and concepts from CMS and from Differential Geometry in a compact Tensorial Framework, which agrees with the new Framework proposed by CMS.