Topological segmentation in three-dimensional vector fields

We present a new method for topological segmentation in steady three-dimensional vector fields. Depending on desired properties, the algorithm replaces the original vector field by a derived segmented data set, which is utilized to produce separating surfaces in the vector field. We define the concept of a segmented data set, develop methods that produce the segmented data by sampling the vector field with streamlines, and describe algorithms that generate the separating surfaces. This method is applied to generate local separatrices in the field, defined by a movable boundary region placed in the field. The resulting partitions can be visualized using standard techniques for a visualization of a vector field at a higher level of abstraction.     

Orthogonal decompositions of 2-D nonhomogeneous discrete random fields

Imposing atotal-order on a two-dimensional (2-D) discrete random field induces an orthogonal decomposition of the random field into two components: Apurely-indeterministic field and adeterministic one. The purely-indeterministic component is shown to have a 2-D white-innovations driven moving-average representation. The 2-D deterministic random field can be perfectly predicted from the field's past with respect to the imposed total-order definition. The deterministic field is further orthogonally decomposed into anevanescent field, and aremote past field. The evanescent field is generated by the columnto-column innovations of the deterministic field with respect to the imposed nonsymmetrical-half-plane total-ordering definition. The presented decomposition can be obtained with respect to any nonsymmetrical-half-plane total-ordering definition, for which the nonsymmetrical-half-plane boundary line has rational slope.     

Learning occlusion-aware view synthesis for light fields

Pattern Analysis and Applications - We present a novel learning-based approach to synthesize new views of a light field image. In particular, given the four corner views of a light field, the...     

Dynamic harmonic fields for surface processing

Harmonic fields have been shown to provide effective guidance for a number of geometry processing problems. In this paper, we propose a method for fast updating of harmonic fields defined on polygonal meshes, enabling real-time insertion and deletion of constraints. Our approach utilizes the penalty method to enforce constraints in harmonic field computation. It maintains the symmetry of the Laplacian system and takes advantage of fast multi-rank updating and downdating of Cholesky factorization, achieving both speed and numerical stability. We demonstrate how the interactivity induced by fast harmonic field update can be utilized in several applications, including harmonic-guided quadrilateral remeshing, vector field design, interactive geometric detail modeling, and handle-driven shape editing and animation transfer with a dynamic handle set.     

Representing higher-order singularities in vector fields on piecewise linear surfaces

Accurately representing higher-order singularities of vector fields defined on piecewise linear surfaces is a non-trivial problem. In this work, we introduce a concise yet complete interpolation scheme of vector fields on arbitrary triangulated surfaces. The scheme enables arbitrary singularities to be represented at vertices. The representation can be considered as a facet-based "encoding" of vector fields on piecewise linear surfaces. The vector field is described in polar coordinates over each facet, with a facet edge being chosen as the reference to define the angle. An integer called the period jump is associated to each edge of the triangulation to remove the ambiguity when interpolating the direction of the vector field between two facets that share an edge. To interpolate the vector field, we first linearly interpolate the angle of rotation of the vectors along the edges of the facet graph. Then. we use a variant of Nielson's side-vertex scheme to interpolate the vector field over the entire surface. With our representation, we remove the bound imposed on the complexity of singularities that a vertex can represent by its connectivity. This bound is a limitation generally exists in vertex-based linear schemes. Furthermore, using our data structure, the index of a vertex of a vector field can be combinatorily determined. We show the simplicity of the interpolation scheme with a GPU-accelerated algorithm for a LIC-based visualization of the so-defined vector fields, operating in image space. We demonstrate the algorithm applied to various vector fields on curved surfaces.     

Topology-preserving smoothing of vector fields

Proposes a technique for topology-preserving smoothing of sampled vector fields. The vector field data is first converted into a scalar representation in which time surfaces implicitly exist as level sets. We then locally analyze the dynamic behavior of the level sets by placing geometric primitives in the scalar field and by subsequently distorting these primitives with respect to local variations in this field. From the distorted primitives, we calculate the curvature normal and we use the normal magnitude and its direction to separate distinct flow features. Geometrical and topological considerations are then combined to successively smooth dense flow fields, at the same time retaining their topological structure     

Efficient Bayesian spatial prediction with mobile sensor networks using Gaussian Markov random fields

In this paper, we consider the problem of predicting a large scale spatial field using successive noisy measurements obtained by mobile sensing agents. The physical spatial field of interest is discretized and modeled by a Gaussian Markov random field (GMRF) with uncertain hyperparameters. From a Bayesian perspective, we design a sequential prediction algorithm to exactly compute the predictive inference of the random field. The main advantages of the proposed algorithm are: (1) the computational efficiency due to the sparse structure of the precision matrix, and (2) the scalability as the number of measurements increases. Thus, the prediction algorithm correctly takes into account the uncertainty in hyperparameters in a Bayesian way and is also scalable to be usable for mobile sensor networks with limited resources. We also present a distributed version of the prediction algorithm for a special case. An adaptive sampling strategy is presented for mobile sensing agents to find the most informative locations in taking future measurements in order to minimize the prediction error and the uncertainty in hyperparameters simultaneously. The effectiveness of the proposed algorithms is illustrated by numerical experiments.     

Simulation of lognormal random fields with varying resolution scale and local average for Darcy flow

The paper presents a new method for generating isotropic realizations of a random field with varying resolution scales and local block averages in one, two, or three dimensions. The random field has a lognormal distribution as found for the hydraulic conductivity in Darcy's flow in hydrology. We also present a fast method for generating anisotropic realizations of aGaussian random field using superposition of harmonic modes. Both methods are implemented in a software package which is presented. The realizations of the rescaled random field are made up ofupscaled local averages of the underlying random field which are consistentwith the level of resolution and which can be conditioned. The approach is motivated by the need to represent engineering properties aslocal averages and to be able to easily condition the realizations to incorporate known data or to change the resolution within sub-regions. The numerical results show that the method is very efficient computationally.     

Rendering deformable surface reflectance fields

Animation of photorealistic computer graphics models is an important goal for many applications. Image-based modeling has emerged as a promising approach to capture and visualize real-world objects. Animating image-based models, however, is still a largely unsolved problem. In this paper, we extend a popular image-based representation called surface reflectance field to animate and render deformable real-world objects under arbitrary illumination. Deforming the surface reflectance field is achieved by modifying the underlying impostor geometry. We augment the impostor by a local parameterization that allows the correct evaluation of acquired reflectance images, preserving the original light model on the deformed surface. We present a deferred shading scheme to handle the increased amount of data involved in shading the deformable surface reflectance field. We show animations of various objects that were acquired with 3D photography.     

Electric and magnetic fields in photoalignment of liquid crystals

The results of investigation of slow surface dynamics (easy axis gliding), induced by secondary illumination of photoaligned substrates with linearly polarized UV or blue light in the presence of electric (magnetic) fields, are presented for the first time. The initial surface orientation of nematic liquid crystal (NLC) was provided, in accordance with the standard photoalignment technique, via preliminary UV treatment of the glass substrates coated by sulfonic azo‐dye SD1 film. The experiments fulfilled for the two geometries, A and B, corresponding to the normal (A) and parallel (B) orientation of fields relatively to liquid crystal (LC) layer, revealed different effects induced by electric (magnetic) fields. For geometry A, strong electric field applied, in combination with a linearly polarized blue light, to the planar layer in a sandwich‐like LC cell with two photoaligned substrates results in simultaneous reorientation of easy axis on both substrates. It demonstrates the possibility of an azimuthal rotation of monodomain planar samples of LCs. For geometry B, usage of “in‐plane” electric (magnetic) fields in the cell, composed of photoaligned and rubbed substrates, speeds up reorientation process of NLC easy axis respectively to pure light‐induced reorientation. It provides electric control of operating times in previously proposed optical rewritable technology.     

Algorithms for solving linear systems over cyclotomic fields

We consider the problem of solving a linear system Ax=b$Ax=b$ over a cyclotomic field. Cyclotomic fields are special in that we can easily find a prime p$p$ for which the minimal polynomial m(z)$m\left(z\right)$ for the field factors into a product of distinct linear factors. This makes it possible to develop fast modular algorithms.     

Computing oriented texture fields

The first step is the analysis of oriented texture consists of the extraction of an orientation field. The orientation field is comprised of the angle and coherence images, which describe at each point the dominant local orientation and degree of anisotropy, respectively. A new algorithm for computing the orientation field for a flow-like texture is presented. The basic idea behind the algorithm is to use an oriented filter, namely the gradient of Gaussian, and perform manipulations on the resulting gradient vector field. The most important aspect of the new algorithm is that it is provably optimal in estimating the local orientation of an oriented texture. An added strength of the algorithm is that it is simpler and has a better signal-to-noise ratio than previous approaches, because it employs fewer derivative operations. We also propose a new measure of coherence, which works better than previous measures. The estimates for orientation and coherence are related to measures in the statistical theory of directional data. We advocate the use of the angle and coherence images as intrinsic images. An analysis of oriented textures will require the computation of these intrinsic images as a first step. In this sense, the computation of the orientation field, resulting in the intrinsic images, is indispensible in the analysis of oriented textures. We provide results from several experiments to indicate the usefulness of the angle and coherence intrinsic images. These results show that the notion of scale plays an important role in the interpretation of textures. Further, measures defined on these intrinsic images are useful for the inspection of surfaces.     

光场显著性检测研究综述

显著性检测一直是计算机视觉领域的关键问题,在视觉跟踪、图像压缩和目标识别等方面有着非常重要的应用。基于传统RGB图像和RGB-D （RGB depth）图像的显著性检测易受复杂背景、光照、遮挡等因素影响,在复杂场景的检测精度较低,鲁棒的显著性检测仍存在很大挑战。随着光场成像技术的发展,人们开始从新的途径解决显著性检测问题。光场数据记录着空间光线位置信息和方向信息,隐含场景的几何结构,能为显著性检测提供可靠的背景、深度等先验信息。因此,利用光场数据进行显著性检测得到了广泛关注,成为研究热点。尽管基于光场数据的显著性检测算法陆续出现,但是缺少对该问题的深刻理解以及研究进展的全面综述。本文系统地综述了基于光场数据的显著性检测研究现状,并进行深入探讨和展望。对光场理论以及用于光场显著性检测的公共数据集进行介绍;系统地介绍了光场显著性检测领域的算法模型和最新进展,从人工设计光场特征、稀疏编码特征和深度学习特征等方面进行全面阐述及分析;通过4个公共光场显著性数据集上的实验数据对不同方法的优缺点进行比较和分析,并结合实际应用指出当前研究的局限性与发展趋势。     

Information extraction from calls for papers with conditional random fields and layout features

For members of the research community it is vital to stay informed about conferences, workshops, and other research meetings relevant to their field. These events are typically announced in calls for papers (CFPs) that are distributed via mailing lists. We employ Conditional Random Fields for the task of extracting key information such as conference names, titles, dates, locations and submission deadlines from CFPs. Extracting this information from CFPs automatically has applications in building automated conference calendars and search engines for CFPs. We combine a variety of features, including generic token classes, domain-specific dictionaries and layout features. Layout features prove particularly useful in the absence of grammatical structure, improving average F1 by 30% in our experiments.     

Detecting stress fields in an optimal structure Part II: Three-dimensional case

This paper is the second part of an investigation on stress fields in an optimal elastic structure. In the first part of this research, Cherkaev and Kucuk (2001), we derived the necessary conditions for the stress field in optimal two-dimensional elastic structures and introduced a method to check whether a structure is optimal. In this paper, we turn our attention to conditions of the stress field in optimal three-dimensional elastic structures. We restate the necessary conditions for minimization of the stress energy for three-dimensional elasticity. We also show that the conditions are realized in optimal microstructures.     

Spatial and field resolution of wire-wound fluxgates in magnetic dipole fields

We have enhanced the field and the spatial resolution of fluxgate magnetometers to measure magnetic dipole fields. With finite element simulations, we studied the flux distribution in the racetrack shaped core of a reference fluxgate magnetometer that was optimized for low noise performance in homogeneous fields. The influence of core length and thickness on the spatial and the field resolution was analyzed. The simulation was used to optimize the size and the location of the detection coil. The performance of new fabricated fluxgates was measured in homogeneous fields and compared with their measurement capabilities in dipole fields. Parameters of interest were the sideband detection signal, the signal-to-noise ratio, the detection limit and the spatial resolution by means of the point spread function. Despite higher noise levels in homogeneous fields, it was found that the field and the spatial resolution in dipole fields can be improved by optimizing the geometry of the core and the detection coil, but both parameters cannot be optimized independently.     

Unsupervised image segmentation using triplet Markov fields

Hidden Markov fields (HMF) models are widely applied to various problems arising in image processing. In these models, the hidden process of interest X is a Markov field and must be estimated from its observable noisy version Y. The success of HMF is mainly due to the fact that the conditional probability distribution of the hidden process with respect to the observed one remains Markovian, which facilitates different processing strategies such as Bayesian restoration. HMF have been recently generalized to “pairwise” Markov fields (PMF), which offer similar processing advantages and superior modeling capabilities. In PMF one directly assumes the Markovianity of the pair (X, Y). Afterwards, “triplet” Markov fields (TMF), in which the distribution of the pair (X, Y) is the marginal distribution of a Markov field (X, U, Y), where U is an auxiliary process, have been proposed and still allow restoration processing. The aim of this paper is to propose a new parameter estimation method adapted to TMF, and to study the corresponding unsupervised image segmentation methods. The latter are validated via experiments and real image processing.     

Computational Schlieren Photography with Light Field Probes

We introduce a new approach to capturing refraction in transparent media, which we call light field background oriented Schlieren photography. By optically coding the locations and directions of light rays emerging from a light field probe, we can capture changes of the refractive index field between the probe and a camera or an observer. Our prototype capture setup consists of inexpensive off-the-shelf hardware, including inkjet-printed transparencies, lenslet arrays, and a conventional camera. By carefully encoding the color and intensity variations of 4D light field probes, we show how to code both spatial and angular information of refractive phenomena. Such coding schemes are demonstrated to allow for a new, single image approach to reconstructing transparent surfaces, such as thin solids or surfaces of fluids. The captured visual information is used to reconstruct refractive surface normals and a sparse set of control points independently from a single photograph.     

Orientation of anisotropic random fields and images

Random field models are often used for characterizing two-dimensional data, i.e. images. Commonly, they exhibit some orientational variability, but, unlike one-dimensional random processes, are lacking in any obvious causality direction. This paper describes how their orientation may be recognized.