Matching Structures by Computing Minimal Paths on a Manifold

The general problem of matching structures is very pervasive in computer vision and image processing. The research presented here tackles the problem of object matching in a very general perspective. It is formulated for the matching of surfaces. It applies to objects having small or large deformation and arbitrary topological changes. The process described hinges on a geodesic distance equation for a family of curves or surfaces embedded in the graph of a cost function. This geometrical approach to object matching has the advantage that the similarity criterion can be used to define the shape of the cost function. Matching paths are computed on the cost manifolds using distance maps. These distance maps are generated by solving a general partial differential equation which is a generalization of the geodesic distance evolution scheme introduced by R. Kimmel, A. Amir, and A. F. Bruckstein (1995, IEEE Trans. Pattern Anal. Mach. Intell.17, 635–640). An Eulerian level-set formulation is also introduced, leading to a numerical scheme used for solving partial differential equations originating from hyperbolic conservation laws, which has proven to be very robust and stable.     

Numerical method for the solution of the transient behavior of bipolar semiconductor devices

A numerical technique is presented which permits a computer solution of the complete set of time dependent partial differential equations governing bipolar semiconductor behavior. The scheme does not require any of the often made assumptions and approximations such as abrupt junctions, quasi-neutrality or restricted injection levels. The resulting solution describes device terminal properties and gives a detailed account of internal parameters as a function of time and distance.The present method is distinguished from others by the use of the technique of quasilinearization which converts the nonlinear boundary value problem into a linear form. The latter is solved iteratively, yielding highly stable and convergent solutions. The method uses the complete form of Poisson's equation and an implicit time advancement formulation to generate a stable time trajectory of the solution. The Scharfetter-Gummel spatial discretization scheme is used for greater accuracy.Computer and experimental results are given and compared for the transient behavior of a p⁺nn⁺ diode structure. Both forward and reverse transients are described.     

隐式曲面两相图像分割的变分水平集模型及对偶方法

本文对曲面上分段常值和分段光滑的两相图像分割的变分水平集模型及其对偶方法进行了研究.图像所在的曲面用静态的符号距离函数的零水平集表达,曲面上图像分割轮廓线用另一动态符号距离函数的零水平集与上述静态的零水平集的交线表达,借助内蕴梯度、内蕴散度的概念平面两相图像分割的变分水平集模型已被推广到隐式曲面上图像分割的变分模型.本...     

Mathematical representation of 2D image boundary contour using fractional implicit polynomial

Implicit polynomial (IP) fitting is an effective method to quickly represent two-dimensional (2D) image boundary contour in the form of mathematical function. Under the same maximum degree, the fractional implicit polynomial (FIP) can express more curve details than IP and has obvious advantages for the representation of complex boundary contours. In existing studies, algebraic distance is mainly used as the fitting objective of the polynomial. Although the time cost is reduced, there are problems of low fitting accuracy and spurious zero set. In this paper, we propose a two-stage neural network with differentiable geometric distance, which uses FIP to achieve mathematical representation, called TSEncoder. In the first stage, the continuity constraint is used to obtain a rough outline of the fitting target. In the second stage, differentiable geometric distance is gradually added to fine-tune the polynomial coefficients to obtain a contour representation with higher accuracy. Experimental results show that TSEncoder can achieve mathematical representation of 2D image boundary contour with high accuracy.     

Pulmonary Lobe Segmentation in CT Examinations Using Implicit Surface Fitting

Lobe identification in computed tomography (CT) examinations is often an important consideration during the diagnostic process as well as during treatment planning because of their relative independence of each other in terms of anatomy and function. In this paper, we present a new automated scheme for segmenting lung lobes depicted on 3-D CT examinations. The unique characteristic of this scheme is the representation of fissures in the form of implicit functions using Radial Basis Functions (RBFs), capable of seamlessly interpolating “holes” in the detected fissures and smoothly extrapolating the fissure surfaces to the lung boundaries resulting in a “natural” segmentation of lung lobes. A previously developed statistically based approach is used to detect pulmonary fissures and the constraint points for implicit surface fitting are selected from detected fissure surfaces in a greedy manner to improve fitting efficiency. In a preliminary assessment study, lobe segmentation results of 65 chest CT examinations, five of which were reconstructed with three section thicknesses of 0.625 mm, 1.25 mm, and 2.5 mm, were subjectively and independently evaluated by two experienced chest radiologists using a five category rating scale (i.e., excellent, good, fair, poor, and unacceptable). Thirty-three of 65 examinations (50.8%) with a section thickness of 0.625 mm were rated as either “excellent” or “good” by both radiologists and only one case (1.5%) was rated by both radiologists as “poor” or “unacceptable.” Comparable performance was obtained with a slice thickness of 1.25 mm, but substantial performance deterioration occurred in examinations with a section thickness of 2.5 mm. The advantages of this scheme are its full automation, relative insensitivity to fissure completeness, and ease of implementation.      

Using SAX representation for human action recognition

Human action recognition is an important problem in Computer Vision. Although most of the existing solutions provide good accuracy results, the methods are often overly complex and computationally expensive, hindering practical application. In this regard, we introduce Symbolic Aggregate approximation (SAX) to address the problem of human action recognition. Given motion trajectories of reference points on an actor, SAX efficiently converts this time-series data to a symbolic representation. Moreover, the distance between two time series is approximated by the distance between their SAX representation, which is straight-forward and very simple. Requiring only trajectories of reference points, our method requires neither structure recovery nor silhouette extraction. The proposed method is validated on two public datasets. It has an accuracy comparable to related works and it performs well even in varying conditions, in addition to being faster compared to the existing methods.     

基于手绘的3D概念模型建模

以笔画为基础,使用变分隐式曲面方法,构造形式自由的3D模型。文中描述了建模的具体步骤,并讨论了每一步骤中需要注意的问题,设计出了可以进行自由绘制的程序。程序运行结果表明,使用变分隐式曲面绘制的模型具有光滑、封闭的特性,而且可以方便地进行融合和其他后续操作。     

Moment characterization of phase noise in coherent optical systems

The statistical characterization of the phase noise introduced by a semiconductor laser in a coherent optical transmission system is a key problem in the system performance evaluation. The authors consider the moment characterization, of the complex random process. Starting from the implicit representation of the probability density function through the Fokker-Planck equation, the authors obtain closed form analytical expressions for the moments of the filtered phase noise both in stationary and nonstationary conditions. Then the use of the moments for the computation of probability densities through orthogonal polynomial series expansion and maximum entropy approach is considered in application examples     

Slow-Polishing Iodine-Based Etchant for CdTe and CdZnTe Single Crystals

We report on new etching solutions for treatment of CdTe and CdZnTe surfaces based on the iodine-emerging etchant composition KIO₃–KI–citric acid (C₆H₈O₇). CdTe samples with (111), (110), and (100) orientations, and also Cd_1?x Zn _x Te (x?=?0.04, 0.1) samples with (111), (110), (100), and (211) orientations were investigated. The dissolution rate was determined as a function of solution composition, etchant storage time, disc rotation speed, and temperature. It was established that this chemical dissolution is diffusion controlled. Study of the chemical composition and structure of (211)B Cd_1?x Zn _x Te surfaces etched under different conditions was carried out. x-Ray photoelectron spectroscopy measurements showed that a stoichiometric surface was achieved after briefly heating the etched surface in a vacuum. Reflection high-energy electron diffraction measurements revealed a high-quality single-crystalline surface layer in samples etched with KIO₃–KI–citric acid solutions as compared with those etched with a bromine–methanol treatment. The etching compositions were shown to be useful for controlled removal of semiconductor material, and also for chemical polishing of CdTe-based surfaces.     

Electromagnetic scattering by an inhomogeneous penetrable material with an embedded resistive sheet

This paper presents the method of moments (mom) formulation for the electromagnetic scattering by an inhomogeneous penetrable material with an embedded resistive sheet. Triangular surface facets and tetrahedral volume cells are used to discretize the scatterer allowing for greater flexibility in the geometric modeling of the material body. The formulation is very general in that it allows for a variety of material configurations : open or closed conducting surfaces, open or closed resistive (thin dielectric) surfaces, solid dielectric/ferrite material volumes, embedded conducting/resistive surfaces in material volumes, and partially embedded conducting/resistive surfaces (cladded materials). Results for a material coated resistive spherical shell and a material propeller blade are presented.     

Region tracking on level-sets methods

Since the work by Osher and Sethian on level-sets algorithms for numerical shape evolutions, this technique has been used for a large number of applications in numerous fields. In medical imaging, this numerical technique has been successfully used, for example, in segmentation and cortex unfolding algorithms. The migration from a Lagrangian implementation to a Eulerian one via implicit representations or level-sets brought some of the main advantages of the technique, i.e., topology independence and stability. This migration means also that the evolution is parametrization free. Therefore, we do not know exactly how each part of the shape is deforming and the point-wise correspondence is lost. In this note we present a technique to numerically track regions on surfaces that are being deformed using the level-sets method. The basic idea is to represent the region of interest as the intersection of two implicit surfaces and then track its deformation from the deformation of these surfaces. This technique then solves one of the main shortcomings of the very useful level-sets approach. Applications include lesion localization in medical images, region tracking in functional MRI (fMRI) visualization, and geometric surface mapping.     

On the Analysis of Cryptographic Assumptions in the Generic Ring Model

The generic ring model considers algorithms that operate on elements of an algebraic ring by performing only the ring operations and without exploiting properties of a given representation of ring elements. It is used to analyze the hardness of computational problems defined over rings. For instance, it is known that breaking RSA is equivalent to factoring in the generic ring model (Aggarwal and Maurer, Eurocrypt 2009). Do hardness results in the generic ring model support the conjecture that solving the considered problem is also hard in the standard model, where elements of ? _n are represented by integers modulo n? We prove in the generic ring model that computing the Jacobi symbol of an integer modulo n is equivalent to factoring. Since there are simple and efficient non-generic algorithms which compute the Jacobi symbol, this provides an example of a natural computational problem which is hard in the generic ring model, but easy to solve if elements of ? _n are given in their standard representation as integers. Thus, a proof in the generic ring model is unfortunately not a very strong indicator for the hardness of a computational problem in the standard model. Despite this negative result, generic hardness results still provide a lower complexity bound for a large class of algorithms, namely all algorithms solving a computational problem independent of a given representation of ring elements. From this point of view, results in the generic ring model are still interesting. Motivated by this fact, we also show that solving the quadratic residuosity problem generically is equivalent to factoring.     

Compression of textured surfaces represented as surfel sets

A method for lossy compression of genus-0 surfaces is presented. Geometry, texture and other surface attributes are incorporated in a unified manner. The input surfaces are represented by surfels (surface elements), i.e., by a set of disks with attributes. Each surfel, with its attribute vector, is optimally mapped onto a sphere in the sense of geodesic distance preservation. The resulting spherical vector-valued function is resampled. Its components are decorrelated by the Karhunen–Loève transform, represented by spherical wavelets and encoded using the zerotree algorithm. Methods for geodesic distance computation on surfel-based surfaces are considered. A novel efficient approach to dense surface flattening/mapping, using rectangular distance matrices, is employed. The distance between each surfel and a set of key-surfels is optimally preserved, leading to greatly improved resolution and eliminating the need for interpolation, that complicates and slows down existing surface unfolding methods. Experimental surfel-based surface compression results demonstrate successful compression at very low bit rates.     

Implicit polynomial representation through a fast fitting error estimation

This paper presents a simple distance estimation for implicit polynomial fitting. It is computed as the height of a simplex built between the point and the surface (i.e., a triangle in 2-D or a tetrahedron in 3-D), which is used as a coarse but reliable estimation of the orthogonal distance. The proposed distance can be described as a function of the coefficients of the implicit polynomial. Moreover, it is differentiable and has a smooth behavior . Hence, it can be used in any gradient-based optimization. In this paper, its use in a Levenberg-Marquardt framework is shown, which is particularly devoted for nonlinear least squares problems. The proposed estimation is a generalization of the gradient-based distance estimation, which is widely used in the literature. Experimental results, both in 2-D and 3-D data sets, are provided. Comparisons with state-of-the-art techniques are presented, showing the advantages of the proposed approach.     

An EBIC equation for solar cells

When an electron beam of a scanning electron microscope (SEM) impinges on an N-P junction, the generation of electron-hole pairs by impact ionization causes a characteristic short circuit current I_SC to flow. The I_SC, i.e. EBIC (electron beam induced current) depends strongly on the configuration used to investigate the cell's response. In this paper we consider the case where the plane of the junction is perpendicular to the surface. An EBIC equation amenable to numerical computations is derived as a function of cell thickness, source depth, surface recombination velocity, diffusion length, and distance of the junction to the beam-cell interaction point for a cell with an ohmic contact at its back surface. It is shown that the EBIC equation presented here is more general and easier to use than those previously reported. The effects of source depth, ohmic contact, and diffusion length on the normalized EBIC characteristic are discussed.     

Equivalent surface impedance of a slot impedance load on the basis of a cavity with an equilateral triangular cross section

The problem of plane-wave excitation of an impedance load on the basis of a slot in an infinite perfectly conducting screen closed from one side by a cavity with an equilateral triangular cross section is considered. The problem is solved by the integral equation method. The numerical solution of the integral equation is performed by the Krylov–Bogolyubov method. For an H-polarized incident wave, the impedance as a function of the slot and cavity sizes and the angle of incidence of a plane wave is calculated.     

三次均匀B样条插值曲线和曲面的矩阵形式

根据三次B样条曲线(CB)的矩阵形式灵活的特点、CB曲线的端点性质和插值曲线在连接点应满足的连续性条件,推导出CB插值(CBI)曲线的矩阵形式,并进一步推广,得到了双CBI曲面的矩阵形式.生成了平面和空间插值曲线、闭合插值曲线和插值面片.与传统方法进行了比较,结果表明,本文方法有较大的优越性和较好的实用价值.     

Study on spectral representation and eigenexpansion based on eigen-operators

The spectral representation and expansion based on eigen-operators were deeply studied.The relations between Green’s function of characteristic differential equation and Hermitian differential and integral operators were given.The inverse relations between Hermitian differential operator and Hermitian integral operator were also studied.The spectral representation of Hermitian differential operators was given.It was also shown that the S-L eigen-equation cannot be used to realize the spectral representations of infinite dimensions in a finite interval.The method is much simpler and clearer than that of Neumann,and has advantages.The eigen-expansion (eigen-decomposition) of the Hermitian integral operator was given,which has the advantages of theoretical generality and comprehensiveness.The incorrect discussion in Wang et al^[2]was correct that it is used to study the representation of characteristic spectrum.The physical and geometric meanings of naming for the long spherical wave function in optimal eigen-expansion were given.     

Adaptive surface extraction from anisotropic volumetric data: contouring on generalized octrees

In this article, we present an algorithm to extract adaptive surfaces from anisotropic volumetric data. For example, this kind of data can be obtained from a set of segmented images from the sampling of an implicit function, or it can be built by using depth images produced by time-of-flight cameras. However, for many applications as geometry modeling, rendering, or finite elements, it is better to use an explicit surface representation. This surface must fit to the geometrical and topological features of the object in order to obtain a good approximation and to avoid topological artifacts. Our algorithm is able to extract adaptive surfaces that accurately approximate the geometry of the original object while minimizing aliasing effects. In addition, our solution is suitable to handle the anisotropy of volumetric representations. In comparison with relevant methods in the state of the art, ours offers a good compromise between mesh quality and precision in the geometrical approximation.