Spline based least squares integration for two-dimensional shape or wavefront reconstruction

In this work, we present a novel method to handle two-dimensional shape or wavefront reconstruction from its slopes. The proposed integration method employs splines to fit the measured slope data with piecewise polynomials and uses the analytical polynomial functions to represent the height changes in a lateral spacing with the pre-determined spline coefficients. The linear least squares method is applied to estimate the height or wavefront as a final result. Numerical simulations verify that the proposed method has less algorithm errors than two other existing methods used for comparison. Especially at the boundaries, the proposed method has better performance. The noise influence is studied by adding white Gaussian noise to the slope data. Experimental data from phase measuring deflectometry are tested to demonstrate the feasibility of the new method in a practical measurement.     

Shape reconstruction from gradient data in an arbitrarily-shaped aperture by iterative discrete cosine transforms in Southwell configuration

The shape reconstruction from gradient data is a common problem in many slope-based metrology applications. In practice, the gradient data may not be ideally available for the whole field of view as expected, due to the aperture or the unmeasurable part of sample. An iterative method by using discrete cosine transforms is addressed in this work to deal with the integration problem with incomplete gradient dataset in Southwell configuration. Simulation indicates that the discrete cosine transform provides better initial values than discrete Fourier transform does, and it converges to a more accurate level by updating with spectrum-based slopes comparing to the slope updates from finite difference in classical method. Experimental results show the feasibility of the proposed approach in a practical measurement.     

Research on three-dimensional shape reconstruction of circular cylindrical flaw

In this article, three-dimensional Born inverse scattering method is modified to convenient form for a cylindrical specimen that includes three-dimensional defect. One aluminum cylinder with flaw model is prepared and ultrasonic measurements are carried out. The measurement area in the modified methods is restricted in the plane perpendicular to the axis of cylindrical specimen. That’s to say that the method is modified to convenient form to use measured waveforms in the x₁ − x₂ plane. The measured wave data are fed into the inversion method and cross-sectional images are obtained. Then, three-dimensional shape reconstruction of flaw model in aluminum specimen is performed by piling up the cross-sectional images. At the same time, we get the numerical results from all directions by finite element method.     

3D shape reconstruction of teeth by shadow speckle correlation method

This paper presents a new method for 3D shape reconstruction in computer-aided dental prosthetics. A specklegram is projected onto the tooth to be measured. This shadow speckle image is recorded and then processed by a digital image correlation method, which enables the computation of 2D shapes based on the similar principle of shadow moiré method. By repeating the procedure for all the sides, i.e., one crown and several side surfaces, local 2D shapes can be measured precisely. Afterwards, these local 2D profiles are merged to form a 3D model, during which certain constraints such as the widths along perpendicular directions are introduced to guide the process. As the height information within an entire image field is recorded instantly, it has the potential to be employed in an intra-oral environment, which would make the patient feel more comfortable during the restoration process. In vitro experiments were carried out on gypsum teeth models and the results proved the effectiveness of the proposed method.     

Point-based integration for 3D object reconstruction from Ladar range images

A method of point-based integration from multiple registered laser radar (Ladar) range images for 3D object reconstruction is presented in this literature. Our method operates surface point data directly and provides a direct way for overlapping data removal. The overlapping areas were detected using a single distance threshold. In order to set the distance threshold, a local point density approach is introduced to solve it. Compared with the mesh-based, volumetric and other points-based integration approaches, our method is simple and fast, and need less storage memory. The approach is performed on various objects with different geometric shapes. The experimental results demonstrate the efficiency and feasibility of our method.     

层析成像图像重建算法综述

介绍了层析成像技术的图像重建算法,并从正向问题数学模型的简化和反向问题数学模型的映射结构的角度比较了各种算法的特点和优劣。研究表明:用本质是线性算法的各种变换方法重建图像存在严重失真,而卷积滤波的引入可以使变换方法的重建效果有所改善;基于导数搜索的迭代算法对初始值依赖性强、收敛速度慢并且容易陷入局部最优解;基于Fourier变换的方法具有本质的局限性;小波变换则可以同时刻画图像时域和频域的细节特征;有限元法通过重建对象像素的智能划分可以简化正问题的复杂性;而具有物理背景的蒙特卡罗法、模拟退火法、遗传算法、粒子滤波法及神经网络法更适合于复杂且非线性的图像重建;智能化、仿生化、并行化以及各种算法的融合是层析成像图像重建算法的发展趋势。     

A method for phase reconstruction in optical three-dimensional shape measurement

In optical three-dimensional shape measurement, a method of improving the measurement precision for phase reconstruction without phase unwrapping is analyzed in detail. Intensities of any five consecutive pixels that lie in the x-axis direction of the phase domain are given. Partial derivatives of the phase function in the x-and y-axis directions are obtained with a phaseshifting mechanism, the origin of which is analysed. Furthermore, to avoid phase unwrapping in the phase reconstruction, we derive the gradient of the phase function and perform a two-dimensional integral along the x- and y-axis directions. The reconstructed phase can be obtained directly by performing numerical integration, and thus it is of great convenience for phase reconstruction. Finally, the results of numerical simulations and practical experiments verify the correctness of the proposed method.     

双曲型守恒律的一种三阶半离散中心迎风格式

对一维双曲型守恒律,给出了一种具有较小数值耗散的三阶半离散中心迎风格式.该格式以Liu和Tadmor提出的三阶无振荡重构为基础,同时考虑了波传播的单侧局部速度.时间离散用保持强稳定性的三阶Runge-Kutta方法.由于不需用Riemann解算器,避免了特征分解过程,保持了中心格式简单的优点.数值算例验证本方法可进一步减小数值耗散,提高分辨率.     

A method for phase reconstruction in the optical three-dimensional shape measurement

In the optical three-dimensional shape measurement, a method of improving the measurement precision for phase reconstruction without phase unwrapping is analyzed in detail. Intensities of any five consecutive pixels that lie in the x-axis direction of the phase domain are given. Partial derivatives of the phase function in the x- and y-axis directions are obtained with a phase-shifting mechanism, the origin of which is analysed. Furthermore, to avoid the phase unwrapping in the phase reconstruction, we derive the gradient of the phase function and perform a two-dimensional integral along the x- and y-axis directions. The reconstructed phase can be obtained directly by performing the numerical integration, and thus it is of great convenience for phase reconstruction. Finally, the results of numerical simulations and practical experiments verify the correctness of the proposed method.     

Aspheric surface reconstruction for scanning interference

A simplified reconstructing method for the aspheric surface testing based on scanning interference technology is presented. The aspheric normal intersects the optical axis at different points with different angles, which is called normal congruence; a normal congruence can identify an aspheric surface. In this method, the test aspheric surface is shifted along the optical axis to scan the tested aspheric surface; meanwhile a series of interferograms and phase maps are obtained. The angles between the normal lines and the aspheric axis are obtained using the positions of zero-phase points, according to the image-forming principle of the camera. Here, Zernike polynomials are applied to analyze the phase maps and extract the zero-phase points. Finally, the absolute coordinates of the test surface is rebuilt through iterative integration. Because both the system deformation and amplification do not affect the reconstruction result, this method can avoid complicated stitching algorithm in the subaperture stitching interferometric method. Experimental results show that the method has high accuracy and reliability.     

双曲型守恒律的一种五阶半离散中心迎风格式

给出一种求解双曲型守恒律的五阶半离散中心迎风格式.对一维问题,该格式以五阶中心WENO重构为基础;对二维问题,用逐维计算的方法将五阶中心WENO重构进行推广.时间方向的离散采用Runge-Kutta方法.格式保持了中心差分格式简单的优点,即不用求解Riemann问题,避免进行特征分解.用该格式对一维和二维Euler方程进行数值试验,结果表明该格式是高精度、高分辨率的.     

3D reconstruction of nanocrystalline particles from a single projection

This paper describes an approach to retrieve the three-dimensional atomic structure of a nanocrystalline particle from the reconstructed electron exit wave function in a single projection direction. The method employs wave propagation to determine the local exit surface of each atomic column together with its mass. The exit wave in between colums is used as internal calibration so as to remove the background noise and improve the precision to the level of single atom sensitivity. The validity of the approach is tested with exit wave functions of a gold wedge reconstructed from simulated images containing different levels of noise.     

Point-wise hierarchical reconstruction for discontinuous Galerkin and finite volume methods for solving conservation laws

We develop a new hierarchical reconstruction (HR) method  and  for limiting solutions of the discontinuous Galerkin and finite volume methods up to fourth order of accuracy without local characteristic decomposition for solving hyperbolic nonlinear conservation laws on triangular meshes. The new HR utilizes a set of point values when evaluating polynomials and remainders on neighboring cells, extending the technique introduced in Hu, Li and Tang [9]. The point-wise HR simplifies the implementation of the previous HR method which requires integration over neighboring cells and makes HR easier to extend to arbitrary meshes. We prove that the new point-wise HR method keeps the order of accuracy of the approximation polynomials. Numerical computations for scalar and system of nonlinear hyperbolic equations are performed on two-dimensional triangular meshes. We demonstrate that the new hierarchical reconstruction generates essentially non-oscillatory solutions for schemes up to fourth order on triangular meshes.     

基于IR-SFS算法空间目标红外影像3D重建

在利用单幅影像的明暗恢复形状（Shape From Shading,SFS）三维重构算法的基础上,提出同时考虑外界辐射源和目标自身红外辐射的IR-SFS（infrared-SFS）算法。首先通过分析SFS算法原理和空间目标的红外成像特性,建立IR-SFS辐射方程并进行了仿真研究,然后利用温度场估计获得红外差值图,在人工合成的理想半球体、半圆柱体卫星红外影像上进行算法测试,并以美国STS107真实红外影像作为实验目标进行三维重建。实验结果表明,所提出IR-SFS算法经过参数优化后,与原SFS算法相比,重建模型的峰值信噪比更高,对STS107顶部舱门、尾翼、机舱、机舱内方形部件具有更佳显示度,整体效果得到明显改善。     

多车种LWR交通流模型的半离散中心迎风格式

对多车种LWR交通流模型,给出一种半离散中心迎风格式,该格式以五阶WENO-Z重构和半离散中心迎风数值通量为基础.WENO-Z重构方法的引入提高了格式的精度,并保证格式具有基本无振荡的性质.时间的离散采用保持强稳定性的Runge-Kutta方法.通过数值算例验证了格式的有效性.     

Surface shape estimation from photometric images

One of the most studied techniques for recovering surface shapes using a computer vision system is the photometric. This method is based on the analysis of one or several images of an object illuminated from a known direction . This kind of images can be considered reflectance maps that give us information of the surface gradient. In computer vision, the problem of recovering 3D information from shaded images is considered an inverse problem. To integrate surface gradient information it is proposed a regularization technique that gives a stable solution of the inverse problem and allows the possibility of reducing errors caused by noise. Results applied on synthetic and real experimental images are presented.     

从一幅载频全息图中实现相位重构的新算法

为了实现对单幅载频下涉图进行相位重构.提出了一种避免相位"解包裹"的简易算法.该算法从载频干涉图中解出所求相位的两个偏导数,然后对两个偏导数积分从而得到所求的相位.利用该算法分别对计算机模拟的干涉图和实验所得干涉图进行相位重构,重构结果均表明该算法能够很好地从载频干涉图样中实现相化重构.并且由于避免了相位"解包裹"的过程,从而简化了相位重构的流程,同时也避免了由相位解包带来的错误或误差.此外,该方法在重构相位时,对干涉图中强度分布的不均匀性不敏感.     

求解对流-扩散-反应问题的改进有限积分法

将求解偏微分方程的有限积分法应用于对流-扩散-反应问题,发现对于非对流占优的对流扩散问题,有限积分法的精度比QUICK法高一个数量级,比传统的有限体积法高两个数量级.处理对流占优的对流-扩散-反应问题时,对流项的离散时引进加权参数,通过调节该参数反映输运的方向性.结果表明这种改进的有限积分法的精度比传统的有限体积法至少高四个数量级,同时明显改进了原来的有限积分法的精度和稳定性.对于对流占优的对流-扩散-反应问题,即使采用粗网格,计算结果也未出现非物理振荡现象,表明改进的有限积分法具有很好的稳定性.     

Contouring of artwork surface by fringe projection and FFT analysis

In the present work, we propose a simple optical method to perform profilometry on works of art. The method is based on the projection of a Ronchi grating onto the surface to be analyzed. When viewed at an angle different from the projection angle, the grid pattern appears deformed by the surface shape. This pattern is digitized, by a high-resolution CCD camera, and then processed using a Fourier transform analysis. The technique is free from the errors caused by higher harmonic components of the grating pattern. Furthermore, the method relies on very simple equipment and it is therefore suitable for in situ measurements. Theoretical details and examples of the technique in operation are given.