EM-GPA: Generalized Procrustes analysis with hidden variables for 3D shape modeling

Aligning shapes is essential in many computer vision problems and generalized Procrustes analysis (GPA) is one of the most popular algorithms to align shapes. However, if some of the shape data are missing, GPA cannot be applied. In this paper, we propose EM-GPA, which extends GPA to handle shapes with hidden (missing) variables by using the expectation-maximization (EM) algorithm. For example, 2D shapes can be considered as 3D shapes with missing depth information due to the projection of 3D shapes into the image plane. For a set of 2D shapes, EM-GPA finds scales, rotations and 3D shapes along with their mean and covariance matrix for 3D shape modeling. A distinctive characteristic of EM-GPA is that it does not enforce any rank constraint often appeared in other work and instead uses GPA constraints to resolve the ambiguity in finding scales, rotations, and 3D shapes. The experimental results show that EM-GPA can recover depth information accurately even when the noise level is high and there are a large number of missing variables. By using the images from the FRGC database, we show that EM-GPA can successfully align 2D shapes by taking the missing information into consideration. We also demonstrate that the 3D mean shape and its covariance matrix are accurately estimated. As an application of EM-GPA, we construct a 2D + 3D AAM (active appearance model) using the 3D shapes obtained by EM-GPA, and it gives a similar success rate in model fitting compared to the method using real 3D shapes. EM-GPA is not limited to the case of missing depth information, but it can be easily extended to more general cases.     

Shape from shading using graph cuts

In this paper, we investigate the applicability of graph cuts to the SFS (shape-from-shading) problem. We propose a new semi-global method for SFS using graph cuts. The new algorithm combines the local method proposed by Lee and Rosenfeld [C.H. Lee, A. Rosenfeld, Improved methods of estimating shape from shading using the light source coordinate system, Artif. Intell. 26 (1985) 125-143] and a global method using an energy minimization technique. By employing a new global energy minimization formulation, the convex/concave ambiguity problem of Lee and Rosenfeld's method can be resolved efficiently. A new combinatorial optimization technique, the graph cuts method, is used for the minimization of the proposed energy functional. Experimental results on a variety of synthetic and real-world images show that the proposed algorithm reconstructs the 3-D shape of objects very efficiently.     

Sensitivity analysis of shape memory alloy shells

This paper presents procedures for efficient design sensitivity analysis for shape memory alloy (SMA) structures modeled with shell elements. Availability of sensitivity information at low computational cost can dramatically improve the efficiency of the optimization process, as it enables use of efficient gradient-based optimization algorithms. The formulation and computation of design sensitivities of SMA shell structures using the direct differentiation method is considered, in a steady state electro-thermo-mechanical finite element context. Finite difference, semi-analytical and refined semi-analytical sensitivity analysis approaches are considered and compared in terms of efficiency, accuracy and implementation effort, based on a representative finite element model of a miniature SMA gripper.     

Color Subspaces as Photometric Invariants

Complex reflectance phenomena such as specular reflections confound many vision problems since they produce image ‘features’ that do not correspond directly to intrinsic surface properties such as shape and spectral reflectance. A common approach to mitigate these effects is to explore functions of an image that are invariant to these photometric events. In this paper we describe a class of such invariants that result from exploiting color information in images of dichromatic surfaces. These invariants are derived from illuminant-dependent ‘subspaces’ of RGB color space, and they enable the application of Lambertian-based vision techniques to a broad class of specular, non-Lambertian scenes. Using implementations of recent algorithms taken from the literature, we demonstrate the practical utility of these invariants for a wide variety of applications, including stereo, shape from shading, photometric stereo, material-based segmentation, and motion estimation.     

Model of Frequency Analysis in the Visual Cortex and the Shape from Texture Problem

This paper addresses the question: at the level of cortical cells present in the primary area V1, is the information sufficient to extract the local perspective from the texture? Starting from a model of complex cells in visual area V1, we propose a biologically plausible algorithm for frequency analysis applied to the shape from texture problem. First, specific log-normal filters are designed in replacement of the classical Gabor filters because of their theoretical properties and of their biological plausibility. These filters are separable in frequency and orientation and they better sample the image spectrum which makes them appropriate for any pattern analysis technique. A method to estimate the local frequency in the image, which discards the need to choose the best local scale, is designed. Based on this frequency analysis model, a local decomposition of the image into patches leads to the estimation of the local frequency variation which is used to solve the problem of recovering the shape from the texture. From the analytical relation between the local frequency and the geometrical parameters, under perspective projection, it is possible to recover the orientation and the shape of the original image. The accuracy of the method is evaluated and discussed on different kind of textures, both regular and irregular, with planar and curved surfaces and also on natural scenes and psychophysical stimuli. It compares favorably to the best existing methods, with in addition, a low computational cost. The biological plausibility of the model is finally discussed.     

单幅图像三维表面重建的算法研究与实现

以单幅二维图像为研究对象,应用SFS的基本理论,首先对二维图像进行了光照的倾角和偏角的估计,在光源坐标系下计算出物体每一点的表面梯度;之后,旋转坐标系,在观察坐标系下得到物体的表面梯度;最后采用三点辛普森公式求出物体表面的高度。整个算法流程简单,求解层次分明,重构满意度较高。     

Laser range scanner based on self-calibration techniques using coplanarities and metric constraints

In this paper, we propose a novel method to achieve both dense 3D reconstruction of the scene and estimation of the camera intrinsic parameters by using coplanarities and other constraints (e.g., orthogonalities or parallelisms) derived from relations between planes in the scene and reflected curves of line lasers captured by a single camera. In our study, we categorize coplanarities in the scene into two types: implicit coplanarities, which can be observed as reflected curves of line lasers, and explicit coplanarities, which are, for example, observed as walls of a building. By using both types of coplanarities, we can construct simultaneous equations and can solve them up to four degrees of freedom. To upgrade the solution to the Euclidean space and estimate the camera intrinsic parameters, we can use metric constraints such as orthogonalities of the planes. Such metric constraints are given by, for example, observing the corners of rectangular boxes in the scene, or using special laser projecting device composed of two line lasers whose laser planes are configured to be perpendicular.     

Optimization of dynamic response using a monolithic-time formulation

The design of systems for dynamic response may involve constraints that need to be satisfied over an entire time interval or objective functions evaluated over the interval. Efficiently performing the constrained optimization is challenging, since the typical response is implicitly linked to the design variables through a numerical integration of the governing differential equations. Evaluating constraints is costly, as is the determination of sensitivities to variations in the design variables. In this paper, we investigate the application of a temporal spectral element method to the optimization of transient and time-periodic responses of fundamental engineering systems. Through the spectral discretization, the response is computed globally, thereby enabling a more explicit connection between the response and design variables and facilitating the efficient computation of response sensitivities. Furthermore, the response is captured in a higher order manner to increase analysis accuracy. Two applications of the coupling of dynamic response optimization with the temporal spectral element method are demonstrated. The first application, a one-degree-of-freedom, linear, impact absorber, is selected from the auto industry, and tests the ability of the method to treat transient constraints over a large-time interval. The second application, a related mass-spring-damper system, shows how the method can be used to obtain work and amplitude optimal time-periodic control force subject to constraints over a periodic time interval. This research was performed while the first author held a National Research Council Research Associateship Award at the Air Force Research Laboratory. An early version of this paper was presented at the 46th AIAA Aerospace Sciences Meeting and Exhibit, Jan 7–10, 2008, Reno, Nevada.     

Optimal hole shape for minimum stress concentration using parameterized geometry models

The goal of this work is to obtain optimal hole shape for minimum stress concentration in two-dimensional finite plates using parameterized geometry models. The boundary shape for a hole is described by two families of smooth curves: one is a “generalized circular” function with powers as two parameters; the other one is a “generalized elliptic” function a and b are ellipse axes) with powers as two parameters and one of the ellipse axes as the third parameter. Special attention is devoted to the practicability of parameterized equations and the corresponding optimal results under the condition with and without the curvature radius constraint. A number of cases were examined to test the effectiveness of the parameterized equations. The numerical examples show that extremely good results can be obtained under the conditions with and without curvature radius constraint, as compared to the known solutions in the literature. The geometries of the optimized holes are presented in a form of compact parametric functions, which are suitable for use and test by designers. It is anticipated that the implementation of the suggested parameterized equations would lead to considerable improvements in optimizing hole shape with high quality.     

交-直-交变频调速器在连轧型钢主传动中的应用

该文介绍变频器在型钢连轧机主传动系统中的应用。在我国,连轧中型钢材生产线屈指可数,轧机采用交流电动机的更是少之又少。交流电动机本身有着直流电动机所不具备的以下优点：没有电刷和换向器、结构简单、坚固耐用、经济可靠,不过因为其系一多变量、强耦合、非线性的时变系统,调速比较困难,随着电力电子技术的迅速发展和计算机控制技术以及现代控制理论的引人,交流调速系统才取得长足进步并得以广泛应用。