Simultaneous and Sequential Reconstruction of Visual Primitives with Bundle Adjustment

In this paper, we compare the various methods for the simultaneous and sequential reconstruction of points, lines, planes, quadrics, plane conics and degenerate quadrics using Bundle Adjustment, both in projective and metric space. In contrast, most existing work on projective reconstruction focuses mainly on one type of primitive. We also compare the simultaneous refinement of all primitives through Bundle Adjustment with various sequential methods were only certain primitives are refined together. We found that even though the sequential methods may seem somewhat arbitrary on the choice of which primitives are refined together, a higher precision and speed is achieved in most cases. Leo Reyes graduated in Computer Engineering at the University of Guadalajara in 1999 and gained his Master’s and Doctoral degrees in Computer Science from the Center of Research and Advanced Studies Guadalajara (Centro de Investigación y Estudios Avanzados del IPN, CINVESTAV Unidad Guadalajara) in 2001 and 2004, respectively. He is currently working on a private company doing automatic inspection research. Eduardo Jose Bayro-Corrochano gained his Ph.D. in Cognitive Computer Science in 1993 from the University of Wales at Cardiff. From 1995 to 1999 he has been Researcher and Lecturer at the Institute for Computer Science, Christian Albrechts University, Kiel, Germany, working on applications of geometric Clifford algebra to cognitive systems. At present he is a full professor at CINVESTAV, Unidad Guadalajara, Computer Science Group and he is responsible for the GEOVIS laboratory. His current research interest focuses on geometric methods for artificial perception and action systems. It includes geometric neural networks, visually guided robotics, color image processing, Lie bivector algebras for early vision and robot maneuvering. He developed the quaternion wavelet transform for quaternion multi-resolution analysis using the phase concept. He is editor and author of the following books: Geometric Computing for Perception Action Systems, E. Bayro-Corrochano, Springer Verlag, 2001; Geometric Algebra with Applications in Science and Engineering, E. Bayro-Corrochano and G. Sobczyk (Eds.), Birkahauser 2001; Handbook of Computational Geometry for Pattern Recognition, Computer Vision, Neurocomputing and Robotics, E. Bayro-Corrochano, Springer Verlag, 2005. He has published over 100 refereed journal and conference papers.     

A unified theory for optimal feedforward torque control of anisotropic synchronous machines

A unified theory for optimal feedforward torque control of anisotropic synchronous machines with non-negligible stator resistance and mutual inductance is presented which allows to analytically compute (1) the optimal direct and quadrature reference currents for all operating strategies, such as maximum torque per current (MTPC), maximum current, field weakening, maximum torque per voltage (MTPV) or maximum torque per flux (MTPF), and (2) the transition points indicating when to switch between the operating strategies due to speed, voltage or current constraints. The analytical solutions allow for an (almost) instantaneous selection and computation of actual operation strategy and corresponding reference currents. Numerical methods (approximating these solutions only) are no longer required. The unified theory is based on one simple idea: all optimisation problems, their respective constraints and the computation of the intersection point(s) of voltage ellipse, current circle or torque, MTPC, MTPV, MTPF hyperbolas are reformulated implicitly as quadrics which allows to invoke the Lagrangian formalism and to find the roots of fourth-order polynomials analytically. The proposed theory is suitable for any anisotropic synchronous machine. Implementation and measurement results illustrate effectiveness and applicability of the theoretical findings in real world.     

Biconic subdivision of surfaces of revolution and its applications in intersection problems

This paper presents a novel method for the subdivision of surfaces of revolution. We develop a new technique for approximating the genertrix by a series of pairs of conic sections. By using an error estimate based on convex combination, an efficient least-squares approach is proposed that yields near-optimal fitting. The resulting surface approximation is shown to be more efficient than other tessellation methods in terms of the number of fitting segments. This in turn allows us to implement efficient and robust algorithms for such surfaces. In particular, novel intersection techniques based on the proposed subdivision method are introduced for the two most fundamental types of intersections – line/surface and surface/surface intersections. The experimental results show that our method outperforms conventional methods significantly in both computing time and memory cost.     

Do blending and offsetting commute for Dupin cyclides?

A common method for constructing blending Dupin cyclides for two cones having a common inscribed sphere of radius r>0 involves three steps: (1) computing the (−r) -offsets of the cones so that they share a common vertex, (2) constructing a blending cyclide for the offset cones, and (3) computing the r -offset of the cyclide. Unfortunately, this process does not always work properly. Worse, for some half-cones cases, none of the blending cyclides can be constructed this way. This paper studies this problem and presents two major contributions. First, it is shown that the offset construction is correct for the case of ≠−r , where is the signed offset value; otherwise, a procedure must be followed for properly selecting a pair of principal circles of the blending cyclide. Second, based on Shene's construction in “Blending two cones with Dupin cyclides”, CAGD, 15 (1998) 643–673, a new algorithm is available for constructing all possible blending cyclides for two half-cones. This paper also examines Allen and Dutta's theory of pure blends, which uses the offset construction. To help overcome the difficulties of Allen and Dutta's method, this paper suggests a new algorithm for constructing all possible pure blends. Thus, Shene's diagonal construction is better and more reliable than the offset construction.     

基于高斯曲面拟合的影像渐晕复原方法

 本文根据影像发生渐晕时灰度分布的特点,提出了一种基于最速下降法的高斯曲面拟合方法,推导了Hesse矩阵的相关参数,较好地解决了不规则高斯曲面拟合的问题,获得了影像整体灰度变化情况,从而实现了影像渐晕现象的复原.仿真结果表明,上述方法能够有效估计出不规则高斯曲面(如渐晕图像灰度值)的相关参数.通过对实际影像的处理结果表明,本文方法能够有效去除影像的渐晕现象,改善图像质量.由于该方法不需要相关的光学和几何参数,因此具有广泛的适用性.     

反射镜拼接渐晕消除方法

根据反射镜拼接型CCD相机拍摄影像时发生渐晕的灰度分布特点,提出了一种基于最速下降法的曲面拟合方法,以消除渐晕现象.对反射镜渐晕的物理模型进行分析,通过仿真提出了一种二维曲面模型来拟合图像灰度补偿算法,推导Hesse矩阵的相关系数,通过Hesse矩阵逐次迭代收敛,最终获得二维曲面的相关参数值.仿真结果表明,上述方法能够...     

A complete, exact and efficient implementation for computing the edge-adjacency graph of an arrangement of quadrics

We present a complete, exact and efficient implementation to compute the edge-adjacency graph of an arrangement of quadrics, i.e. surfaces of algebraic degree 2. This is a major step towards the computation of the full 3D arrangement. We enhanced an implementation for an exact parameterization of the intersection curves of two quadrics, such that we can compute the exact parameter value for intersection points and from that the edge-adjacency graph of the arrangement. Our implementation is complete in the sense that it can handle all kinds of inputs including all degenerate ones, i.e. singularities or tangential intersection points. It is exact in that it always computes the mathematically correct result. It is efficient measured in running times, i.e. it compares favorably to the only previous implementation.     

基于推广B 样条细分方法的曲面混合

提出用推广B 样条细分曲面来混合多张曲面的方法,既适用于一般网格曲面,又适用于推广B 样条参数曲面混合。根据需要选择阶数和张力参数,可全局调整整张混合曲面的形状。中心点和谷点的计算都设置了形状参数,可局部调整混合部分形状。推导出二次曲面细分初始网格计算公式,并将3 阶推广B 样条细分曲面混合方法用于多张二次曲面混合,与已有的二次曲面混合方法相比具有明显的优势。     

用有理双三次Bezier曲面片混合二次曲面

提出一种二次曲面混合方法，混合曲面由2张有理双三次B6zier曲面片构成，它们之间保持G^2连续，混合曲面与二次曲面间保持G^1连续．给出了混合曲面片控制顶点的显式表示，通过修改2类混合参数可以直观地调节混合方向及混合曲面的形状．另外，混合5个圆锥曲面的例子表明，该方法为多个二次曲面的混合问题提供了有效途径．