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多视几何中的最优三角化方法研究
其他题名A Study on Optimal Triangulation in Multiple View Geometry
张强
学位类型工学博士
导师吴福朝
2011-12-03
学位授予单位中国科学院研究生院
学位授予地点中国科学院自动化研究所
学位专业模式识别与智能系统
关键词最优三角化 次优三角化 Sampson近似 多视三角化 直线三角化 Optimal Triangulation Suboptimal Triangulation Sampson Approximation Multi-view Triangulation Line Triangulation
摘要计算机视觉的核心问题是三维重建问题,其中利用多视几何的方法估计射影空间中的空间点和直线的问题已经存在很多方法。但这些现存的方法中,有些没有注意到提取图像点和直线时产生的误差,对噪声较为敏感;有些虽然考虑到了测量误差的影响,但计算复杂性太大。本文对射影空间中空间点和直线的三角化方法进行了深入的研究,所完成的工作如下: 1.两视的点三角化方法:基于基本锥面,提出了求解测量点到基本锥面上最近点的最优三角化方法。这种方法虽然仍要求解一元六次方程,但它的欧氏变换不再依赖于测量点,它的方程的次数不再依赖于图像次序。为了减少计算复杂度,基于生成锥面、生成线和Sampson序列,又提出了三种满足对极几何约束的次优方法。这三种次优方法的估计精度与最优三角化方法相当,但运算时间却大为减少。 2.多视的点三角化方法:提出了最小化L2-范数几何距离的优化准则。基于该优化准则,提出计算复杂性较小的Sampson近似迭代算法;为了进一步减少迭代次数,提出了沿共轭梯度方向的迭代算法。相比黄金标准算法,这两种迭代算法的计算复杂度明显减少,而计算精度几乎与之相同。 3.三视的直线三角化方法:提出了两种新的直线三角化方法。基于Plucker坐标表示,提出在满足Klein曲面约束下最小化代数距离的次优算法。这种算法得到的代数误差不会超过最小代数误差的两倍。基于图像上新的直线表示,又给出了以点-线-线三焦张量为约束条件最小化测量端点沿测量直线法线方向到估计直线距离的优化准则,并且提出了一种运算时间更短但精度与黄金标准算法几乎相同的迭代算法。
其他摘要3D reconstruction is a key problem in computer vision and many algorithms based on multiple view geometry have been proposed for the 3D point or 3D line reconstruction in projective space. In these existing algorithms, some of them are more sensitive to noise due to not fully taking into account the measurement errors of image point and image line; others are of high computational complexity although the impacts of measurement error are taken into account. This study is focused on 3D point and 3D line reconstruction in projective space. The main work is summarized as follows: 1. Point Triangulation from Two Views: Based on the fundamental cone, a new optimal triangulation framework is proposed, in which the nearest point on fundamental cone to the measure point is searched. Although this triangulation needs finding out the root of 6-degree polynomial, the Euclidean transformation in it doesn’t depend on the measured point and the degree of the polynomial doesn’t depend on the order of images. To reduce the computational load, three efficient suboptimal algorithms based on generating cone, generating line and Sampson sequence are proposed. Our proposed three suboptimal al-gorithms can achieve comparable estimation accuracy compared with the optimal trian-gulation, but with much less computational load. 2. Point Triangulation from Multiple Views: A L2-norm distance optimality criterion is proposed. Based on this criterion, a simple Sampson approximation iterative algorithm is introduced for the point triangulation from multiple views. In addition a fast iterative algorithm based on conjugate gradient is also proposed to speedup the iteration. Compared with the Gold Standard algorithm, our proposed two iterative algorithms can achieve comparable estimation accuracy, but with lower computational complexity. 3. Line triangulation from Three Views: Two new algorithms are proposed. Based on Plucker coordinates, the first algorithm minimizes the algebraic distance under Klein qu-adric constraint to obtain a suboptimal solution. The algebraic distance of the suboptimal solution is less than double of the optimal solution. Via a new line representation in image, the second algorithm minimizes the normal distance from the measured endpoint to the estimated line under point-line-line tensor constraint using an iterative method. This algorithm can achieve comparable estimation accuracy compared with the Gold Standard algorithm, but with much less computational load.
馆藏号XWLW1697
其他标识符200818014628075
语种中文
文献类型学位论文
条目标识符http://ir.ia.ac.cn/handle/173211/6407
专题毕业生_博士学位论文
推荐引用方式
GB/T 7714
张强. 多视几何中的最优三角化方法研究[D]. 中国科学院自动化研究所. 中国科学院研究生院,2011.
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