Pose estimation from a single image using tensor decomposition and an algebra of circulants
Pose estimation from a single image using tensor decomposition and an algebra of circulants
复制标题
使用张量分解和循环代数从单个图像估计姿势
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Ning Hao
中科院分区：
文献类型：
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作者：
R. Hoover;Karen S. Braman;Ning Hao
简化和对象分类（识别和姿态估计）是机器人、机器人视觉和工业自动化中的重要工具。本文提出了一种新的方法来降维和物体分类的三维刚性物体。该方法是基于张量分解和一个新定义的循环代数的最新发展。特别地，在右张量乘法算子下，三阶张量可以写成三阶张量的乘积，其中左张量和右张量是张量正交的，内张量是奇异元组的对角张量.这种新的发展允许定义适当的张量奇异值分解（SVD），并具有张量主成分分析（PCA）的自然扩展。与传统的PCA进行比较，它表明，目前的方法是能够恢复显着更多的信息，从图像序列使用一个小得多的子空间维数。此外，它示出，对于大多数对象，准确的姿态估计可以从一个单一的子空间维度。
Dimensionality reduction and object classification (recognition and pose estimation) serve as important tools in robotics, robotic vision, and industrial automation. The current paper presents a new approach to dimensionality reduction and object classification of three-dimensional rigid objects. The approach is based upon recent developments in tensor decompositions and a newly defined algebra of circulants. In particular, it is shown that under the right tensor multiplication operator, a third order tensor can be written as a product of third order tensors in which the left and right tensors are tensor-orthogonal and the inner-tensor is a diagonal tensor of singular-tuples. This new development allows for a proper tensor singular value decomposition (SVD) to be defined and has natural extension to tensor principal component analysis (PCA). Comparisons are made with traditional PCA and it is shown that the current approach is capable of recovering significantly more information from an image sequence using a much smaller subspace dimension. Further, it is shown that for most objects, accurate pose estimation can be performed from a single subspace dimension.