二视图几何与多视图几何的张量表达  

TENSOR EXPRESSION OF TWO-VIEW AND MULTI-VIEW GEOMETRY

作　　者：王君 柏锦萱 徐常青 Wang Jun;Bai Jinxuan;Xu Changqing(School of Mathematical Sciences,Suzhou University of Science and Technology,Suzhou 215009)

机构地区：[1]苏州科技大学数学科学学院,苏州215009

出　　处：《高等学校计算数学学报》2024年第1期83-96,共14页Numerical Mathematics A Journal of Chinese Universities

摘　　要：1引言计算机视觉传统的目标主要涉及多视图的三维重构[15,26,27],即从两幅或更多幅图像中重建三维对象.给定视图之间足够多的点(或线)对应关系,就可能计算出多视图张量,并在相差一个射影等价的意义下从多视图张量中提取出摄像机的原始投影矩阵.这类问题目前解决的方案和技术已较成熟,且在人工智能[6]、摄影测量[24,25]、图像分析[23]等领域有较好的应用.This paper mainly studies the corresponding relation of points in 2-view geometry and multi-view geometry.Firstly,we introduce the basic knowledge of higher order tensors,then study the characteristics of basic matrix and expound the relationship between basic matrix and camera matrix pair.We also introduce the concept of the corresponding point tensor by the generalization of matrix K-R product and simplify the correspondence of multi-view tensors by introducing tensor compression multiplication.

关 键 词：投影矩阵 张量 计算机视觉 人工智能 射影等价 三维重构 图像分析 摄影测量 

分 类 号：O213[理学—概率论与数理统计]