| 基于坐标归一化和奇异值分解的直接线性变换解法 |
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| 引用本文： | 周拥军,寇新建.基于坐标归一化和奇异值分解的直接线性变换解法[J].测绘科学,2008(Z1). |
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| 作者姓名： | 周拥军 寇新建 |
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| 作者单位： | 上海交通大学 船舶海洋与建筑工程学院 |
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| 摘 要： | 直接线性变换方法是数字摄影测量和计算机视觉领域最常用的解析处理方法之一,特别适用于未检校数码相机的三维测量,但直接线性参数间的相关性、物方控制的约束和设计矩阵元素数量级的较大差异,均可导致法矩阵严重病态,从而影响解的稳定性。本文借鉴改进的八点基本矩阵估计算法,采用基于坐标归一化和奇异值分解的解法,即首先将像点和物点坐标进行相似变换得到归一化坐标后组成法矩阵,其次利用矩阵奇异值分解方法代替常规的最小二乘方法,模拟和真实数据表明,此方法可以有效提高解算精度和稳定性。
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| 关 键 词： | 直接线性变换 归一化 奇异值分解 数字摄影测量 |
A direct solution for direct linear transformation based on image coordinate normalization and Singular Value Decomposition |
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| ZHOU Yong-jun KOU Xin-jian.A direct solution for direct linear transformation based on image coordinate normalization and Singular Value Decomposition[J].Science of Surveying and Mapping,2008(Z1). |
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| Authors: | ZHOU Yong-jun KOU Xin-jian |
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| Abstract: | Direct linear transformation(DLT)is a widely used analytical approach in digital photogrammetry and computer vision fields,especially for 3D measurement with uncalibrated digital cameras.However,the correlation of the DLT parameters,the ohject space constraints,and the amount difference of the normal equation terms induce the vital ill-condition for normal equation,which will influence the accuracy and stability for computation.Inspired by Hartley's improved 8 point fundamental matrix estimation algorithm, two improvements are made for traditional algorithm,First the image coordinates and object coordinates are normalized with a simple similar transformation,then singular value decomposition(SVD)method is performed to solve least square problem instead of tradition- al methods.The simulated data experiment and the real image data computation indicate that the improved algorithm could improve the estimation accuracy and stability. |
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| Keywords: | direct linear transformation normalization singular value decomposition digital photogrammetry |
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