【OpenCV】 DLT 算法 (Direct linear transformation)

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OpenCV 计算外参的函数 cvFindExtrinsicCameraParams2, 用到了 DLT 方法来计算初始的外参参数.

Intro

from wikipedia:

Direct linear transformation (DLT) is an algorithm which solves a set of variables from a set of similarity relations:

$$x_k\propto A{y}_{k}fork=1,...,N$$

where $x_k$ and $y_k$ are known vectors, $\propto$ denotes equality up to an unknown scalar multiplication, and $A$ is a matrix(or linear transformation) which contains the unknown to be solved.

This type of relation appears frequently in projective geometry. Practical examples include the relation between 3D points in a scene and their projection onto the image plane of a pinhole camera, and homographies.

DLT 主要用来解决两组相似分布的变量的对应关系, 一般求解的是比例关系, 确定了系数还可以变为等式关系. 系数矩阵 $A$就是要求解的变量. 这个常用在投影几何中, 比如 3D 物点和 2D像点之间的对应关系, 或者 Homographies.

求解的就是这个 linear transformation, 特点就是直接求, 不绕弯子, directly.

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Ref

• DLT – Wikipedia
• 第七章 – 直接线性变换解法 : 超级详细, 超级完善
• DLT算法的易错之处 : 这个博客说了为什么实际使用中 DLT 之前要先进行 归一化
• Triangulation求解3D坐标-直接线性转换（Direct Linear Transformation-DLT）算法 : 这篇博客讲解了在实际 3D 重建中使用 DLT 的场景