问题描述
在假设相机模型为正交摄影机的情况下，如何从运动的角度来对正交摄影机和透视相机摄影机进行结构建模?
Under the assumption that the camera model is orthographic, how do orthographic and perspective camera models in structure from motion?
此外，这些技术有何不同?
Also, how do these techniques differ from each other?
推荐答案
假设您有一个静态场景和移动摄像机(或者等效地，是一个刚性移动场景和静态摄像机)，并且您想从两个场景中重构场景的几何形状和摄像机的运动或更多图像.重建通常基于获得点对应关系，即您具有一些方程，需要针对这些点和摄像机运动求解这些方程.
Say you have a static scene and moving camera (or equivalently, rigidly moving scene and static camera) and you want to reconstruct the scene geometry and camera motion from two or more images. The reconstruction usually based on obtaining point correspondences, that is you have some equations which ones should be solved for the points and camera motion.
该解决方案可以基于非线性最小化，也可以基于各种近似值.相机可以通过正交投影或透视投影来近似.在最简单的SFM情况下，可以通过正交投影(或更一般而言，通过弱透视投影)来近似相机，在这种情况下，场景可以按比例恢复.但是，由于正交投影的特性，垂直于像平面的平移永远无法恢复.
The solution can be either based on nonlinear minimization or on various approximations. The camera can be approximated by orthographic or perspective projection. In the simplest SFM case the camera can be approximated by orthographic projection (or more generally by weak perspective projection), where the scene can be recovered up to scale. But translation perpendicular to image plane can never be recovered due to the properties of orthographic projection.
较新的SfM方法使用透视投影，因为使用正交投影我们无法恢复所有信息.通过全透视投影，我们可以恢复例如沿光轴的平移.也就是说，几何形状和完整运动可以恢复到全局比例因子.
Newer SfM methods use perspective projection, because with orthographic projection we can’t recover all information. With full perspective projection we can recover for example the translation along optical axis. That is the geometry and full motion can be recovered up to global scale factor.
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