中文摘要：

在分层三维重建中, 从射影重建到仿射重建是一个关键步骤, 而模约束是从射影重建提升到仿射重建的一种重要方法, 其本质在于确定无穷远平面对应的三维向量. 模约束成立的前提是三维重建中所有图像对应的摄像机的内参数相同, 针对当无任何关于待重建场景的先验信息或摄像机运动的先验信息时, 模约束是唯一的对无穷远平面的可行约束的提法, 文中指出, 保持摄像机的一个或多个内参数不变, 进而对摄像机进行标定, 是三维重建从射影重建到度量重建的本质, 而模约束不过是这种本质属性当所有内参数均保持不变下的一种特殊形式.

英文摘要：

Upgrading a projective reconstruction to an affine one is a key step in stratified 3D reconstruction from images, and the modulus constraint is an important approach for doing it, which in essence is to deter-mine the 3D normal vector of the plane at infinity. The basis of the modulus constraint is all the images have the same intrinsic parameters, and it is even claimed in some literatures that the modulus constraint is the unique existing constraint for upgrading the projective reconstruction to an affine one if the a priori knowl-edge on the scene or camera motion is unavailable. In this short note, we show that keeping one or some in-trinsic parameters unchanged during the image acquisition, or with one or some known intrinsic parameters, by which cameras are fully calibrated, is the minimum and basic demand of 3D metric reconstruction, and the modulus constraint is in fact not the unique existing constraint, it is merely a special case that all the pa-rameters must keep constant.