A Note on the Modulus Constraint in Stratified 3D Reconstruction

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 determine 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 knowledge on the scene or camera motion is unavailable. In this short note, we show that keeping one or some intrinsic 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 parameters must keep constant.