General SFM methods give poor results for images captured by constrained motions such as planar motion of concentric mosaics (CM). In this paper, we propose new SFM algorithms for both images captured by CM and composite mosaic images from CM. We first introduce 1D affine camera model for completing 1D camera models. Then we show that a 2D image captured by CM can be decoupled into two 1D images: one 1D projective and one 1D affine; a composite mosaic image can by rebinned into a calibrated 1D panorama projective camera. Finally we describe subspace reconstruction methods and demonstrate both in theory and experiments the advantage of the decomposition method over the general SFM methods by incorporating the constrained motion into the earliest stage of motion analysis.