From a non-central panorama, 3D lines can be recovered by geometric reasoning. However, their sensitivity to noise and the complex geometric modeling required has led these panoramas being very little investigated. In this work we present a novel approach for 3D layout recovery of indoor environments using single non-central panoramas. We obtain the boundaries of the structural lines of the room from a non-central panorama using deep learning and exploit the properties of non-central projection systems in a new geometrical processing to recover the scaled layout. We solve the problem for Manhattan environments, handling occlusions, and also for Atlanta environments in an unified method. The experiments performed improve the state-of-the-art methods for 3D layout recovery from a single panorama. Our approach is the first work using deep learning with non-central panoramas and recovering the scale of single panorama layouts.