Structure-From-Motion Without Correspondence From Tomographic Projections by Bayesian Inversion Theory

In conventional tomography, the interior of an object is reconstructed from tomographic projections such as X-ray or transmission electron microscope images. All the current reconstruction methods assume that projection geometry of the imaging device is either known or solved in advance by using e.g., fiducial or nonfiducial feature points in the images. In this paper, we propose a novel approach where the imaging geometry is solved simultaneously with the volume reconstruction problem while no correspondence information is needed. Our approach is a direct application of Bayesian inversion theory and produces the maximum likelihood or maximum a posteriori estimates for the motion parameters under the selected noise and prior distributions. In this paper, the method is implemented for a two-dimensional model problem with one-dimensional affine projection data. The performance of the method is tested with simulated and measured X-ray projection data