Abstract: 

This paper addresses the problem of reconstructing the density of scene from multiple projection images produced by modalities such as x-ray, electron microscopy, etc. where an image value is related to the integral of the scene density along a 3D line segment between a radiation source and a point on the image plane. While computed tomography (CT) addresses this problem when the absolute orientation of the image plane and radiation source directions are known, this paper addresses the problem when the orientations are unknown is akin to the structure-from-motion (SFM) problem when the extrinsic camera parameters are unknown. We study the problem within the context of reconstructing the density of protein macro-molecules in Cryogenic Electron Microscopy (cryo-EM), where images are very noisy and existing techniques use several thousands of images. In a non-degenerate configuration, the viewing planes corresponding to two projections, intersect in a line in 3D. Using the geometry of the imaging setup, it is possible to determine the projections of this 3D line on the two image planes. In turn, the problem can be formulated as a type of orthographic structure from motion from line cor- respondences where the line correspondences between two views are unreliable due to image noise. We formulate the task as the problem of denoising a correspondence matrix and present a Bayesian solution to it. Subsequently, the ab- solute orientation of each projection is determined followed by density reconstruction. We show results on cryo-EM im- ages of proteins and compare our results to that of Electron Micrograph Analysis (EMAN) -- a widely used reconstruction tool in cryo-EM.

Results: 

[A]	[B]

The left images in [A] and [B] show the top and side views of a macro-molecule called GroEL produced from a 11.5 Å reconstruction in a publicly available Molecular Structure Database. The second images show the initial model estimated using EMAN -- A widely used tool in cryo-EM. The right images show the initial model estimated using our method. The same dataset was used to generate the two initial models.

[A]	[B]
[C]	[D]

The figure shows a comparison of our method with EMAN. The columns in the figure denote different stages of refinement starting with the initial model shown in the first column. [A] and [B] show the refinement of the top and side views of the initial model obtained using EMAN while [C] and [D] show the refinement of the top and side views of the initial model obtained using our method. The refinement is done using routines available in EMAN. The ground truth is shown in Fig. 1. Using the initial model obtained by EMAN, the refinement procedure starts to converge after the fourth iteration. In contrast, the gross shape of the GroEL is already visible in the second refinement iteration on our initial model.

• Satya P. Mallick, Sameer Agarwal, David J. Kriegman, Serge J. Belongie, Bridget Carragher, Clinton S. Potter "Vision in the Small: Reconstructing the Structure of Protein Macromolecules from Cryo-Electron Micrographs ", British Machine Vision Conference, Volume I, Pages 1-6, September 2006, Edinburgh, United Kingdom.

• S. M. Stagg, G. C. Lander, J. Pulokas, D. Fellmann, A. Cheng, J. D. Quispe, S. P. Mallick, R. M. Avila, B. Carragher, and C. S. Potter, " Automated cryoEM data acquisition and analysis of 284,742 particles of GroEL", Journal of Structural Biology, Volume 155, Issue 3,September 2006, Pages 470-481.

• Satya P. Mallick, Sameer Agarwal, David J. Kriegman, Serge J. Belongie, Bridget Carragher, Clinton S. Potter "Structure and View Estimation for Tomographic Reconstruction: A Bayesian Approach.", Computer Vision and Pattern Recongnition, Volume II, Pages 2253-2260, June 2006, New York.