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Processing and Reconstruction of Cryogenic Electron Microscope Tomography Images. Automatic tracking of fiducial markers across very low SNR images. Fernando Amat Farshid Moussavi Mark Horowitz LBL meeting-September 2006. Cryogenic Electron Microscope Tomography.

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processing and reconstruction of cryogenic electron microscope tomography images

Processing and Reconstruction of Cryogenic Electron Microscope Tomography Images

Automatic tracking of fiducial markers across very low SNR images

Fernando Amat

Farshid Moussavi

Mark Horowitz

LBL meeting-September 2006

cryogenic electron microscope tomography
Cryogenic Electron Microscope Tomography
  • Take ~100 electron microscope images at different tilt angles and with finite dose budget (low SNR)
  • Align, reproject 2D images, do 3D reconstruction.
  • Quality of 3D reconstruction directly related to quality of 2D preprocessing.
brief problem statement
Brief problem statement

Caulobacter Images

?

Very low SNR, faint features. Use fiducial markers.

Automatically find accurate correspondences in images for alignment.

outline
Outline
  • A Probabilistic Framework solution
  • Results
  • Future work
  • Discussion/Conclusions
steps of preparation for reconstruction
Steps of Preparation for Reconstruction
  • Incomplete and unreliable data at first
  • Incorrect decisions cause more incorrect decisions downstream (errors propagate)

Robust probabilistic framework

probabilistic framework
Probabilistic Framework
  • Maximum Likelihood Estimation. We want to find assignment to variables X ,Θ,y that maximizes :

P(X ,Θ,y |O)

  • X , the set of 3D marker locations ‹R3xM,
  • y, the set of trajectories across images ‹ R2xMxN
  • Θ, set of microscope parameters
  • O, the set of observed peaks in the 2D images ‹ R2xMxN
  • (M=number of contours, N=number of images)
probabilistic framework cont d
Probabilistic Framework (cont’d)
  • But we have the observed peaks, not the trajectories.
  • Correspondence is a discrete problem.
  • Projection model estimation is a continuous optimization problem.
  • We need to split the problem

P(X ,Θ,y|O)=P(X ,Θ|y,O) * P(y|O)

Projection model Correspondence

probabilistic framework block diagram

Aligned, reprojected images to 3D

Reconstruction

Feature

Detection/

Location

Correspondence

Projection Model Estimation

2D

Images

Probabilistic framework: block diagram

Finds O (peaks) Finds argmax P(y|O) Finds argmax P(X ,Θ|y,O)

{y} {X ,Θ}

correspondence

M1

K1

M2

K2

M3

K3

Mm

Kk

Correspondence
  • What is probability p(M->K) that i-th peak in image 1 corresponds to j-th peak in image 2?
  • Bipartite graph matching problem- O(N!)
  • Scores for individual matches may not be informative enough (look at groups of matches)

How to make decisions with all this uncertainty?

Markov Random Fields

correspondence using markov random fields
Correspondence using Markov Random Fields
  • Discrete problem in nature
  • We estimate joint pairwise correspondence for all peaks in image 1 and 2 at the same time
  • Use simple geometric constraints
    • No use of projective model->robust to distortions
    • Invariant to translations->no need of prealign images
  • Complexity is exponential in number of peaks
  • Use approximate techniques which treat a joint distribution over M variables as a collection of pairwise distributions (complexity becomes O(M2))
projection model
Projection model
  • Find the solution to:

D([x,y]T-[R|t][X Y Z 1]T) (1)

    • [x,y]: known points from correspondence
    • [R|t]: projective model (partially unknown)
    • [X Y Z]: 3D markers position (unknown)
    • D(): cost function
  • (1) is the ML solution to P(X ,Θ|y,O) assuming certain error model distribution for reprojection errors (related to D())
results caulo 19 tomogram
Results: Caulo 19 tomogram

Manual reconstruction by Luis R. Comolli

results caulo 19 tomogram1
Results: Caulo 19 tomogram

Fully automatic reconstruction

results cykr he1 tomogram
Results: CyKR-He1 tomogram

Manual reconstruction by Luis R. Comolli

results cykr he1 tomogram1
Results: CyKR-He1 tomogram

Fully automatic reconstruction

results
Results
  • Other tomogram reconstructions for different specimens are available.
  • They are not shown here to keep the talk short.
future work
Future work
  • Occlusion: solve problems in high tilt angles for group of markers
  • Speed up the process
  • Extend Markov Random Fields correspondence to multiple images
  • Iterate correspondence and 3D model estimation using Expectation-Maximization if results are not satisfactory in one single pass
discussions conclusions
Discussions/Conclusions
  • Fully automated process to align images with fiducial markers: only a template of a marker is needed as an input
  • Accuracy results comparable to manual alignment in very low SNR images
  • Robust to distortions and error propagation