Summary

1
3-D Reconstruction of DNA Filaments from Stereo
Cryo-Electron Micrographs
Mathews Jacob, Thierry Blu and Michael Unser

• Summary

3-D Reconstruction (Active contour algorithm)
Steerable filter implementation
We propose an algorithm for the 3-D
reconstruction of DNA filaments from a pair of
stereo cryo-electron micrographs. The underlying
principle is to specify a 3-D model of a filament
-- described as a spline curve -- and to fit it
to the 2-D data using a snake-like algorithm. To
drive the snake, we constructed a ridge-enhancing
vector field for each of the images based on the
maximum output of a bank of rotating matched
filters. The magnitude of the field gives a
confidence measure for the presence of a filament
and the phase indicates its direction. We also
propose a fast algorithm to perform the matched
filtering. The snake algorithm starts with an
initial curve (input by the user) and evolves it
so that its projections on the viewing plane are
in maximal agreement with the corresponding
vector fields.

• Semi-automatic Tracking
• 3-D spline curve
• Implicit internal energy
• Easy optimization
• Projected onto image planes
• Projection also spline curve
• Optimized to maximize the cost function
• Conjugate gradients optimization
• Distance map to enhance convergence

Cubic Bspline
Minimum eigen value and the corresponding eigen
vector of
Vector field on the kth image
Stereo views separated by 30 degrees
Optimally elongated second order template
Curve projection onto image plane
Visualization of 3-D reconstruction
Challenges

• Maximally flat along the axis of orientation

• Extremely Noisy
• Ill posed due to few views
• At least 2 possible curves exist

Corresponding points
Ridge enhancing vector field
Thresholded vector field
Conclusions
Phase

• 2-D Ridge Enhancing Vector Field
• Rotational Matched Filtering
• Confidence measure and direction
• Steerable filter implementation
• Semi-automatic tracking - Snake Fit
• 3-D curve model
• Cubic bspline representation
• Projections matched with 2-D vector fields
• Conjugate gradients optimization

Magnitude

• Rotated Matched Filtering