3 D Reconstruction of DNA Filaments from Stereo

3 -D Reconstruction of DNA Filaments from Stereo Cryo-Electron Micrographs Mathews Jacob, Thierry Blu and Michael Unser Biomedical Imaging Group, Swiss Federal Institute of Technology, Lausanne (EPFL) Summary 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. 3 -D Reconstruction (Active contour algorithm) • Semi-automatic Tracking • 3 -D spline curve Cubic Bspline • Implicit internal energy Minimum eigen value and the corresponding eigen vector of Stereo views separated by 30 degrees § Easy optimization • Projected onto image planes • Projection also spline curve • Optimized to maximize the cost function Vector field on the kth image Optimally elongated second order template • Conjugate gradients optimization • Distance map to enhance convergence Visualization of 3 -D reconstruction Challenges • Extremely Noisy • Ill posed due to few views • At least 2 possible curves exist • Maximally flat along the axis of orientation Corresponding points Ridge enhancing vector field Phase Thresholded vector field Conclusions • 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 bigwww. epfl. ch Curve projection onto image plane