Summary

We developed a parametric active-contour algorithm for reconstructing the 3D shape of DNA filaments from a matched pair of tilted cryo-electron micrographs.

Main Contribution

We proposed a model-based algorithm 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 specify 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. 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.

To accelerate the computation of the rotating matched filter, we introduced the concept of projection-steerable filtering. Specifically, we consider an elongated blob-like template whose projection in any direction can be expressed as a linear combination of a few basis functions (derivatives of Gaussians). The weights are simple functions of the 3-D orientation and the required inner-products between the basis functions and the micrographs are evaluated by separable filtering.