Abstract: Systems and methods are described for the fully automatic, template-free locating and extracting of a plurality of two-dimensional projections of particles in a micrograph image. A set of reference images is automatically assembled from a micrograph image by analyzing the image data in each of a plurality of partially overlapping windows and identifying a subset of windows with image data satisfying at least one statistic criterion compared to other windows. A normalized cross-correlation is then calculated between the image data in each reference image and the image data in each of a plurality of query image windows. Based on this cross-correlation analysis, a plurality of locations in the micrograph is automatically identified as containing a two-dimensional projection of a different instance of the particle of the first type. The two-dimensional projections identified in the micrograph are then used to determine the three-dimensional structure of the particle.

Abstract: Methods and systems are described for digitally reconstructing an unknown 3D structure of a target molecule using orthogonal extension. A plurality of 2D images of the target molecule are captured by an imaging system. An estimated low-order moment of the unknown 3D structure (e.g., a covariance matrix) is calculated based on the 2D images. A homologous molecule having a known 3D structure is identified and at least one expansion coefficient of the known structure of the homologous molecule is determined. At least one estimated expansion coefficient for the unknown structure is calculated based at least in part on the estimated low order moment of the unknown structure and the at least one expansion coefficient of the known structure. An estimated 3D reconstruction of the target molecule is then generated based on the at least one estimated expansion coefficient for the unknown structure of the target molecule.

Abstract: Methods and systems are described for digitally reconstructing an unknown 3D structure of a target molecule using orthogonal extension. A plurality of 2D images of the target molecule are captured by an imaging system. An estimated low-order moment of the unknown 3D structure (e.g., a covariance matrix) is calculated based on the 2D images. A homologous molecule having a known 3D structure is identified and at least one expansion coefficient of the known structure of the homologous molecule is determined. At least one estimated expansion coefficient for the unknown structure is calculated based at least in part on the estimated low order moment of the unknown structure and the at least one expansion coefficient of the known structure. An estimated 3D reconstruction of the target molecule is then generated based on the at least one estimated expansion coefficient for the unknown structure of the target molecule.

Abstract: Systems and methods are described for the fully automatic, template-free locating and extracting of a plurality of two-dimensional projections of particles in a micrograph image. A set of reference images is automatically assembled from a micrograph image by analyzing the image data in each of a plurality of partially overlapping windows and identifying a subset of windows with image data satisfying at least one statistic criterion compared to other windows. A normalized cross-correlation is then calculated between the image data in each reference image and the image data in each of a plurality of query image windows. Based on this cross-correlation analysis, a plurality of locations in the micrograph is automatically identified as containing a two-dimensional projection of a different instance of the particle of the first type. The two-dimensional projections identified in the micrograph are then used to determine the three-dimensional structure of the particle.