# A common lines approach for ab-initio modeling of molecules with tetrahedral and octahedral symmetry

arXiv: https://arxiv.org/abs/2206.08623 · HTML: https://mlsanity.com/paper/2206.08623/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jun 2022.

## Built on by (most cited first, 1 of 1)

- [Orientation Estimation of Cryo-EM Images for Molecules with Arbitrary Symmetry by Semidefinite Programming](https://mlsanity.com/paper/2610.18691/) (2026)

## Abstract (arXiv)

A main task in cryo-electron microscopy single particle reconstruction is to find a three-dimensional model of a molecule given a set of its randomly oriented and positioned noisy projection-images. In this work, we propose an algorithm for ab-initio reconstruction for molecules with tetrahedral or octahedral symmetry. The algorithm exploits the multiple common lines between each pair of projection-images as well as self common lines within each image. It is robust to noise in the input images as it integrates the information from all images at once. The applicability of the proposed algorithm is demonstrated using experimental cryo-electron microscopy data.