A package for noise reduction in electron tomography with Anisotropic Nonlinear Diffusion

J.J. Fernández (1,2,3), S. Li (1,4), V. Lucic (5)

(1)  MRC Laboratory of Molecular BiologyCambridge CB2 2QH, UK.
(2) Dept. Computer Architecture. Univ. Almeria. 04120 Almeria. Spain.
(3) Centro Nacional de Biotecnologia - CSIC, Madrid, Spain. (present address)
(4) Dept. Biochemistry and Biophysics. UCSF. USA. (present address)
(5) Dept. Structural Biology, MPI Biochemistry, Martinsried, Germany.

Contact: @


This package implements a 3D anisotropic nonlinear diffusion method for filtering noise in tomograms. The package comprises two programs, tomoeed and tomoand. The first program, tomoeed, contains an optimized implementation of the EED (Edge-Enhancing Diffusion) mode. It has significantly reduced memory requirements and uses code optimization and multithreading to exploit current multicore computers. Furthermore, options to help tune the parameter are provided. The second program, tomoand, combines the EED (Edge-Enhancing Diffusion) and CED (Coherence-Enhancing Diffusion) diffusion modes simultaneously. The processing of the voxels as CED or EED is based on a threshold computed from an area of the input volume that contains only noise. Globally, the program analyzes each voxel in the volume to define if it is part of (1) an isotropic feature or noise or (2) a plane-like or line-like feature. For the former (1), EED is applied, i.e. structure-preserving filtering is applied to smooth the volume, but preserving edges. For the latter (2), CED is applied, i.e. the idea is to enhance the structures: in lines, smoothing is applied along the lines; For planes, smoothing is applied across the plane. The present version of tomoand contains some new improvements, such as a strategy to further smooth the background, the automatic tuning of the parameters related to EED and CED, the stopping criterion based on Noise Estimate Variance, and finally code optimization and multithreading are used to reduce the processing time.

A detailed description of the procedure implemented in the package are described in the following articles:

An improved algorithm for anisotropic nonlinear diffusion for denoising cryotomograms
J.J. Fernandez, S. Li.
Journal of Structural Biology 144:152-161, 2003.

Anisotropic nonlinear filtering of cellular structures in cryoelectron tomography
J.J. Fernandez, S. Li.
Computing in Science and Engineering 7(5):54-61, 2005.

Three-dimensional anisotropic noise reduction with automated parameter tuning. Application to electron cryotomography
J.J. Fernandez, S. Li, V. Lucic.
Lecture Notes in Computer Science 4788:60-69, 2007.

Please, cite (any of) these articles if you use TOMOAND in your works.

Current version: September 2011

Available material:
  • Documentation in PDF:      tomoand.pdf   ,   tomoeed.pdf  

  • Binaries for x86-based platforms under linux (64 and 32 bits)

  • Binaries for Intel-based Macs under OSX (10.6 and onwards)

The development of tomoand has been supported by the Medical Research Council, the Spanish MEC and MCI, J.Andalucia, Human Frontier Science Program, European Molecular Biology Organization and the 3DEM Network of Excellence.

Copyright by the authors.