Basic image processing for EM Carlos Óscar S. Sorzano Instruct Image Processing Center

Basic image processing What’s an image? Image coding Sampling Basic operations with an image Fourier transform

What’s an image? Quantization (bits) Sampling (pixels)

Image coding

Image coding Demo

What’s an image? Quantization (bits) Sampling (pixels)

Spatial sampling Demo

Pixel size for EM Desired resolution: R (e.g., 4Å) Nyquist Sampling rate: (e.g., <2Å/pixel) (e.g., <1.67Å/pixel) Typical Sampling rate:

So, what?

Image level operations

Pixel level operations

Demo Histogram normalization

Pixel level operations Histogram stretching

Pixel level operations Image normalization

Pixel level operation Mean=0 Stddev=1 Normalization Sorzano, C. O. S.; de la Fraga, L. G.; Clackdoyle, R. & Carazo, J. M. Normalizing projection images: A study of image normalizing procedures for single particle three-dimensional electron microscopy Ultramicroscopy, 2004, 101,

Group level operations Demo

Group level operations

Demo Sharpening

Group level operations Sharpening Fernández, J. J.; Luque, D.; Castón, J. R. & Carrascosa, J. L. Sharpening high resolution information in single particle electron cryomicroscopy. J Struct Biol, 2008, 164,

Group level operations Smoothing

Group level operations Correlation

Group level operations Correlation

Geometric transformations

Interpolation Demo

Downsampling/Binning Sorzano, C. O. S.; Iriarte-Ruiz, A.; Marabini, R. & Carazo, J. M. Effects of the downsampling scheme on three-dimensional electron microscopy of single particles Proc. of IEEE Workshop on Intelligent Signal Processing, 2009 Remind Nyquist

Fourier Transform Original waveDecompositionApproximation DemoDemo Fourier Transform 2D DemoDemo Fourier Transform 1D DemoDemo Sine waves

Fourier Transform

Filters in Fourier space Demo

Filters in Fourier space Demo Demo band pass filter

Quasi optical filtering

Deconvolution in Fourier space

Central slice theorem Nogales, Scheres. Molecular Cell, 58: (2015)

Central slice theorem Nogales, Scheres. Molecular Cell, 58: (2015)

Central slice theorem Nogales, Scheres. Molecular Cell, 58: (2015)

Projection Matching Nogales, Scheres. Molecular Cell, 58: (2015)

Projection matching and Central Slice Theorem Nogales, Scheres. Molecular Cell, 58: (2015)

Conclusions The quality of an image depends on its bit depth and its sampling rate Being a matrix of numbers, we can perform many operations with images at the level of: – Full images – Pixels – Groups of pixels – Geometrical transformations – Transformations Fourier transforms are one of the most important transformations for EM