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

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

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

4. Image coding

5. 202 189 195 221 248 248 240 244 232 228 234 212 189 172 171 182 186 211 191 191 222 247 250 247 245 238 234 205 148 110 128 148 159 171 205 181 184 222 250 255 255 250 238 191 97 58 80 97 106 123 130 192 182 197 237 250 255 255 240 175 97 96 104 104 94 87 84 70 184 188 214 244 253 255 232 163 123 140 159 153 153 143 128 107 77 188 221 250 255 230 139 116 122 128 145 145 139 110 166 175 152 120 209 241 255 211 113 90 97 96 99 110 109 94 43 104 153 110 84 235 255 191 87 70 70 69 73 47 46 47 38 15 41 66 33 25 250 176 70 51 46 35 27 31 24 23 18 17 18 24 30 23 11 166 64 35 31 20 20 20 21 21 14 11 14 18 51 93 77 35 51 46 33 18 12 18 23 18 17 15 11 25 40 103 212 204 122 63 46 24 12 8 33 61 35 40 33 8 37 64 89 244 255 231 66 38 24 17 12 47 90 67 58 71 35 54 74 80 248 255 255 94 76 63 30 14 47 96 109 56 67 69 63 57 163 255 255 255 125 119 107 71 20 37 90 113 106 63 47 74 153 250 255 255 255 143 151 145 135 115 87 84 93 117 135 155 175 199 222 234 234 227 142 148 149 149 139 119 125 115 97 107 94 130 145 148 155 149 181 148 151 151 149 151 148 148 128 112 116 93 129 140 132 122 129 168 156 158 161 151 146 152 158 142 138 135 123 133 143 142 140 159 174 165 163 169 168 166 165 159 149 153 151 146 151 158 168 171 181 186 169 174 181 184 182 182 178 171 172 176 174 182 188 194 197 198 192

6. Image coding Demo

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

8. Spatial sampling Demo

9. 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:

10. So, what?

11. Image level operations

14. Pixel level operations

15. Demo Histogram normalization

16. Pixel level operations Histogram stretching

17. Pixel level operations Image normalization

18. 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, 129-138

19. Group level operations Demo

20. Group level operations

21. Demo Sharpening

22. 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, 170-175

23. Group level operations Smoothing

24. Group level operations Correlation

25. Group level operations Correlation

26. Geometric transformations

28. Interpolation Demo

29. 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

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

31. Fourier Transform

34. Filters in Fourier space Demo

35. Filters in Fourier space Demo Demo band pass filter

36. Quasi optical filtering

39. Deconvolution in Fourier space

42. Central slice theorem Nogales, Scheres. Molecular Cell, 58: 677-689 (2015)

43. Central slice theorem Nogales, Scheres. Molecular Cell, 58: 677-689 (2015)

44. Central slice theorem Nogales, Scheres. Molecular Cell, 58: 677-689 (2015)

45. Projection Matching Nogales, Scheres. Molecular Cell, 58: 677-689 (2015)

46. Projection matching and Central Slice Theorem Nogales, Scheres. Molecular Cell, 58: 677-689 (2015)

47. 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