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FEM: feature-enhanced map.

Afonine PV, Moriarty NW, Mustyakimov M, Sobolev OV, Terwilliger TC, Turk D, Urzhumtsev A, Adams PD - Acta Crystallogr. D Biol. Crystallogr. (2015)

Bottom Line: This is followed by restricting the map to regions with convincing density and the application of sharpening.The final map is then created by combining a series of histogram-equalized intermediate maps.In the test cases shown, the maps produced in this way are found to have increased interpretability and decreased model bias compared with the starting 2mFobs - DFmodel σA-weighted map.

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Affiliation: Physical Biosciences Division, Lawrence Berkeley National Laboratory, One Cyclotron Road, MS64R0121, Berkeley, CA 94720, USA.

ABSTRACT
A method is presented that modifies a 2mFobs - DFmodel σA-weighted map such that the resulting map can strengthen a weak signal, if present, and can reduce model bias and noise. The method consists of first randomizing the starting map and filling in missing reflections using multiple methods. This is followed by restricting the map to regions with convincing density and the application of sharpening. The final map is then created by combining a series of histogram-equalized intermediate maps. In the test cases shown, the maps produced in this way are found to have increased interpretability and decreased model bias compared with the starting 2mFobs - DFmodel σA-weighted map.

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Fourier map distribution along the Mg—O—H line (blue) and its histogram-equalized version (red). Left, original map; right, map truncated with ρtrunc = 0 if ρ < 0.05. Note the enhancement of noise peaks as a result of applying HE (left, red line).
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fig15: Fourier map distribution along the Mg—O—H line (blue) and its histogram-equalized version (red). Left, original map; right, map truncated with ρtrunc = 0 if ρ < 0.05. Note the enhancement of noise peaks as a result of applying HE (left, red line).

Mentions: The histogram-equalization (HE) method (see, for example, Hummel, 1975 ▶, 1977 ▶) is used to transform map values over the entire unit-cell volume to generate a uniform distribution of map values. This method nonlinearly (but monotonically) transforms the image values to enhance the contrast and is a routine tool in the digital image-processing field. Fig. 12 ▶ illustrates the effect of HE applied in two dimensions to a photograph. The method works similarly in three dimensions when applied to Fourier maps. After applying HE to a crystallographic map the strong and weak peaks become more equal (Fig. 13 ▶). Obviously, the noise is equalized as well (compare Figs. 14 ▶a and 14 ▶b), so it is essential that it is maximally removed before applying HE. Fig. 15 ▶ provides an additional (and somewhat simpler) illustration of the effect of HE on a 1 Å resolution Fourier map calculated using a test model of three atoms (Mg, O and H) placed in a P1 box. The three atoms were chosen specifically to yield map peaks of very different heights.


FEM: feature-enhanced map.

Afonine PV, Moriarty NW, Mustyakimov M, Sobolev OV, Terwilliger TC, Turk D, Urzhumtsev A, Adams PD - Acta Crystallogr. D Biol. Crystallogr. (2015)

Fourier map distribution along the Mg—O—H line (blue) and its histogram-equalized version (red). Left, original map; right, map truncated with ρtrunc = 0 if ρ < 0.05. Note the enhancement of noise peaks as a result of applying HE (left, red line).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4356370&req=5

fig15: Fourier map distribution along the Mg—O—H line (blue) and its histogram-equalized version (red). Left, original map; right, map truncated with ρtrunc = 0 if ρ < 0.05. Note the enhancement of noise peaks as a result of applying HE (left, red line).
Mentions: The histogram-equalization (HE) method (see, for example, Hummel, 1975 ▶, 1977 ▶) is used to transform map values over the entire unit-cell volume to generate a uniform distribution of map values. This method nonlinearly (but monotonically) transforms the image values to enhance the contrast and is a routine tool in the digital image-processing field. Fig. 12 ▶ illustrates the effect of HE applied in two dimensions to a photograph. The method works similarly in three dimensions when applied to Fourier maps. After applying HE to a crystallographic map the strong and weak peaks become more equal (Fig. 13 ▶). Obviously, the noise is equalized as well (compare Figs. 14 ▶a and 14 ▶b), so it is essential that it is maximally removed before applying HE. Fig. 15 ▶ provides an additional (and somewhat simpler) illustration of the effect of HE on a 1 Å resolution Fourier map calculated using a test model of three atoms (Mg, O and H) placed in a P1 box. The three atoms were chosen specifically to yield map peaks of very different heights.

Bottom Line: This is followed by restricting the map to regions with convincing density and the application of sharpening.The final map is then created by combining a series of histogram-equalized intermediate maps.In the test cases shown, the maps produced in this way are found to have increased interpretability and decreased model bias compared with the starting 2mFobs - DFmodel σA-weighted map.

View Article: PubMed Central - HTML - PubMed

Affiliation: Physical Biosciences Division, Lawrence Berkeley National Laboratory, One Cyclotron Road, MS64R0121, Berkeley, CA 94720, USA.

ABSTRACT
A method is presented that modifies a 2mFobs - DFmodel σA-weighted map such that the resulting map can strengthen a weak signal, if present, and can reduce model bias and noise. The method consists of first randomizing the starting map and filling in missing reflections using multiple methods. This is followed by restricting the map to regions with convincing density and the application of sharpening. The final map is then created by combining a series of histogram-equalized intermediate maps. In the test cases shown, the maps produced in this way are found to have increased interpretability and decreased model bias compared with the starting 2mFobs - DFmodel σA-weighted map.

Show MeSH