Model bias in cryo-EM - Einstein from noise

 

 
 
In the article of Maxim Shatsky et al.  entitled "A Method for the Alignment of Heterogeneous Macromolecules from Electron Microscopy" (J Struct Biol. 2009, 166(1): 67–78. doi:10.1016/j.jsb.2008.12.008.), the authors show that pure noise images aligned to a reference image give an average image resembling the reference. This is a perfect example of the model bias occurring during the 2D classification step. Let's do it!!!

1- Pre-processing

In the article, they chose the iconic image of Einstein by Arthur Sasse. I just crop and resize this image in 128x128. Additionally, I convert it in 32-bits (Image > Type > 32-bits) and rescale the image in order to have a zero mean and a sigma equal to 1.0 (Process > Math > Macro with a formula v=(v-mean)/stdev ). To get the values of mean and stdev, the simplest way is to calculate the histogram (Analyze > Histogram) (Fig.1).

Fig.1: Reference image inspired by those used in the article of Shatsky et al. This image is copyrighted and I did not granted permission, so this image will be removed upon request.

2. 2D alignment by cross-correlation

3. The source code

The script below is composed of three parts:

• (i) Initialization 
• (ii) Creation of the stack of gaussian noise slices
• (iii) 2D alignment of noise to the reference by cross-correlation

 

The computation of the average image from the "aligned" stack is not included in the script. You can easily do that in (Image > Stacks > Z-Project and choose Average Intensity).

 

+++ IJ JavaScript snippet +++

	/*
	Model Bias by aligning from a reference
	Jean-Christophe Taveau
	2022/07/19
	*/
	IJ.log('\\Clear');
	// Einstein
	const ref = IJ.getImage();
	const refName = ref.getTitle();
	const size = ref.getWidth();
	const half = ref.getWidth()/2.0;
	// Create stack of N images of pure gaussian noise
	const N=300;
	const noise = IJ.createImage("Noise", "32-bit black", size, size, N);
	const stack = noise.getImageStack();
	for (let i=0; i < stack.getSize();i++) {
	stack.getProcessor(i+1).noise(1.0);
	}
	noise.show();
	// Align to a reference
	for (let i=0; i < stack.getSize();i++) {
	let tmp = new ImagePlus("NoiseFrame",stack.getProcessor(i+1));
	tmp.show();
	IJ.run(tmp, "FD Math...", `image1=${refName} operation=Correlate image2=NoiseFrame result=Result_${i} do`);
	let corrmap = WindowManager.getImage(`Result_${i}`);
	const ce = new ContrastEnhancer();
	ce.setNormalize(true);
	ce.stretchHistogram(corrmap,0.0);
	// Force update
	corrmap.updateAndDraw();
	IJ.log(`${i}: ${corrmap.getTitle()}`);
	let maxFinder = new MaximumFinder();
	const list = maxFinder.getMaxima(corrmap.getProcessor(), 0.8, 0);
	// IJ.log(`${i+1}: ${list.xpoints.length},${list.ypoints.length},${list.xpoints[0]},${list.ypoints[0]}`);
	const tx = half - list.xpoints[0];
	const ty = half - list.ypoints[0];
	noise.setSlice(i+1);
	IJ.run(noise, "Translate...", `x=${-tx} y=${-ty} interpolation=Bilinear slice`);
	tmp.close();
	corrmap.close();
	}

view raw model_bias_in_reference_alignment.js hosted with ❤ by GitHub

+++End of JavaScript snippet +++

 

4. Results 

 

Fig. ???: Correlations maps

 

Fig. ???: Aligned noisy images

Fig. ???: Average Images calculated from 25,100, 500, and 1000 noisy images, respectively.

 

 Thank you for reading.

5. Other crazybiocomputing posts

Further readings are available in ...

• CryoEM Series  [Link]
• Image Processing TOC [Link]