Learning Tomography: Playing with dots

Last post [Link] was devoted to the problem of rotation center during the reconstruction process. Here is a small exploration of the various patterns that can be observed...


Here is a test input image composed of five dots drawn with the pencil Tool ...

Fig.1: Five dots respectively located at (185;198), (101;169), (150;135), (75;85), and (201;72) in a 256x256 8-bit black image.

or use the following macro/script...

// Sample image
newImage("FiveDots", "8-bit Black", 256, 256, 1);
setColor(255,255,255);
setPixel(185,198,255);
setPixel(101,169,255);
setPixel(150,135,255);
setPixel(75,85,255);
setPixel(201,72,255);

and the corresponding sinogram computed with the script sinogram.js [Link] ...

Fig.2: Sinogram of Fig.1.

1- Moving the rotation center along X-axis...

Four sinograms were calculated by shifting along the X axis its rotation center in the range of [-20;+20] and reconstructed with the script backProjImproved.js leading to the images of Fig. 3.

Fig.3: Reconstructions calculated from sinograms whose rotation centers are shifted along X of -20, -10,+10, +20, respectively. The dots appear as arcs whose radii correspond to the shift value and whose orientation (down- and upwards) is related to the X-shift sign.

As seen in the previous post with Lena [Link], the dots appear as arcs pointing down- or upwards depending of the sign of the shift and whose radii correspond to the shift values. Moreover, the arcs obtained from different shifts are not centered but are all starting from the original position of the dots (Fig. 4).

Fig.4: Superimposition of the input image (green dots) and the arcs (in red) obtained in Fig.3. For sake of clarity, the dots were dilated.

Note: To create the image of Fig. 4, download montage of Fig.3, then, convert it into a stack with Image > Stack >Tools> Montage to Stack... and choose 4, 1, and 2 as parameters, then use Image> Color > Merge Channels... to build a RGB image.

2- Shifting along Y-axis...

And now, what about shift along the Y-axis ? To answer this question, the same procedure as before is used ... and the result is ...



Dots but moving along the arcs

In conclusion, if your projections contain dotted features, their shapes can inform you if the centration is good or not ?


Hope this helps.

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Other crazybiocomputing posts

Further readings are available in ...

• Learning Tomography Series  [Link]
• Image Processing TOC [Link]