Before starting the image preprocessing, in the next section, here is the presentation of different methods of compositing images. As we saw in the section on suggested exposure times, the assembly of several images makes it possible to reduce the background noise and thus improve the richness of the details revealed.
There are at least 4 methods of compositing:
- The additive method
- The average
- The median method
- The Sigma-clip method
I remind you that the compositing of several images makes it possible to reduce the noise according to the following formula:
% remaining noise = 1 / √ number of images
For example, compositing 10 images reduces noise by 68,4%, 20 images 77,6%, 50 images 85,9%… For more details, see the table in the section on suggested exposure times.
The longer the exposure time per image, the more we are exposed to picking up stray signals such as airplane light trails, shooting stars, satellites, cosmic rays, etc. It will be seen that methods make it possible to attenuate and even completely eliminate these parasites.
1- The additive method
The additive method essentially consists of adding the images. It therefore increases the signal proportionally for each image added. The main drawback of this method is that it tends to saturate the stars. The stars become "Clipper". The result is a loss of detail in bright places in the image (like the nucleus of a galaxy). In addition, it does not eliminate light interference when taking photos as well as hot pixels (Bad Pixels) which may persist even after subtracting the Black image (dark). On the other hand, it makes it possible to take full advantage of the noise reduction formula presented above.
2- The average (Averaging in English)
As its name suggests, the average is used to add the images and make an average of them. For example, if we took 10 images, it will add the images and divide the whole by 10. Its main advantage is to avoid overexposing or saturating the stars. It also makes it possible to fully benefit from the noise reduction formula. However, it does not eliminate light interference when shooting and hot pixels (Bad Pixels).
3- The median method
At first glance, the median method may look like the mean except that it does not retain extreme values. For each pixel, it retains the central value (or central values). For example in the following sequence of 5 images (in 8 bits) classified in ascending order: 98, 99, 101, 102, 255, the median value retained will be 101 for this pixel while the average will be 131. OWe immediately notice that pixel 255, representing a hot pixel, will not be retained in the median although it will be part of the average. Its main advantage is therefore to eliminate the light interference captured when taking photos and the remaining hot pixels. On the other hand, it does not make it possible to fully benefit from the noise reduction formula. Indeed, by just retaining the central value (or the central values), it cannot benefit from the noise reduction offered by the integration of several images, thus letting appear more background noise (grain) in the image. .
4- The Sigma-clip or Sigma Combine method
The Sigma-clip method, also called Sigma Combine and Standard Deviation, uses a sophisticated noise reduction algorithm. It allows you to take full advantage of the noise reduction formula. It does not saturate the stars in addition to eliminating light interference when shooting and hot pixels.
To work well, it requires more effort than other methods. Before using it, the intensity of the images to be stitched must be normalized. This normalization makes it possible to balance the signal so that it is identical for all the images to be assembled. This normalization is important, especially if the imaging session is performed over more than one night. Then, we must align the images between them (instead of immediately composing the images, we align them individually with respect to each other without stitching them together). Standard alignment methods such as one or two guide star (s), Drizzle, etc. are used. From this moment the method can be used correctly (it should be noted that the Maxim DL software allows all these steps to be carried out in a single operation).
The noise reduction algorithm is mainly used to compare the images with each other. If a small number of images contain information that the majority do not have, it erases that information in the composite result. For this reason, it is recommended to take at least 10 individual images for the comparison between the images to work well. The evaluation is carried out pixel by pixel. He is doing then the average of the pixels retained thus making it possible to maximize the noise reduction formula. It is therefore a very effective method to remove light interference when shooting and hot pixels. Regarding the latter, they always appear in the same place on each of the individual images. When aligning images, repositioning each individual image on the guide star moves the hot pixels onto the individual images. As they are no longer in the same place on each aligned image, the algorithm erases these hot pixels in the composite result. To improve the efficiency of cleaning hot and cold pixels (black points), it is recommended to acquire the images in Dithering.
The Sigma-clip method offers a choice of filters ranging from 1 to 3 (with the majority of theosoftware). On average, over a large number of images, filter 3 retains about 98% of the pixels. The filter 1, 68%. It is therefore suggested to start with filter 3 and if the faults do not all disappear, to progress to filter 2 and so on. Therefore, the more the value of the filter is reduced, the more there are information rejections considered as noise. It is therefore necessary to proceed by trial and error until the defects disappear and the production of the most beautiful image. The following graphic shows the effect of the filters on the selected pixels:
Here is a GIF animation demonstrating the effectiveness of the Sigma-Clip compositing method:
Preprocessed H-Alpha image (subtraction of Black, Bias and division of PLU) of the Crescent Nebula NGC6888 with the indication of the noises picked up during the acquisition of the image and the remaining hot pixels. Watch the disappearance of these noises after Sigma-Clip integration of the images using filter 2.
Here is a table summarizing the advantages of each method:
| Methods | Avoid saturation stars |
Maximize reduction formula noise |
Eliminates parasites bright when taking view |
Eliminate remaining hot pixels |
| additives | x | |||
| Average | x | x | ||
| Median | x | x | x | |
| Sigma clip | x | x | x | x |
As shown in the table, the method that meets all the criteria is l'integration Sigma-clip. So I recommend that you use the Sigma-Clip method for integrating your deep sky images by taking at least 10 individual images.
All astronomical image preprocessing software offers the Average method. This is not the case for the Sigma-clip method. Here is a partial list of software that manages the'integration Sigma-clip:
- Maxim DL (Sigma Clip and Standard Deviation Mask)
- Nebulosity (Standard Deviation)
- DeepSkyStacker (Kappa-Sigma clipping)
- Iris
If your preprocessing software does not offer the Sigma-clip compositing method, here is un free software that manages it very good :
This software is very sophisticated. It offers two noise reduction algorithms: The Sigma-clip standard and the Standard Deviation Mask developed by Ray Gralak, author of this application. The software offers several settings to obtain the most beautiful image. It also allows one-click comparison of the results of the mean, median and Sigma-clip methods. You can then use your favorite preprocessing software to subtract the black and split the PLU, align the preprocessed images, and then use this software to perform the Sigma-clip integration. It should be noted that for the choice of filter, the software asks to enter a Sigma Value (Sigma Value, also called Sigma Factor in the Maxim DL software). The proposed value is 0.5 which is the equivalent of filter 3 and is calculated as follows (see the graph on the effect of filters above):
6 0.5 x = 3
6 representing the maximum filter that retains all pixels or all images (see graph).
It should be noted that the evaluation is carried out pixel by pixel. So it is not necessarily the same image that is rejected for each pixel, which is the strength of this method. To maximize the noise reduction formula, it is therefore necessary to start with filter 3 and, if necessary, progress to the lower filters until the disappearance of light interference when shooting and (or) hot pixels.
It should also be noted that the median method will retain only XNUMX images (or XNUMX pixels) that we take XNUMX images or XNUMX images because it only retains the central values (average of the XNUMX central pixels for an even sequence and a single pixel for an odd sequence). It will therefore provide a more noisy image than the medium and Sigma-clip methods. It is for this reason that I do not recommend using this method because it does not meet the purpose of compositing images which is to significantly reduce noise by integrating several images compared to just one. For more details on the median calculation, click on this lien. For those interested, here is a Mathematical comparison between average, median and Sigma-clip.
Richard Beauregard
The Sky Astro-CCD
Revised 2021/04/26