Image Processing - Filters

Image processing filters encompass a group of tools that are extremely useful for astrophotography. Filters fall into two main categories, Kernel filters and Frequency domain filters. In this article, I will discuss some of the more commonly used filters that are useful for astrophotographers. These are also equally useful for normal daylight photography.

The Power of Filters

The easiest way to understand the importance of filters is to see some real examples. The following images are shown with the left hand half unprocessed and the right-hand half processed with a specific filter.

Sharpening : Perhaps the most important application of filters is sharpening. Here is the result of using a wavelet sharpening filter on the planet Jupiter. As can be seen, there is a vast improvement in visible detail.

The original image on the left is very, but application of a wavelet filter dramatically improves detail

Star Removal : Another type of filter is called a "minimum" filter which is good at removing stars. This may seem an odd action to perform on a photograph of the stars, but there are times an image may contain so many stars that broader background detail such as dust lanes and nebula become obscured. Here is an example showing the Milky Way, an area with a high density of stars. Notice how much clearer the Milky Way dust lane structures are in the filtered right-hand side.

This image of the Milky Way is densely packed with stars. A minimum filter has been applied to the right-hand side of the image to remove most of the stars.

Remove Banding : It is unusual to see electrical interference or strong banding in images these days, but this can usually be repaired using a Fourier Transform "Notch" filter. Here is an example.

Image shows strong interference, resulting in zebra stripe pattern. The right half of the image has been processed using fourier transform techniques.

Kernel Filters

Kernel filters are a class of processing that recalculates a pixel brightness level based on the pixel levels of adjacent pixels. There are many useful applications of these filters including sharpening and noise suppression. We will now look at how a Kernel filter works.

Here is an image of a galaxy (NGC4945 in the constellation Centaurus) that has been enlarged to clearly show individual pixels. In this instance, we wish to apply a minimum filter with a 3 x 3 Kernel. The Kernel refers to the group of pixels used as the filter sample.

The following image demonstrates how a single pixel is processed using a minimum filter. At the left is a yellow 3x3 grid which represents the filter kernel which is the selection pixels used to compute the output pixel on the right.

Zooming in to see the kernel pixels more clearly, the middle left pixel has the lowest value and is, therefore, the minimum value to be used for the output pixel. This process is then repeated for every pixel to complete the image.

The 3x3 minimum filter is perhaps the most simple filter available. However, there is no restriction on the size and shape of the kernel.

Median Filter

In a median filter the filtered pixel brightness is equal to the median of all the kernel pixel values.

3x3 median filter. The median of the Kernel Pixel "P" brightness value is computed and inserted into Filtered Image Pixel "O'"

The median filter becomes stronger if the kernel size is increased beyond 3x3 (say to 5x5 or 7x7). The following image demonstrates the effect of increasing median filter strength. A typical application for this filter in noise reduction or as a low-pass filter.

The effect of median filters of different strength on an image of galaxy NGC4945. Median filters are handy for reducing background noise in images

Gaussian Blur Filter

The Gaussian blur filter uses a kernel with unique weighting factors placed on each pixel that match a gaussian distribution. For example, in the simplest 3x3 gassian blur filter the weighting factors appear as shown here.

This means that in the input image the central pixel has the most weight for calculating the output pixel, with decreasing weight been given to adjacent pixels. In a mathematical sense it takes on the following form.

3x3 weighted filter used in Gaussian filters. The Filtered Image Pixel "O'" brightness is equal to the sum of the products of the Kernel Pixels "P" values and their weighting factor.

The result of applying a Gaussian filter is similar to the median filter but the overall brightness of objects are preserved giving a blur effect. By controlling the width of the Gaussian kernel the amount of blurring can be altered. Here is the effect of a Gaussian filter applied to the galaxy image.

The effect of increasing strength of gaussian filter on an image of galaxy NGC4945

One application of a Gaussian filter is to reduce noise in an image, and if done gently will not impact detail significantly. Another big application of Gaussian filters is in sharpening, which will examine next.

Unsharp Masking

A major application of the Gaussian filter is Unsharp Masking, which is a technique for sharpening an image. Unsharp Masking is performed by simply subtracting a blurred copy of the image from itself. Let's look at this process by starting with an image of Jupiter and applying a Gaussian blur to it.

Jupiter unprocessed on the left, and the same image passed through a gaussian blur filter on the right

Watch what happens when we partly subtract the blurred imaged from the original unprocessed image. Note that the percentage given is the strength of subtraction (New Image = Original Image - Percentage x Blur Image).

Various amounts of unsharp masking shows additional detail not visible in the original image above

It is very clear that there is a considerable amount of additional detail now visible in the. However, the last image is starting to look like "overprocessed". It is often a matter of balancing the strength of the filter.

Although there has been a good improvement in detail it is possible to do better, using wavelet filters. To understand wavelet filters imagine repeating the above unsharp mask operation but with several different levels of Gaussian blur. Here is an example of Unsharp masking versus wavelet filtering.

Comparision of an original image (RAW), compared to it's Unsharp Masked version (UM) and the version with Wavelet sharpening applied (Wave)

Filters - Frequency Domain

Frequency domain filters use Fourier transform functions to allow filtering based on frequency domain rather than the spatial domain. To see how this might be useful, let's look at the following example of an image that has been severely damaged by electrical interference. Although this looks unrecoverable it can be repaired using the following technique.

An image of Jupiter effected by electrical interference type banding

The first step is to transform the image into the frequency domain using a Fast Fourier Transform (FFT) function which is available in many processing applications. The output of the FFT will appear similar to the following (left-hand image). If the FFT image was normal it would typically just have a bright cross in the middle without the 2 satellite spots indicated with green arrows. These spots are caused by the banding we saw above. In the right-hand image, the 2 spots have been cloned out.

What happens when we now apply the inverse FFT to restore the right-hand FFT image from above? Here is the result and as you can see the bands have been removed and all the real detail is intact. Please note I used actual data, and FFT processing for this, the only thing that was simulated was drawing a set of bands across the image.

Like magic the interference bands are gone - using FFT's

Conclusions

This was an overview of some of the applications of filters in imaging processing of astronomical images. I hope you found this information useful and perhaps you will find some use for filters in your own photography.

References

1. Buil, Christian. CCD Astronomy: Construction and Use of an Astronomical CCD Camera. Richmond, VA: Willmann-Bell, 1995.
2. Berry, Richard, and James Burnell. The Handbook of Astronomical Image Processing. Richmond, VA: Willmann-Bell, 2011.

NOTE: All images in this article are the author's, please credit @terrylovejoy if you wish to use any of them.