Wavelet Processing Screen

Wavelet Processing Screen

As promised, I coded up an add-on to AviStack that performs wavelet based image enhancement. The functionality is similar to the Wavelets found in RegiStax, but are subtely different as you’ll see in a moment. But before I tell you more about the new capability coming to AviStack, I’d like to thank Michael Theusner, author of AviStack, for giving me the opportunity to contribute, and Cor Berrevoets, author of RegiStax, for discussing the Wavelet implementation in RegiStax with me. This wavelet processing capability should appear in V1.74 of AviStack.

There are a lot of different ways to define and work with wavelets. Wavelets are most commonly used in image compression. For the image enhancement process, we use something called a stationary wavelet transform. Basically, this is a special case of the wavelet transform where the image is not decimated between levels in the filter bank. A filter bank is a way of describing how an image is decomposed through the application of smoothing functions called kernels. The original image is smoothed by convolution with a kernel and the difference between the original and smoothed version is called a layer 1. The smoothed version is then convolved with another broader kernel. The difference between those two are called layer 2. This iterative process is repeated for every kernel/layer in the filter bank.

For image enhancement, the kernels are selected to capture or represent detail in the image at certain resolution scales. This module uses a Gaussian kernel and the resolution scale is represented by the Sigma value (sigma * 2.35 = FWHM for a Gaussian). Each layer has a Sigma as well as an Amplitude. Normally, if you take the last smoothed image from the filter bank and add in all of the layers you get the original image. If instead, you multiply a layer by a factor other than 1, you can enhance or suppress the detail associated with that layer. The Amplitude value in each filter/layer is just the multiplicative factor (well almost as you’ll see). At least that is the way it works in RegiStax. In my version for AviStack, I decided to streamline the code significantly, by adding the Layer times the Amplitude to the original image. So with AviStack, setting all of the amplitudes to zero gives the original image. It is a subtle but important difference that you’ll need to remember if you are a regular RegiStax user. Based on a quick survey of RegiStax users, I decided to only implement a Gaussian kernel. I could not find anyone who uses the default. One thing that worried me while enhancing images in RegiStax was that I could easily blow out the highlights. So for AviStack, I added a Show Clipping button which shows the user which pixels will be clipped to white if the image is saved as a 16-bit format. Lastly, I added a control to adjust the image gamma. I think you will find that this wavelet processing is very fast compared to RegiStax, so the results of any changes you make are immediately displayed. I’m not sure whether most RegiStax users fully understood the implications of the Initial and Step controls, so I did not implement them. The user is expected to select the appropriate Sigma value – which in almost all cases should increase with successive layers (see figure as an example). Let’s get on with an introduction on how to use wavelets in AviStack.

Usage:
There are six sets of controls for the six wavelet levels. Each set is comprised of a Sigma and Amplitude control. The Sigma control sets the width of the Gaussian for that wavelet. The current valid range of Sigma is from 0.16 to 2.00. The Amplitude control determines how strongly the wavelet is applied to the image. Its range is from -20 to 200. Clicking on any slider or Clicking & Dragging the slider bar will allow you to change the value. For single step adjustment (0.01), arrows are provided at each end. Results are displayed for the entire image immediately (or after the button release of a Drag). Near the edge of the image, data required for the wavelet does not exist. Rather than create data, the wavelet is not applied and instead the image is cropped. The number of pixels cropped from each side can be estimated by the following formula (#pixels = Integer( (largest sigma) / 0.16666)). So, if the largest sigma is 0.3 then 1 pixels will be cropped from each side. Two will be cropped if the largest sigma is 0.34 – and so on.

Pressing and holding the Show Clipping button below the wavelet controls will show where the processed image goes beyond the 16-bit range of TIFF or PNG files. Bright pixels with values beyond 65535 display as black while this button is held down. It is useful for monitoring the effect of wavelet processing on the detail in the brightest areas of the image.

There is a control to adjust the gamma. Again, results are displayed immediately.

There are a set of save buttons for FIT, 16-bit TIFF and 16-bit PNG files. Selecting one of these will bring up the usual save dialog. The file name defaults to the name of the original file with ‘_wvs’ appended followed by the appropriate suffix for the file type.

Finally, the two remaining buttons complete wavelet processing and return the use to the main AviStack screen. These currently do exactly the same thing – exit the wavelet screen, but will behave differently in a future version of AviStack.

Differences from RegiStax:
While these controls should be familiar to a RegiStax user, there are differences. The Sigma value is roughly equivalent to the RegiStax value times 2. Unlike RegiStax, the Sigma should get larger with successive layers since there is no other scaling being applied to the width. The Amplitude setting is a multiplicative factor applied to the wavelet. Unlike RegiStax where an amplitude of 1 represents no change, the enhancement of wavelet layers in AviStack are effectively turned off of by setting the amplitude to 0. Any zero amplitude layer followed by a non-zero amplitude layer is still calculated and impacts subsequent wavelet layers. Only those wavelets that are needed are applied. For example, If the third wavelet is the last non-zero amplitude layer, then only 3 layers of wavelets are used (as seen in the figure). Negative amplitude combined with larger sigma in the last layer used has the effect of reducing the degree of clipping in the brightest areas of the image.