On an image, convolution can be thought of as a process to blur or remove the contrast in an image. If you are already familiar with the concept and just want to run Convolve, you can jump to Convolution kernel and Invoking Convolve and skip the lengthy introduction on the basic definitions and concepts of convolution.
There are generally two methods to convolve an image. The first and more intuitive one is in the “spatial domain” or using the actual image pixel values, see Spatial domain convolution. The second method is when we manipulate the “frequency domain”, or work on the magnitudes of the different frequencies that constitute the image, see Frequency domain and Fourier operations. Understanding convolution in the spatial domain is more intuitive and thus recommended if you are just starting to learn about convolution. However, getting a good grasp of the frequency domain is a little more involved and needs some concentration and some mathematical proofs. However, its reward is a faster operation and more importantly a very fundamental understanding of this very important operation.
Convolution of an image will generally result in blurring the image because it mixes pixel values. In other words, if the image has sharp differences in neighboring pixel values103, those sharp differences will become smoother. This has very good consequences in detection of signal in noise for example. In an actual observed image, the variation in neighboring pixel values due to noise can be very high. But after convolution, those variations will decrease and we have a better hope in detecting the possible underlying signal. Another case where convolution is extensively used is in mock images and modeling in general, convolution can be used to simulate the effect of the atmosphere or the optical system on the mock profiles that we create, see Point spread function. Convolution is a very interesting and important topic in any form of signal analysis (including astronomical observations). So we have thoroughly104 explained the concepts behind it in the following sub-sections.
|• Spatial domain convolution||Only using the input image values.|
|• Frequency domain and Fourier operations||Using frequencies in input.|
|• Spatial vs. Frequency domain||When to use which?|
|• Convolution kernel||How to specify the convolution kernel.|
|• Invoking astconvolve||Options and argument to Convolve.|
In astronomy, the only major time we confront such sharp borders in signal are cosmic rays. All other sources of signal in an image are already blurred by the atmosphere or the optics of the instrument.
A mathematician will certainly consider this explanation is incomplete and inaccurate. However this text is written for an understanding on the operations that are done on a real (not complex, discrete and noisy) astronomical image, not any general form of abstract function