Convolution - A new visualisation and intuition plus examples.

Here I explain the concept of discrete image convolution with a new visualisation and examples.
I also illustrate the properties of convolution.
CONTENTS
========
00:00 Intro
00:37 Images as functions
04:02 Terms and Symbols used in Convolution
06:18 The Convolution Process
09:18 A new way to look at convolution - integral transform projection
10:59 Examples 1 - Spatially invariant PSF and blurring
13:38 Properties of convolution
16:52 Examples 2 - Spatially variant PSF and sharpening
19:03 Inverse filtering and deconvolution (Intro)
20:36 Conclusions
SUPPORT PUMA
============
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1. Become a Patron: / pumamicroscope
2. Donate via PayPal: www.paypal.com/donate/?hosted...
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5. Consider purchasing your optics and related supplies from our affiliated online optics store, OptArc.co.uk ( www.optarc.co.uk/ )
---
OTHER LINKS
===========
My preprint on integral transform deconvolution:
hal.science/hal-04489222/file...
The deconvolve.net website:
www.optarc.co.uk/deconvolve/
FOR FURTHER INFORMATION
=======================
1. Open access write-up about PUMA on the FreeCAD blog:
blog.freecad.org/2023/02/13/a...
2. The official PUMA GitHub page where you can download the specs and source files to build or customise your own PUMA system:
github.com/TadPath/PUMA
3. The scientific peer reviewed publication on PUMA that was published in 2021 in the Journal of Microscopy (a journal of the Royal Microscopical Society) available here:
pubmed.ncbi.nlm.nih.gov/34151...
onlinelibrary.wiley.com/doi/1...
Thanks for your interest in the PUMA microscope system.
PJT 11/04/24

[@oni2ink]

I regularly use convolutions but this video still allows you to go deeper into the subject. Very interesting and well explained. I surprisingly didn't see the time go by!

[@landspide]

Great! Can't wait for the frequency domain continuation.

[@PUMAMicroscope]

Thanks. I'm currently working on the Fourier videos.

[@kochipj]

For someone working in the optics community, I think this is the natural form of thinking about convolution, e.g. if you want to resolve a double-star system you have to superimpose the PSFs for both to check if you can resolve them from each other.

[@francoclsm6251]

Thx! Tadrous. After watching this excellent video, my understanding of the concept of convolution has deepened. Looking forward to the next video.👍

[@PUMAMicroscope]

Thanks for the feedback.

[@aa18812]

Thank you so much. I have been toying with the use of deconvolution for astrophotography images, but was never sure what it was or how it worked. This is the most intuitive explanation I've found and it all makes total sense.

[@PUMAMicroscope]

Thanks. I will be doing more deconvolution later. Next up will be my series on the Fourier transform - so stay tuned for that.

[@shrinivasganti90]

Great explanation as always ❤

[@PUMAMicroscope]

Thanks.