Hello,
I have an A-level student (in France) who would like to prepare his end of year oral examination in maths talking about image processing. He seems to be a complete novice in the matter, he also talked about special effects in cinema. He knows basic stuff like differentiation, integration, probabilities (binomial distribution but not much more) and vectors but not matrices and such. It is only a 5 minute presentation with 10 min of question time.
I am completely stumped as to what direction to give him, especially as he is not a natural at maths…
Any pointers would be helpful !
Personally, I would go for linear algebra, though this will require some knowledge of matrices.
One could then talk about initial matrices multiplied by a transformation matrix to give a result matrix. This could be extended to multiple transformations using a chain of matrices.
He could bring in an analogy, comparing it to the Heisenberg and Dirac formulation of quantum mechanics.
I would feed the good worthy some Grant Sanderson (3blue1brown) videos. Study both his style of presentation (manner) and content (matter). As you (probably) know, the former gets one through the door, the latter gets one the job. Obviously, that worthy should not copy ( plagiarize ) Sanderson’s work: with millions of views, these videos would be instantly recognizable by anyone in academia. Deconstruct and rebuild along one’s own lines.
You have a lot of experience with the maths of the channel mixer. The matrix from the manual is easily converted into nine linear algebra equations and the three sets to modify red/green/blue colours. Your pupil can show that e.g. the red channel can be augmented by increasing the red pixels or by swapping blue/green to red. As known it boils down to modifying the regression coëfficiënts.
You are an experienced math teacher and photographer, so the task ahead is within your reach, I feel
Instead of using matrices, try framing things in terms of linear operators. What your student should be doing is discussing the way one does transforms, as @Pieter_Zanen indicates the channel mixer would be a good example.
A 5 min presentation is very short, probably too short. So my advice would be to skip the matrix algebra and restrict your pupil to the linear equation for one single colour. Just give him the equation and let him explain that by increasing the (red) regression coëfficiënt he can increase the red pixels. By increasing the other two coëfficiënts he will turn the blue/green pixels into red.
I think that is a feature, not a bug ( “I apologize for writing such a long letter. I did not have time to write a short one.” ); it is really hard to capture the essential ideas, tersely, yet efficiently. I am content to blather and blatherandblather… but when they tell me to put up and shut up — then I know that my work is cut out for me. Grasping the art of editorial triage is likely the most important lesson to come out of this exercise. Good luck to both teacher and student.
Easy enough to explain the idea, plus one or two example of modes, sufficient for a 5 m talk. Make sure that you have other classes of mode lined up for the 10 m grilling.
Thanks for the ideas, blend modes seem to be the easiest to get across. I dislike the idea behind this oral examination, it is tailor-made for literary subjects but not for scientific ones. The students are not allowed to use a board. It makes things very difficult.
We’ll get through it, you can always tell if a student has worked hard so they usually get good marks.
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