A few months ago I wrote a post Mathematics in Color, in which I discussed some mathematical aspects of color and showed how a simple change of basis from RGB color space to LAB color space can enable dramatic color changes to be done very easily.
Over the last decade most recent developments in digital imaging software such as Adobe Lightroom and Adobe Photoshop have been based on advanced mathematics, yet many of the most powerful and useful transformations that one can make to an image are based on elementary mathematics and have been possible since the early versions of the products. For example, with every click of the healing brush—which might, for example, be used to remove a stray piece of litter in a landscape or a skin imperfection in a portrait—Photoshop solves a partial differential equation. Yet global operations such as changes to colour and contrast can be done with commands (and in particular, masks) that amount to simple addition and multiplication operations.
I’ve just launched a new blog on photography and digital imaging in which one theme will be exploiting elementary mathematics in digital imaging. The first post shows how the much-used Clarity tool in Lightroom and Photoshop can be applied in a more effective way by taking what amounts to a componentwise linear combination of the images before and after Clarity has been applied.
Some MATLAB commands can be “applied to themselves”. A good example is help help, which provides help on the help function. For what other functions fun is fun fun a legal statement that produces something interesting? Here are some examples (by no means an exhaustive list).
Can you see why these are legal and guess what the effect of these calls will be? Search for “command-function duality” in the MATLAB help for some clues.
Are there any legal triple invocations? Yes, for example
and and and
char char char
isa isa isa
max max max
Indeed char can be iterated as many times as you like, but and and isa can be iterated three times but not twice.
If you think of additional interesting examples, please add them to the comments below.
After making my original choice of books (ones that I use in my research) I realized that it was pitched at too high a level for a general audience. Identifying my revised choice was not easy, as I wanted to select books that contain a significant applied mathematics content, yet most books at the popular level are focused on pure mathematics.