Fundamentals of Computer Science I: Media Computing (CS151.02 2007F)

Transforming Images

This reading is also available in PDF.

Summary: We explore how to expand the power of color transformations, first by applying them to images rather than to individual pixels then by combining them into new transformations.

Contents:

From Transforming Pixels to Transforming Images

If you think back to the end of the previous reading on transforming RGB images, you may recall that we were starting to write filters that transformed not just individual colors but whole images. Here is one set of commands that transforms a four-by-three image called canvas.

(image.transform-pixel! canvas 0 0 rgb.complement)
(image.transform-pixel! canvas 0 1 rgb.complement)
(image.transform-pixel! canvas 0 2 rgb.complement)
(image.transform-pixel! canvas 1 0 rgb.complement)
(image.transform-pixel! canvas 1 1 rgb.complement)
(image.transform-pixel! canvas 1 2 rgb.complement)
(image.transform-pixel! canvas 2 0 rgb.complement)
(image.transform-pixel! canvas 2 1 rgb.complement)
(image.transform-pixel! canvas 2 2 rgb.complement)
(image.transform-pixel! canvas 3 0 rgb.complement)
(image.transform-pixel! canvas 3 1 rgb.complement)
(image.transform-pixel! canvas 3 2 rgb.complement)

That's an awful lot of typing. (Even though it seems that we've been typing a lot over the past few days, we do want to type less, and will look for techniques for doing so.) More importantly, this technique does not adapt itself easily to images of different sizes or to typical-sized images. (In a 200x200 image, which is still fairly small, there are 40,000 positions. No one wants to type that many lines of code, particularly when it is that repetitive.)

So, how do we write filters? DrFu includes a pair of helpful procedures, (image.map transformation image) and (image.map! transformation image). The first builds a new image by setting each pixel in the new image to the result of applying the given transformation to every pixel in another image. The second changes an existing image by applying the transformation in place. You will explore the differences between the two in the lab.

In Scheme, map typically means something akin to do to each portion of this thing. So, image.map means do to each pixel. When we learn about lists, Scheme's primary mechanism for grouping other kinds of values, we'll find that there's a version of map that does something with each element of the list. There's even an rgb.map that lets us do something to each component of an RGB color.

You'll note that the order of the parameters in image.map is a bit different than you'd expect. In almost every operation so far, the first parameter is the primary object being used or affected. Here, the first parameter is the color transformation being applied to each pixel. Why the difference? Because the tradition with map is to make the function the first parameters. As we'll see again and again, there are multiple customs for how one writes or designs procedures, and sometimes these customs come into conflict.

Using image.map (or image.map!) and the color transformations we learned in the previous reading, we can now transform images in a few basic ways: we can lighten images, darken images, complement images (and perhaps even compliment the resulting images), and so on and so forth.

Composing Transformations

We are almost done on our quest to learn how to write filters. We've learned some new functions provided by DrFu, such as the transformations. We've learned about one new technique, refactoring, which involves writing new functions that encapsulate common code. However, we have not yet learned how to write these refactored procedures. We've seen that Scheme permits procedures to take other procedures as parameters, and that this permission supports refactoring. Finally, we've learned a new kind of operation, map, which lets us do something to every component of a compound value. All this put together lets us write some simple filters. For example, we can write one line of Scheme code to make a a picture bluer.

> (image.map! rgb.bluer picture)

But what if we want more interesting filters, ones that can't be described with just a single built-in transformation? One thing that we can do is to combine transformations. There are two ways to transform an image using more than one transformation: You can do each transformation in sequence, or you can use function composition, an old mathematical trick, to first combine the transformations. Consider, for example, the problem of lightening an image and then increasing the red component. We can certainly write the following:

> (image.map! rgb.lighter picture)
> (image.map! rgb.redder picture)

However, what we really want to do is make each pixel in the picture lighter and then redder. In mathematics, when you want to build a function that does the work of two functions, you compose those functions. In DrFu, the compose operator lets you combine multiple functions into one. Here's a new function that makes colors lighter and then redder.

> (define lr (compose rgb.redder rgb.lighter))
> (define sample (cname->rgb "blue violet"))
> (rgb->string (lr sample))
"183/111/175"

Using function composition, we can therefore rewrite the earlier transformation as

> (image.map! lr picture)

or, as simply,

> (image.map! (compose rgb.redder rgb.lighter) picture)

What's the big difference between this instruction and the series of two instructions? In effect, we've changed the way you sequence operations. That is, rather than having to write multiple instructions, in sequence, to get something done, we could instead insert information about the sequencing into a single instruction. By using composition, along with nesting, we can then express our algorithms more concisely and often more clearly.

Reviewing Key Concepts

In most of the initial readings for this course, you were learning some basic operations that you could use in writing algorithms. In this reading, while you learned about new operations, they were a different kind of operation. image.map, image.map!, and compose all provide a way to add control to your program. The two maps do something to each component of the image, the composition sequences operations within a single Scheme instruction.

 

History

 

Disclaimer: I usually create these pages on the fly, which means that I rarely proofread them and they may contain bad grammar and incorrect details. It also means that I tend to update them regularly (see the history for more details). Feel free to contact me with any suggestions for changes.

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Samuel A. Rebelsky, rebelsky@grinnell.edu

Copyright © 2007 Janet Davis, Matthew Kluber, and Samuel A. Rebelsky. (Selected materials copyright by John David Stone and Henry Walker and used by permission.) This material is based upon work partially supported by the National Science Foundation under Grant No. CCLI-0633090. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. This work is licensed under a Creative Commons Attribution-NonCommercial 2.5 License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc/2.5/ or send a letter to Creative Commons, 543 Howard Street, 5th Floor, San Francisco, California, 94105, USA.