Laboratory: Transforming Images

Summary: In this laboratory, you will extend the operations you've used to transform colors into operations that transform images.

Reference:

(image-set-pixel! image column row rgb-color): MediaScheme GIMP Procedure. Set the pixel at the specified position to the new color.
(image-variant image fun): MediaScheme GIMP Procedure. Create a new image of the same width and height as image, each of whose pixels is computed by applying fun to the color of the corresponding pixel in image.
(image-transform! image fun): MediaScheme GIMP Procedure. Transform image in place by setting each pixel to the result of applying fun to that current pixel color.
(compose f g): Traditional Higher-Order Procedure. Build a one-parameter procedure that applies g to its parameter, and then f to that result. ((compose f g) x) is the same as (f (g x)).
(o f₁ f₂ ... f_n-1 f_n): Traditional Higher-Order Procedure. Build a one-parameter procedure that applies each f, in turn, starting with f_n and working backwards. The composition, when applied to a value, x, produces the same result as (f₁ (f₂ (... (f_n-1 (f_n x))))).
(rgb-lighter rgb-color): MediaScheme Color Procedure. Build a lighter version of the given color.
(rgb-darker rgb-color): MediaScheme Color Procedure. Build a darker version of the given color.
(rgb-redder rgb-color): MediaScheme Color Procedure Build a redder version of the given color.
(rgb-greener rgb-color): MediaScheme Color Procedure. Build a greener version of the given color.
(rgb-bluer rgb-color): MediaScheme Color Procedure. Build a bluer version of the given color.
(rgb-rotate rgb-color): MediaScheme Color Procedure. Rotate the three components of the given color, setting the red component to the value of green, green to the value of blue, and blue to the value of red.
(rgb-phaseshift rgb-color): MediaScheme Color Procedure.“Phase shift” the color by adding 128 to components less than 128 and subtracting 128 from components greater than 128.
(rgb-complement rgb-color): MediaScheme Color Procedure. Compute the psuedo-complement of the given color.
(image-transform-pixel! image column row func): MediaScheme GIMP Procedure. Modify the pixel at (col,row) in image by applying func to its old color and setting that pixel to the resulting color.

Preparation

In this laboratory, you will be creating a few images and manipulating others. We will also be working with some colors.

a. Create a new 4x3 image, call it canvas, show it, and zoom in to at least 16x resolution. (Note that a shortcut for zooming in is to expand the window and then use View->Zoom->Fit Image in Window.)

b. Load an existing PNG or JPEG image of your choice, call it picture, and show it. Please choose an image that is not too large (say, not much more than 250x250). If you'd like, you can find the image from the reading at /home/rebelsky/MediaScheme/Images/kitten.png.

Exercises

Exercise 1: Image Variants

a. Set a few pixels in canvas to colors of your choice. Leave others black or white.

b. What do you expect to happen when you use image-variant to complement each pixel in canvas, using the following instruction?

> (image-show (image-variant canvas rgb-complement))

c. Check your answer experimentally.

d. What do you expect to have happen if you use image-variant to complement each pixel in picture? (You would use nearly the same instruction, substituting picture for canvas.)

e. Check your answer experimentally.

Exercise 2: Transforming “In Place”

Although we emphasized image-variant in the reading, the MediaScheme library also provides a procedure, (image-transform! image colortrans), that changes the image, rather than creating a new image.

a. If you have not done so already, set a few pixels in canvas to colors of your choice. Leave others black or white.

b. What do you expect to happen when you use image-transform! to complement each pixel in canvas, using the following instruction?

> (image-transform! canvas rgb-complement)

c. Check your answer experimentally.

d. What do you expect to have happen if you use image-transform! to complement each pixel in picture? (You would use nearly the same instruction, substituting picture for canvas.)

e. Check your answer experimentally.

f. What do you expect to have happen if you once again complement each pixel in picture?

g. Check your answer experimentally.

Exercise 3: Undoing Transformations

a. What do you expect to have happen if you use image-transform! to redden each pixel in canvas?

b. Check your answer experimentally.

c. You may have noticed that in exercise 2, we were able to undo the complement transformation by complementing again. Is there an easy way to undo the redden operation? (You do not have to write code; just explain how to do it.)

d. Are there transformations or sequences of transformations that would be impossible to undo? (That is, can you do something to an image such that there is nothing that you can do to the revised image that will bring back the original image?)

Exercise 4: Pure Transformations, Revisited

As you may have just observed, there are times that transforming an image can be dangerous, because we cannot easily undo some transformations (at least not without the magic “Undo” menu item). In spite of this problem, many programmers still prefer side-effecting operations like image-transform!.

With your partner, come up with some reasons that it may be advantageous to use image-transform! rather than image-variant. Be prepared to share those reasons with your classmates.

Exercise 5: Composition

Consider the following definitions.

(define much-darker (compose rgb-darker rgb-darker))
(define red (rgb-new 255 0 0))

a. What color do you expect (much-darker red) to compute? (Answer the question in terms of red, green, and blue values.)

b. Check your answer experimentally.

c. Set the top-left pixel of canvas to red.

d. What effect do you expect the following instruction to have?

(image-transform-pixel! canvas 0 0 (compose rgb-lighter rgb-lighter))

e. Check your answer experimentally.

f. What effect do you expect the following instruction to have?

(image-transform-pixel! canvas 0 0 
                        (compose rgb-lighter (compose rgb-lighter rgb-lighter)))

g. Check your answer experimentally.

Exercise 6: Composition and Order of Operations

Consider the composition (compose rgb-darker rgb-phaseshift).

a. Does this darken the image first or phase-shift the image first?

b. Does it matter? That is, do you get the same result either way?

c. Check your answer experimentally, using image-variant to compute the new images.

Exercise 7: Undoing Transformations

Earlier in this lab, we saw that some transformations had natural inverses and some did not. For example, if you complement a color twice, you get the original color. For many colors, if you lighten and then darken the color, you get the original color. (If any of the components is very large, then we may not be able to restore the original color.)

a. Consider the rgb-redder operation. How would you write an inverse to that operation using only the basic transformations along with composition? (That is, you do not get to write a lambda expression.)

b. Test your answer using image-variant. For example, if you decided that the answer was to make the image greener and bluer, you might write something like the following.

(define redder-canvas (image-variant canvas rgb-redder))
(define not-redder-canvas (image-variant redder-canvas (compose rgb-greener rgb-bluer)))
(image-show redder-canvas)
(image-show not-redder-canvas)

In case you were wondering, making the image greener and bluer does not invert the redder operation.

Exercise 8: Anonymous Transformations

a. Consider the following instruction. What effect do you expect it to have on the red component of each pixel? What effect do you expect it to have on the overall image?

> (image-show (image-variant picture
                             (lambda (rgb)
                               (rgb-new (modulo (+ (rgb-red rgb) 128) 255) 
			                (rgb-green rgb)
					(rgb-blue rgb)))))

b. Check your answers experimentally.

c. Write an instruction to build a variant of picture in which the green component of each pixel is set to 255.

d. Write an instruction to build a variant of picture in which the red component is restricted to the range [64..192], with numbers above 192 dropped to 192 and numbers below 64 raised to 64. In writing this, you may want to rely on the bound procedure you used in a previous lab.

e. Write an instruction to build a variant of picture in which the red component is set to 255 minus the red component.

Explorations

Explorations are intended for students interested in further exploring the design aspects of these techniques. They also provide students who finish early with extra activities that may challenge them in different ways. You may do them in any order.

Exploration 1: Combining Transformations

While we only have a few basic transformations, there are, in some sense, an infinite number of ways to combine them. Try to find an interesting composition of basic transformations that someone might want to use as a filter.

Exploration 2: Arithmetic Transformations, Revised

As you have undoubtedly noticed, RGB colors are represented as integers. That means that we can transform colors with arithmetic operations as well as with component based operations. What do you think the following operations will do to your image? Try some of them to find out. Then, try a few of your own devising.

(define t1 (lambda (c) (* 2 c)))
(define t2 (lambda (c) (* 3 c)))
(define t2 (lambda (c) (* -1 c)))
(define t3 (lambda (c) (* 256 c)))
(define t4 (lambda (c) (quotient (+ color-red c) 2)))
(define t5 (lambda (c) (- c color-blue)))

Make sure you save your work regularly. Some of these procedures have the potential to crash the GIMP or MediaScript.

Extra 3: Your Own Transformations

Try developing your own interesting RGB transformation procedures and applying them to picture.