Functional Problem Solving (CSC 151 2014F) : Labs
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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
)
(image-variant
image
fun
)
image
, each of whose pixels is computed
by applying fun
to the color of the
corresponding pixel in image
.
(image-transform!
image
fun
)
image
in place by setting
each pixel to the result of applying fun
to
that current pixel color.
(compose
f
g
)
((compose f g) x)
is the same as (f (g x))
.
(o
f1
f2
...
fn-1
fn
)
f
, in turn, starting with
fn
and
working backwards. The composition, when applied to a value,
x
, produces the same result as
(f1
(f2
(...
(fn-1
(fn x)))))
.
(irgb-lighter
irgb-color
)
(irgb-darker
irgb-color
)
(irgb-redder
irgb-color
)
(irgb-greener
irgb-color
)
(irgb-bluer
irgb-color
)
(irgb-rotate
irgb-color
)
(irgb-phaseshift
irgb-color
)
(irgb-complement
irgb-color
)
(image-transform-pixel!
image
column
row
func
)
col
,row
)
in image
by applying
func
to its old color and setting that
pixel to the resulting color.
If you did not already do the preparation from the self-check in the reading, please do it now.
As you may have 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.
Consider the following definitions.
> (define much-darker (compose irgb-darker irgb-darker)) > (define red (irgb 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 irgb-lighter irgb-lighter))
e. Check your answer experimentally.
f. What effect do you expect the following instruction to have?
> (image-transform-pixel! canvas 0 0 (compose irgb-lighter (compose irgb-lighter irgb-lighter)))
g. Check your answer experimentally.
Consider the composition (compose irgb-darker irgb-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.
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 irgb-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 irgb-redder)) > (define not-redder-canvas (image-variant redder-canvas (compose irgb-greener irgb-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.
a. Consider the following instructions. What effect do you expect them 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 (color) (irgb (modulo (+ (irgb-red color) 128) 255) (irgb-green color) (irgb-blue color)))))
b. Check your answers experimentally.
c. Write instructions to build a variant of picture
in which
the green component of each pixel is set to 255.
d. Write instructions 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 instructions to build a variant of picture
in which
all the components are 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.
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.
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.
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.
Try developing your own interesting RGB transformation procedures and
applying them to picture
.