Description
To solve the first 3 problems of this problem set, you will need to install the image processing
package ImageMagick, available at www.imagemagick.org. (Linux users may get it by
using the software update utility). This package provides the command convert, that can
be used from the command line prompt. The command has a complicated language of
options, and is capable to performing all the standard image processing operations. However,
you only need to be familiarized with the following 3 operations:
convert –rotate 90 input.jpg output.jpg
convert –scale 50%x25% input.jpg output.jpg
convert +append input1.jpg input2.jpg output.jpg
The first command rotates the input.jpg image 90º clockwise, and writes the result into
the output.jpg image. The second command scales the input.jpg image 50% on the
horizontal direction, and 25% on the vertical direction, and writes the result into
output.jpg (obviously, the percentages can be any values between 0-100). The third
command collates input1.jpg and input2.jpg along the horizontal direction, and
places the result in file output.jpg.
You are encouraged to test the commands above on the sample images a.jpg and b.jpg
provided with the problem set.
Submission: In IVLE, in the cs2104 workbin, you will find a folder called “Homework
submissions”. In that folder, there are currently 3 subfolders: PS3P01, PS3P02, and
PS3P03. The last two digits of the folder name indicate the solution that is to be submitted into
that folder: the solution to Question 1 into PS3P01, and so on (that is, you need to submit 3
separate solutions to 3 problems). A solution should consist of a single text file that can be
compiled, or loaded into the interpreter of interest and executed. You should provide as much
supplementary information about your solution as you can, in the form of program comments.
Moreover, if you work in a team, state the members of the team at the beginning of the file, in a
comment. You do not need to submit the same file twice, one submission per team is sufficient.
15 marks
The theme of this problem set is compiling a graphic description language into sequences of
image processing commands. The image processing commands can only be from among the
three listed above. The only parts that you will be allowed to change in these commands
are:
• The names of input and output files
• The scaling percentages in the second command.
You will not be allowed to change the angle of rotation, nor will you be allowed to use other
options of the convert command.
As an example of using these commands, consider the following scenario. Assume that the
images a.jpg and b.jpg are the following:
Consider now the following sequence of commands passed to the shell (either bash, or
cmd.exe):
convert -scale 50%%x50%% a.jpg o111.jpg
convert -scale 50%%x50%% b.jpg o1121.jpg
convert -rotate 90 o1121.jpg o112.jpg
convert +append o111.jpg o112.jpg o11.jpg
convert -rotate 90 o11.jpg o1.jpg
convert -scale 50%%x50%% a.jpg o2111.jpg
convert -rotate 90 o2111.jpg o211.jpg
convert -scale 50%%x50%% b.jpg o212.jpg
convert +append o211.jpg o212.jpg o21.jpg
convert -rotate 90 o21.jpg o2.jpg
convert +append o1.jpg o2.jpg o.jpg
The final image, o.jpg, looks like this:
Problem 1 [4 marks, submit to PS3P01] [A]
We define the following graphics description language. An Image is either:
• A Prolog atom, representing the .jpg image file with the same name (i.e. the atom a
represents the file a.jpg, assumed to be of size 640×640)
• The Prolog term beside(Image1,Image2) represents the image obtained by
collating the images resulting from the evaluation of the terms Image1 and Image2
along the horizontal axis (Image1 should be placed to the left of Image2). Both
images should be shrunk horizontally to half their size, so that the result has the same
size as each of the original images.
• The Prolog term rotate(Image) represents the image obtained by rotating 90º
clockwise the image resulting from the evaluation of the term Image.
All the resulting images are expected to be of size 640×640, the same as the size of the
original images.
For instance, the term
beside(rotate(beside(a,rotate(b))),rotate(beside(rotate(a),b)))
represents the o.jpg image presented above.
Write a predicate called montage that takes two arguments: a graphic description
expression, and an output file name. The predicate should compile the graphic description
expression given in its first argument into a sequence of convert commands which, when
run at the command prompt, generate the described image. The generated commands should
place the result image in the file whose name is given as the second argument to the
predicate.
For instance, the following query:
?- Prog = beside(rotate(beside(a,rotate(b))),rotate(beside(rotate(a),b))),
montage(Prog,o).
should generate the sequence of commands given above, in the introductory part of the
problem set (remember, the atom o stands for the file o.jpg). Note that the predicate should
simply print the commands on the screen, and not be responsible for running them. The user
is expected to copy and paste the commands into the shell window in order to produce the
output. The temporary file names used in the process of generating the final output are not a
compulsory requirement of this problem. You should feel free to come up with your own
naming scheme, as long as the final image is placed in the file with the specified name.
Problem 2 [1 marks, submit to PS3P02] [A]
We expand the language we defined in Problem 1 with assignment. Our new programs have
the format:
filename1 = Expr1 ; filename2 = Expr2 ; … ; filename = ExprN
The semantics of these programs is the following. The result of evaluating Expr1 should be
placed in filename filename1.jpg. Now, Expr2 may reference filename1, and, after
its evaluation, the result should be placed in filename2. This continues sequentially till all
the assignments in the program are exhausted. Every new expression may reference all the
filenames previously defined. For instance, the expression
x=rotate(beside(a,rotate(b)));y=rotate(beside(rotate(a),b));o=beside(x,y)
should evaluate to the same o.jpg image as before. Write a predicate ma (as in Montage
with Assignment), that takes a program of the format described above as argument, and
writes out the convert commands that generate each file on the left side of an assignment.
Problem 3 [4 marks, submit to PS3P03] [A]
Consider the following set of images:
n=0 n=1 n=2
n=3 n=4 n=5
Write a predicate called tile, which takes 3 arguments. The first argument is the level of
the image, represented by the value of n underneath each picture in the set given above. The
second is the input image, which should be a for the set above. The third argument is the
name of the output image. Thus, the 6 images given above should be generated by the output
of the following queries:
?- tile(0,a,output0).
?- tile(1,a,output1).
?- tile(2,a,output2).
?- tile(3,a,output3).
?- tile(4,a,output4).
?- tile(5,a,output5).
Problem 4 [2 marks, submit to PS3P04] [C]
Consider a binary encoding of natural numbers as reversed lists of bits. Thus, the list [1,1,0,1]
stands for the binary representation 1011, equal to 11 (eleven) in base 10. Write a Prolog predicate
add that implements the addition of numbers represented in this way. The predicate should allow for
the following interaction:
?- add([1,0,1],[1,1],X). % 5+3=8
X = [0,0,0,1]
Problem 5 [2 marks, submit to PS3P05] [C]
For the binary encoding described in Problem 4, write a multiplication predicate that works in a
similar manner. Your solution should reuse the predicate developed in the previous exercise.
Sample interaction:
?- mul([1,0,1],[1,1],X). % 5*3=15
X = [1,1,1,1]
Problem 6 [2 marks, submit to PS3P06] [C]
Declare the operator $= that evaluates expressions made up of binary lists as operators, and the
multiplication and addition operators * and +.
Sample interactions:
?- X $= [1,1]+[0,1]*[0,1]. % 7 = 3+2*2
X = [1,1,1]
?- X $= ([1,1]+[0,1])*[0,1]. % 10 = (3+2)*2
X = [0,1,0,1]
Hint: Reuse the predicates defined in the previous two problems. Perform an appropriate op
declaration for the $= predicate; this declaration should be similar to the one for the operator = .