Introductory Labs

Follow the instructions on https://www.fel.cvut.cz/user-info/matlab.html.

Statistical Pattern Recognition Toolbox contains variety of algorithms which you will implement by yourself during this course (you can use them as an inspiration) and contains also many support functions which we will use throughout the semester.

Download the latest version of the toolbox from https://gitlab.fel.cvut.cz/smidm/statistical-pattern-recognition-toolbox. Unpack the content of the .zip file into your working directory (you should be able to find it next week!). To be able to use the toolbox, you have to set the path to it:

1. Run Matlab
2. Change the path to the directory where you unpacked the toolbox (use cd command or the path combo box at right top of the Matlab window)
3. Running stprpath will set the path and do initialization of the toolbox

Now you can switch to any other directory and still use the functions from the STPR toolbox.

To verify the paths try to run demo_ocr.

We will be using MATLAB programming language during the whole semester. It is necessary for you to be as familiar with it as possible, since the labs are time limited and the tasks are often challenging. It may happen that you spend more time looking for MATLAB syntax of some function instead of solving the problem itself.

For the case you are not too sure about your MATLAB skills, here are few useful links:

• Getting started with MATLAB. Nicely structured tutorial from Indiana University.
• MATLAB tutorial from Clarkson University.
• One A4 paper cheatsheet pdf.
• Image processing hints.
• How to make your code in MATLAB run fast BMVA Summer School: Matlab Programming Laboratory (Chapter 2, Vectorisation)
• Use following MATLAB commands to access the documentation:

  help ops % short help on MATLAB operators and special characters
  doc sum % documentation for the sum function
  lookfor transpose % searches for string "transpose" in the documentation

In most of the assignments there will be a set of simple questions. Answering the questions should help you to solve the assignment. All questions need to be answered correctly to get the points for the assignment.

Fill the correct answers to your answers.txt file.

question1 : gen_zero_matrix
question2 : 'x*' # enclose special characters in tick marks, also known as single quotation marks.
question3 : '^'  # enclose special characters in tick marks, also known as single quotation marks.
question4 : [a,d,e]
question5 : [b,f]

In the first part of today’s assignment, you will start with some simple matrix manimulation tasks.

AVOID THE USE OF ANY LOOPS IN YOUR PROGRAM!

Your goal is to complete a function output = matrix_manip(A, B), where A and B are input matrices and output is a resulting structure containing results of operations described below.

To have some data to work with, use matrices A and B from assignment_basics.m:

A = [16     2     3    13;
      5    11    10     8;
      9     7     6    12;
      4    14    15     1]
 
B = [ 3     4     9     4     3     6     6     2     3     4;
      9     2    10     1     4     3     7     1     3     5]

Function should work on general input matrices, not only for above prescribed A and B matrices or matrices with the same dimensions. Dimensions of the input matrices will be always suitable for all of the following tasks.

1. Find the transpose of the matrix A and return it in output.A_transpose. Example result:

   >> output.A_transpose
    
   output.A_transpose =
    
      16     5     9     4
       2    11     7    14
       3    10     6    15
      13     8    12     1

   Hint: Search documentation with lookfor command.
2. Select the third column of the matrix A and return it in output.A_3rd_col.

   >> output.A_3rd_col
    
   output.A_3rd_col =
    
         3
        10
         6
        15

   Hint: You need to use matrix indexing with colon : character.
3. Select last two rows from last three columns of the matrix A and return the matrix in output.A_slice.

   >> output.A_slice
    
   output.A_slice =
    
         7   6  12
        14  15   1

4. Find all positions in A greater then 3 and increment them by 1. Afterwards add column of ones to the matrix. Save the result to output.A_gr_inc.

   >> output.A_gr_inc
    
   output.A_gr_inc =
    
        17     2     3    14     1
         6    12    11     9     1
        10     8     7    13     1
         5    15    16     1     1

   Hint: Try > operator on the whole matrix. Use [] to construct the new matrix and ones function to create a vector with ones.
5. Create matrix C such that $C_{i,j} = \sum_{k=1}^n A\_gr\_inc_{i,k} \cdot (A\_gr\_inc^T)_{k,j}$ and store it in output.C.

   >> output.C
    
   output.C = 
    
       499   286   390   178
       286   383   351   396
       390   351   383   296
       178   396   296   508

   Hint: No loops are needed, try it on a paper with a 2×2 matrix.
6. Compute $\sum_{c=1}^n c \cdot \sum_{r=1}^m A\_gr\_inc_{r,c}$:

   >> output.A_weighted_col_sum
    
   output.A_weighted_col_sum =
    
       391

   Hint: You will need colon : special character to generate ranges, per element array multiplication .* and sum() function.
7. Subtract a vector $(4,6)^T$ from all columns of matrix B. Save the result to matrix output.D.

   >> output.D
    
   output.D = 
    
        -1     0     5     0    -1     2     2    -2    -1     0
         3    -4     4    -5    -2    -3     1    -5    -3    -1

   Hint: Use repmat command to replicate a matrix .
8. Select all column vectors in the matrix D, which have greater euclidean distance than the average euclidean distance.

   >> output.D_select
    
   output.D_select =
    
           0     5     0    -2
          -4     4    -5    -5

   Hint: You can find useful element-wise power of two .^2 and find function that returns indices of non zero elements of a matrix. Euclidean length of a vector can be calculated with the norm function, but for calculating length of all column vectors in a matrix you need to do it with your own code. No loops are needed!

In this part of the assignment, you are supposed to work with a simple input data which contains images of letters. We will use similar data structures later on during the labs. Do the following:

Note: Plotting and displaying of images should be implemented only in assignment_basics.m.

1. In the data_33rpz_cv01.mat data file, the following variables are stored:
   • images (3D array of 2000 10×10 grayscale images)
   • Alphabet (letters in the images, not full alphabet is included)
   • labels (indexes of the images into Alphabet array).
2. Inspect all images at once with the code:

   ims = permute(images,[1 2 4 3]); % The images must be ordered by the 4th dimension.
   montage(ims); colormap gray;

   Hint: check documentation for functions imshow, imagesc, subplot, montage.
3. For a given letter, compute its mean image. This means taking all images in the dataset displaying that letter, and making pixel-wise mean. Use your name initials (if present in the dataset) and save them as initial1_mean.png and initial2_mean.png (use any letter if any of your initials is not present in the dataset). You will probably encounter a problem with non-decimal numbers in the image matrix. You can avoid it by using the uint8 function before returning the mean image.
   • For the purpose of mean image calculation, complete the function:

     letter_mean = compute_letter_mean(letter_char, Alphabet, images, labels)

     where letter_char is a character (e.g. 'A', 'B', 'C') representing the letter whose mean we want to compute, Alphabet, images and labels are loaded from the provided data, and letter_mean is the resulting mean image.
4. Compute an image feature x - a sole number characterizing an image. It is defined as:

   x = sum of pixel values in the left half of image - sum of pixel values in the right half of image

   Then make a histogram of feature values of all images of a letter. Complete a function for the feature histogram computation:

   lr_histogram = compute_lr_histogram(letter_char, Alphabet, images, labels, num_bins)

   where letter_char is a character representing the letter whose feature histogram we want to compute, Alphabet, images and labels are loaded from the provided data, num_bins is the number of histogram bins and lr_histogram is the resulting histogram (num_bins long vector containing counts of items in the corresponding bins).
   • For reference the following histogram was computed for letter A with 10 bins:

     >> compute_lr_histogram('A', Alphabet, images, labels, 10)
      
     ans =
      
          1     1     3     6    12    27    24    20     5     1

   • Hint: use hist function to compute the histogram.
   • Plot feature histograms of your initials into one figure to compare them and save the figure as initials_histograms.png.