Lab (2) - Image Processing using MATLAB

Objectives:
In this lab you will learn about:
Image Histogram
Thresholding

Please DO NOT Print this lab as it will not appear correctly

Preparations:
Please  save your files and images under My Document folder on your PC.  Also, you need to open a MS Word file so you can keep your results in that file.  Save that file also under the same directory.  You can simply copy images from MATLAB screen to MS Word.  To copy a MATLAB screen shot into the MS Word file, first click on the screen you wish to copy, then hold down the Alt or Ctrl key (there is small difference between the two), and press PrntScrn key at the same time.  This copies the screen shot into the buffer, you now need to go to MS Word screen and paste it either by using the Edit option or by pressing Ctrl V.  Make sure the cursor is at the location you want to copy the image.  Also it is possible to save MATLAB images in different image formats.  For this use the option Save As under File to save the files.

Image Histogram
What is a histogram?
Histogram is a statistical technique that helps us learn about the data.  The way it works is that we break the intensity range in some intervals that are usually called bins.  Then we go through the entire image and we count the number of intensity values in each range.  At the end we make a table or plot the intensity vs. the number of times those intensity values are seen.  Let's look at an example so we understand this better.  Consider the matrix (you can imagine this matrix as an image) given below:

myImage = [ 23 120 34 255  4  120 200  200
120  87 62 120 23  4  0 87
23  4  0  0  120  200  200  120
23  62  250  0 120 200  34  62
23 120 34 255  4  250 200  200
120  23  62 120 23  4  0 87
23  4  0  0  120  200  255  120
23  255  250  0 120 200  34  62]

Let's find out what intensity values we have in this image, and the count how many of each.

Intensity         Count (number of times we observe the intensity value)
=======    =======================================
0                   8
4                   6
23                 9
34                 4
62                 5
87                 3
120              13
200               9
250               3
255               4

Suppose we want to divide the range of intensity values into 5 equally sized intervals (bins) and count the occurrences of each intensity values in each bin.  5 equally sized bins between 0 to 255 are 51 units apart (almost).  Thus, we set our 5 bins between 0-50, 51-101, 102-152, 153-203, and 204-255.  I had an extra number (255) and put that in the last bin.  So the last bin is a bit larger, but we don't have any 254 anyway.  So now we will count the numbers in each bin as:

Intensity  greater than or equal to 0 AND less than 50 (0, 4, 23, and 34)  -- counts for Bin1  = 27
Intensity  greater than or equal to 51 AND less than 101 (62, and 87)  -- counts for Bin2 = 8
Intensity  greater than or equal to 102 AND less than 152  counts for Bin3 = 13
Intensity  greater than or equal to 153 AND less than 203  counts for Bin4 =  9
Intensity  greater than or equal to 204 AND less than or equal 255  counts for Bin5 = 7

Note that I had to make an exception in the last bin by including 255.  We will make a table for these data:

BinNo       Count (in that bin)
====       ==============
1               27
2               8
3               13
4               9
5               7

In MATLAB, type:
bin = [1 ; 2 ; 3;  4;  5]
bin =
     1
     2
     3
     4
     5

counts = [27; 8; 13; 9; 7]
counts =
    27
     8
    13
     9
     7

bar(bin, counts)
bargrapgh
This another representation of the 8-by-8 matrix you just had.  Remember I asked you to imagine that the initial 8-by-8 matrix was an image.  I think we can agree that such a histogram can be another representation of an image.

Assignment
Generate a histogram for bins of size 5.  i.e, use 0-4, 5-9, 10-14, ...  add the last bin the same way as above.  Include the histogram in your MS Word file.

Assignment
Generate a histogram for bins of size 1.  Thus every intensity value is a bin.

Reading and Creating the histogram of an image in MATLAB

When you work with a real image, of course, there are many pixels and it is much harder to count them one-by-one.  We can use a computer program to do this for us.  In MATLAB we can use a predefined function to do it.  If you have already save the following images and still have the original ones, you can skip Step 1.  If you do not have them or are not sure, just resave them again.

Step 0: Right click on each image and save it in your My Document folder.


im1  im2

Step 1:
leftImage = imread('The name you have given to the left image.jpg');

rightImage = imread('The name you have given to the right image.jpg');

imshow(leftImage)
figure, imshow(rightImage)

Step 2:

Now that you have your image data stored in leftImage and rightImage, you can create their histograms. Note that by default the total number of intensities will be used as the number of bins, thus in this example since the image is an 8-bit gray-scale image we use 256 bins.

figure, imhist(leftImage);  % To create the histogram of the left image

figure, imhist(rightImage);  %To create the histogram of the right image

Make sure to save the resulting images and corresponding histograms in your MS Word file.

Assignment
Make your observations.  What similarities do you observe?  What differences do you observe?

What do you think an importance of image histogram is?

Can you explain why you see such a large number at the low intensity range?

Assignment
You can also change the number of bins using the imhist command as:
imhist(imageData, N)

where imageData is the same as what you have used before and N is number of bins you want to use.  For example if we want to create a histogram for the left image with 10 bins we will use:
figure, imhist(leftImage, 10); 

Create histograms with 5, 15, and 30 bins for each of the images.  What do you learn from this experiment?
 
Assignment
Consider the original two images once again.  We want to compute the inverted image for each one.  The invert image is an image where the black intensities are replaced with the white ones and the gray levels are adjusted depending on their positions in the intensity range. 

Here is an example for an 8 bit image (an image that has intensities between 0 to 255).
A = [2  123  200  0
24 56  86  1
255  211 200 10
255 255 0  0]

The inverted image of A is:
InvertedA = [253   132    55   255
   231   199   169   254
     0    44    55   245
     0     0   255   255]

I am sure you have already figure out how I have computed the inverted image for A.  Now you need to compute the inverted image for the two images I have given you in the lab and find their default histograms  as well.

Make sure to copy the resulting images and their histograms in your MS Word file. 

Make your observations by comparing the histograms of inverted images to the corresponding histograms of the original images.