Description
Title: Histogram Equalization In this lab, you will implement a function that performs histogram equalization on a grayscale image. You can assume all images are grayscale and have values from 0 to 255.
Read through this assignment in detail before starting.
The lab consists of two experiments:
1. Performing histogram equalization on a dark image to improve how it looks. 2. Performing histogram equalization on a light image to improve how it looks.
See the Python script test_HistogramEqualization.py which performs these two experiments. You can use this script. Your task in this lab is to write the Python functions compute_histogram()and equalize() in the file My_HE_functions.py.
Read through the Python script test_HistogramEqualization.py to see how it:
• Reads the dark image that you will be applying histogram equalization to:
Lab_04_image1_dark.tif.
• Shows the image. • Creates a numpy matrix from the dark image so we can access its pixels. NOTE THAT WE WE ARE CREATING A FLOAT32 ARRAY SINCE WE WILL BE DOING FLOATING POINT OPERATIONS IN THIS LAB.
• Calls the function compute_histogram() to compute the normalized histogram of the dark image. We will be using a length 256 numpy vector to represent the histogram of a grayscale image. You will need to write this function.
• Calls the function plot_histogram() to plot the histogram of the dark image. This function is
provided for you.
• Prints the mean and standard deviation of the pixel values in the dark image. • Calls the function equalize() to apply histogram equalization to the dark image. This function returns a numpy matrix with the pixel values of the equalized image. You will need to write this function.
• Calls the function compute_histogram() to compute the normalized histogram of the
equalized dark image.
• Calls the function plot_histogram() to plot the histogram of the equalized dark image. • Prints the mean and standard deviation of the pixel values in the equalized dark image. • Repeats the above for the light image Lab_04_image2_light.tif.
In the file My_HE_functions.py, write the following functions:
1. Write the function compute_histogram() that takes a numpy matrix representing a grayscale image as input and outputs a length 256 numpy vector representing the normalized histogram of the image. Here’s the code I used to create this vector
hist = np.zeros(shape=(256))
Once you have calculated the values of the histogram vector, these values should range from 0 to 1 and should sum to 1.
Be aware that when you use the pixel values to index into the histogram vector, you will probably need to typecast them as integers. For example,
hist[int(image_pixels[m][n])] += 1
If you don’t do this, you will likely get the error “IndexError: only integers, slices (:), ellipsis (…), numpy.newaxis (None) and integer or boolean arrays are valid indices.”
2. Write the function equalize() that takes a numpy matrix representing a grayscale image as input and outputs a numpy matrix representing the histogram equalized version of the image. This function should:
• Compute the normalized histogram of the input image by calling your function
compute_histogram().
• Create a length 256 numpy vector representing the transformation function that you will apply
to the pixels of the input image to create the output image.
• Compute the entries in this transformation vector using the normalized histogram computed
above. This vector can be considered a look-up-table that you index into with the input image pixel value and the value at that index is the output image pixel value. T should be computed using equation 3.3-8 (3rd edition) or equation 3-15 (4th edition) in the text.
• Create a numpy matrix representing the pixel values of the output image. This should be the
same size as the input image.
• Use the transformation vector to transform each pixel in the input image to the pixel in the
output image.
Once you have written the two functions compute_histogram() and equalize() you should be able to run the provided Python script test_HistogramEqualization.py. Here is the terminal output that I get when I run it:
Dark image has mean = 82.816910 and standard deviation = 60.353374 Equalized dark image has mean = 128.906438 and standard deviation = 73.687541
Light image has mean = 182.023697 and standard deviation = 39.150688 Equalized light image has mean = 129.067739 and standard deviation = 74.119361
Your values might not be exactly the same as mine but they should be close.
Note/remember:
• When the function plot_histogram() uses the matplotlib library to display the
histogram, you will need to close the figure window for the script to keep running. • To save a histogram plot to file, click the save/disk icon in the matplotlib window. • Provide comments for key lines of code. • Provide headers for your functions. Headers are comments which appear right after the function declaration that summarize what the function does its calling syntax, the input and output parameters, and the function history. You must provide headers for the two functions you will write: compute_histogram() and equalize().
Questions:
1. Discuss if you think the histogram equalized versions are visual improvements over the dark and light
images.
2. Discuss how this improvement is reflected in the differences between the histograms of the dark/light
images and the histograms of their equalized versions.
3. Discuss how this improvement is reflected in differences between the mean and standard deviations of the pixel values in the dark/light images and the mean and standard deviations of the pixel values in their equalized versions.
4. What was the most difficult part of this assignment?
What to submit:
A lab report as a single PDF containing:
• Lab number and title, your name, your lab section, your TA’s name, and the date. • Abstract: In a few sentences, describe the purpose of this lab. • Figures containing the dark image, the plot of the histogram of the dark image, the equalized version of the dark image, and the plot of the histogram of the equalized version of the dark image.
• A table containing the mean and standard deviation of the pixel values of the dark image and the
equalized version of the dark image.
• The above two bullet points for the light image. • Questions: Your answers to the four questions above. • The Python script: test_HistogramEqualization.py (This could be exactly the same as
the one provided or one with some modifications.)
• The Python
file My_HE_functions.py which
compute_histogram() and equalize().
contains your
two
functions:
See Lab_04_sample_report.pdf as an example.
What your report will be graded on
• Whether you included an abstract. • Whether your report includes the figures you were asked to include and they have appropriate
captions.
• Whether you included a table with mean and standard deviation of the pixel values of the
dark/light image and their histogram equalized versions.
• Whether you answered the assignment questions. • Whether your report includes the code you were asked to include. • Whether your code is correct. • Whether your code is commented and your functions have headers.
