Objectives: This lab revisits important concepts covered in the Week 1 and Week 2 lectures and aims to make you familiar with implementing specific algorithms.

Materials: The sample images to be used in all the questions of this lab are available in WebCMS3. You are required to use OpenCV 3+ with Python 3+.

Submission: Question 4 below is assessable after the lab. Submit your source code for this   question as a Jupyter notebook (.ipynb) which includes all output (see coding requirements  below) by the above deadline. The submission link will be announced in due time. Questions 1-3 are exercises for yourself to get experience with image processing and will not be             assessed. Only Question 4 will be assessed.

1. Contrast Stretching

Contrast is a measure of the range of intensity values in an image and is defined as the        difference between the maximum pixel value and minimum pixel value. The full contrast of an 8-bit image is 255 (max) – 0 (min) = 255. Any value less than that means the image has  lower contrast than possible. Contrast stretching attempts to improve the contrast of the   image by stretching the range of intensity values using linear scaling.

Assume that I is the original input image and 0 is the output image. Let a and b be the        minimum and maximum pixel values allowed (for an 8-bit image that means a = 0 and b = 255) and let c and d be the minimum and maximum pixel values found in I. Then the           contrast-stretched image 0 is given by the function:

0(x, y) = (I(x, y) − c) ( ) + a                                  (1)

Question 1: Write an algorithm that performs contrast stretching as per Equation (1) above.

Read the given gray-scale image Cat.png and run your algorithm to see whether it indeed improves the image quality. The result should look like this:

Also write an algorithm that finds the coordinates of the minimum pixel value and the             coordinates of the maximum pixel value in an image. Do not use the existing library                 functions for these tasks but write your own code (see coding requirements below). Run it     on both the input image and the output image and print the values of these pixels to confirm whether your contrast stretching algorithm works correctly.

2. Histogram Calculation

The histogram of an image shows the counts of the intensity values. It gives only statistical  information about the pixels and removes the location information. For a digital image with L gray levels, from 0 to L − 1, the histogram is a discrete function h(i) = ni where i ∈       [0, L − 1] is the ith gray level and ni is the number of pixels with that gray level.

Question 2: Write an algorithm that computes the histogram of an image. Do not use         existing library functions for computing the histogram but write your own code to perform this task (see coding requirements below). Then run your algorithm on Cat.png and its        contrast enhanced version from Question 1 and visually compare the histograms (you may use existing functions to plot the histogram array computed by your algorithm).

3. Image Smoothing

Reduction of noise (random intensity variations) in images can be achieved using image         filtering. Salt and pepper noise, impulse noise, and Gaussian noise are some of the                  commonly observed types of noise in images. Different types of smoothing filters are suited for different types of noise. A smoothing filter is often called a low-pass filter as it allows low frequency components of the image to pass though (regions with similar intensity values)     while suppressing high frequency components (edges or noise).

Question 3: Implement a mean (uniform) filter and a median filter. Do not use the existing     library functions for convolution and image filtering but write your own code to perform this task (see coding requirements below). Perform noise removal on the input image Moon.png. Try both filters with different filter sizes, observe the differences in results, and decide which is the best filter and kernel size for this image.

Here is an example result (part of the image):

Input                                                                        Filtered

4. Edge Detection

Edges are an important source of semantic information in images. They occur in human          visual perception at divisions between areas of different intensity, colour, or texture. A gray- scale image can be thought of as a 2D landscape with areas of different intensity living at       different heights. A transition between areas of different intensity in an image I means there must be a steep slope, which we formalise as the gradient (vector):

∇I = ( aI  aI

(2)

As the image I is discrete, we need to approximate the continuous derivatives aI/ax and

aI/ay by finite differences. Simple examples of convolution kernels that perform finite differencing are the Sobel filters defined as follows:

−|

Notice that the calculations may produce negative output pixel values. Thus, make sure you use the right data types for the calculations and the output image.

After that, compute the gradient magnitude image :

‖∇I‖ = l()2 + ()2                                                         (3)

In other words, create a new output image having the same size as the input image and the Sobel images, and then for every pixel in the output image compute the value as the square root of the sum of the squared value of the Sobel image aI/ax and the squared value of the Sobel image aI/ay at that pixel position.

Here again, notice that the calculations may produce intermediate values outside the 8-bit range. Thus, make sure you use the right data types for the calculations.

The final result should look like this: