Main Examination Period 2021 — May — Semester B
ECS776P IMAGE PROCESSING
Duration: 3 hours
Note: Answer all the FOUR questions using font size no smaller than 11 and the answer to each question must be done in no more than 4 pages.
Question 1 (Point Processing)
Consider the 4x5 image with a dynamic range of [0-9] as in Figure 1:
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Figure 1: Image of size 4x5
where S1-S2-S3- …S8-S9 are the 9 digits of your student number, from left to right.
For example, if your student number is 123456789, the original image you use for this question is
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(a) Find the transformation for histogram equalisation of the original image and give the resulting image after histogram equalisation has been applied. [10 Marks]
(b) By using the histogram of the image obtained in (a), describe a simple method to threshold the image and give the result. [5 Marks]
(c) Find the mean and the standard deviation of the image pixel values by using the histogram of the image obtained in (a). [6 Marks]
(d) For an increasing function of point transformation, s = af(r + b), where r and s are the input and output intensities, respectively, and a and b are two constants. If we wish to preserve the intensity dynamic range [0,255], how can we find the two constants a and b? What are the values for a and b iff(r) = log10 (r)? [4 Marks]
Question 2 (Image Coding)
Consider the 4x5 image with a dynamic range of [0-9] as in Figure 2:
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Figure 2: Image of size 4x5
where S1-S2-S3- …S8-S9 are the 9 digits of your student number, from left to right.
For example, if your student number is 123456789, the original image you use for this question is
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(a) Give the mathematical representation of Gray code for natural binary number
bn−1bn−2 ⋯ b3 b2 b1 b0 , and find the bit-planes of the Gray code of the original image in Figure 2. [9 Marks]
(b) Calculate the entropy of the image in Figure 2. [5 Marks]
(c) Find the Huffman code of the image in Figure 2. [11 Marks]
Question 3 (General image processing operations and image sampling)
(a) In Figure 3, the first image (0) is the original image and all the other images (1)-(7) are the results of the application of some image processing operations on (0). Identify what operation has been used to produce each of the images (1)-(7) from image (0), and explain your answers.
Figure 3: Original image (0) and the processed results (1-7) [15 Marks]
(b) Give two methods in mathematical terms to transform. pixel values after image enhancement to a dynamic range from 0 to 255 for display. Explain the difference between the two methods. [5 Marks]
(c) Suppose that a satellite image has the pixel size of 10 metres by 10 metres. Answer the following questions:
i) What is the size of the image for a ground area of 12300 metres by 23400 metres?
ii) If the image has 2 components, the dynamic range for one component is from 100 to 200 , and the dynamic range for the other component is from 200 to 400, how many megabytes do we need to store the whole image without compression? [5 Marks]
Question 4 (image filtering)
(a) Show how a 3x3 mask can be obtained to approximate the second-order derivative of an
image f(x, y), [5 Marks]
(b) For a piece of a line in an image, [3,2,4,3,13,12,14,13], show the result of the convolution with the one-dimensional version of the mask obtained in (a). Indicate where the edges would be detected and explain why. Use replicate border extension for the convolution. [8 Marks]
(c) What is the Laplacian of Gaussian? What is the Difference of Gaussians? What is the difference between LoG and DoG filters? [6 Marks]
(d) Use your student number to fill in the following 3x3 image below
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Figure 4: Image of size 3x3
where S1-S2-S3- …S8-S9 are the 9 digits of your student number, from left to right.
For example, if your student number is 123456789, the original image you use for this question is
Then give the results for 2-pixel border extension with the image by using three border extension methods. [6 Marks]