代做ECS776P IMAGE PROCESSING Main Examination Period 2021代做迭代

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:

S1	S5	S9	S4	S2
S2	S6	S1	S5	S1
S3	S7	S2	S6	S8
S4	S8	S3	S1	S9

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

1	5	9	4	2
2	6	1	5	1
3	7	2	6	8
4	8	3	1	9

(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:

S1	S5	S9	S4	S2
S2	S6	S1	S5	S1
S3	S7	S2	S6	S8
S4	S8	S3	S1	S9

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

1	5	9	4	2
2	6	1	5	1
3	7	2	6	8
4	8	3	1	9

(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

S1	S2	S3
S4	S5	S6
S7	S8	S9

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

1	2	3
4	5	6
7	8	9

Then  give  the  results  for  2-pixel  border  extension with  the  image  by  using  three  border extension methods. [6 Marks]