IGNOU MMTE 3 SOLVED ASSIGNMENT

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MMTE 3 2025 - English

Course Code: MMTE-003

Assignment Code: MMTE-003/TMA/2025

Maximum Marks: 100

1. a) The arithmetic decoding process is the reverse of the encoding procedure. Decode the message 0.23355 given the coding model.

Symbol	Probability
a	0.2
e	0.3
i	0.1
o	0.2
u	0.1
!	0.1

b) A binary image contains straight lines oriented horizontally, vertically, at 45°, and at - 45°. Give a set of 3 x 3 masks that can be used to detect 1-pixel breaks in these lines. Assume that the intensities of the lines and background are 1 and 0, respectively.

2. a) Suppose that an image f(x, y) is convolved with a mask of size n x n (with cofficients 1/n²) to produce a smoothed image .

i) Derive an expression for edge strength (edge magnitude) of the smoothed image as a function of mask size. Assume for simplicity that n is odd and that edges are obtained using the partial derivatives

ii) Show that the ratio of the maximum edge strength of the smoothed image to the maximum edge strength of the orginal is 1/n. In other words, edge strength is inversely proportional to the size of the smoothing mask.

b) Explain how the MPP algorithm behaves under the following conditions: b

i) 1-pixel wide, 1-pixel deep indentations.

ii) 1-pixel wide, 2-or- more pixel deep indentations.

iii) 1-pixel wide, 1-pixel longprotrusions.

iv) 1-pixel wide, n-pixel long protrusions.

3. a) Find an expression for the signature of each of the following boundaries, and plot the signatures.

i) An equilateral triangle

ii) A rectangle

iii) An ellipse

b) Consider a linear, position-invariant image degradation system with impulse response

Supose that the input to the system is an image cosnsiting of a line of infinitesimal width located at x = a, and modeled by f(x, y) = 8(x-a), where 8 is an impulse. Assuming no noise, what is the output image g(x, y)?

4. a) Define the terms 'Sampling' and 'Quantization' in context of digital image processing. A medical image has size 8x8 inches, the sampling reduction is 5 cycles/mm, calculate the number of pixels required for the medical image.

b) What do you understand by the term "Entropy" in context of any digital image? Calculate the entropy for the symbols, where probability distribution is given below:

Symbol	Probability
1	0.4
2	0.3
3	0.1
4	0.1
5	0.1

5. a) What is Discrete Fourier Transform (DFT)? Find DFT of the function:

b) Apply Prewitt operators and Sobel operators for the image given below:

6. a) Two images, f (x,y) and g (x,y), have histograms he and hg. Give the condition under which you can determine the histograms of

i) f(x,y)+g(x, y)

ii) f(x,y)-g(x,y)

iii) f(x, y)xg(x, y)

iv) f(x,y)+g(x,y)

b) Write an expression for 2-D continuous convolution.

7. a) An automobile manufacturer is automating the placement of certain components on the bumpers of a limited-edition line of sports cars. The components are colour coordinated, so the robots need to know the colour of each car in order to select the appropriate bumper component. Models come in only four colours: blue, green, red, and white. Find a solution based on imaging and determine the colour of each car, keeping in mind that cost is the most important consideration.

b) Consider the two image subsets, S₁ and S2, shown in the following figure. For V = {1}, determine whether these two subsets are (i) 4-adjacent, (ii) 8-adjacent, or

(iii) m-adjacent.

8. a) Prove that both 2-D continuous and discrete Fourier transforms are linear operations.

b) Consider a 3x3 spatial mask that averages the four closet neighbours of a point

(x, y), but excludes the point itself from the average.

i) Find the equivalent filter, H (u, v), in the frequency domain.

ii) Show that your result is a lowpass filter.

9. The white bars in the test pattern shown are 7 pixels wide and 210 pixels high. The separation between bars is 17 pixels. What would this image look like after application of

i) A 3×3 arithmetic mean filter?

ii) A 7x7 arithmetic mean filter?

iii) A 9×9 arithmetic mean filter?

10. a) Consider an 8-pixel line of intensity data, (108,139,135,244,172,173,56,99). If it is uniformly quantized with 4-bit accuracy, compute the rms error and rms signal-to- noise ratios for the quantized data.

b) Prove that, for a zero-memory source with q symbols, the maximum value of the entropy is log q, which is achieved if and only if all source symbols are equiprobable. [Hint: Consider the quantity log q-H(z) and note the inequality In x ≤x-1]

MMTE 3 2026 - English

Assignment

Course Code: MMTE-003

Assignment Code: MMTE-003/TMA/2026

Maximum Marks: 100

1. a) Show that Sobel masks can be implemented by one pass of differencing mask of the form [−1 0 1](or its vertical counterpart) followed by a smoothing mask of the form [1 2 1] (or its vertical counterpart).

b) Explain the Hough transform for edge linking with suitable example.

2. a) Propose a gray level slicing algorithm capable of producing the 4-bit plane of an 8-bit monochrome image.

b) Explain the functioning of an adaptive, local noise reduction filter.

3. Given an image with uniform histogram. Explain the effect of applying following compression techniques:

i) Huffman,

ii) Golomb,

iii) LZW,

iv) Prediction coding, and

v) Optimal Quantization

4. a) Explain in detail the adaptive mean and median filters.

b) Obtain mean and variance of the following noise pdfs:

i)

ii)

iii)

5. a) In image restoration, how are the noise parameters estimated?

b) Assume that the noise is estimated as exponential, with mean Variance . How will you estimate the parameter 'a' of pdf of exponential Noise?

6. a) Suppose a low-pass spatial filter is formed by averaging the four immediate neighbours of a point (x, y) but excluding the point itself. Find the equivalent filter H(u,v) in the frequency domain.

b) Apply the perception algorithm to the following pattern classes:

,

.

Let and

Also, Sketch the decision surface.

7. a) Perform histogram equalization for the following histogram.

Gray level	0	1/7	2/7	3/7	4/7	5/7	6/7	7/7
Number of occurrences	400	700	800	900	500	400	196	200

b) A bullet is 2.5 cm long, 1cm wide and its range of speed is . The bullet is flight is captured by a camera that exposes the scene for k sec and the bullet occupies 10% of the horizontal resolution of frames. Find

i) Automatic segmentation of the bullet.

ii) Automatic determination of speed of the bullet.

8. a) Given that

where f and g are real images and h is a spatial filter.

Obtain G(u,v), in terms of F(u,v), and H(u,v), the 2–D Fourier transform of g(x,y).

b) Describe the homographic filtering. Explain why the filtering scheme is effective for the applications it is used.

9. Filter the given gray level image with

i) mean filter using zero padding

ii) 3×3 weighted mean filter using zero padding with mask



iii) 3×3 median filter processing only such pixels that have all the needed neighbours.

iv) Laplacian filter with the given mask and reflecting the border pixels.



10. a) Define the following with suitable examples

i) Unsharp marking

ii) High boost filtering

iii) High frequency filtering.

b) Given an image f(x,y) with Fourier transform F(u,v) obtain the fourier transform of .

c) Given that the 2-D Fourier Tranform is real and even, obtain the constraints on the image characteristics.

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Course Name	M.Sc. Mathematics with Applications in Computer Science
Course Code	MSCMACS
Programm	Courses
Language	English

 

 

 

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