IGNOU MMTE-003 Solved Assignment 2024, M.Sc. MACS

IGNOU MMTE-003 Solved Assignment 2024 | M.Sc. MACS

Solved By – Narendra Kr. Sharma – M.Sc (Mathematics Honors) – Delhi University

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IGNOU MMTE-003 Assignment Question Paper 2024

mmte-003-solved-assignment-2024-ff79897d-d25e-4830-beb3-d263cf85ddfe

mmte-003-solved-assignment-2024-ff79897d-d25e-4830-beb3-d263cf85ddfe

MMTE-003 Solved Assignment 2024
  1. 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, S 1 S 1 S_(1)S_1S1 and S 2 S 2 S_(2)S_2S2, shown in the following figure. For V = { 1 } V = { 1 } V={1}\mathrm{V}=\{1\}V={1}, determine whether these two subsets are (i) 4-adjacent, (ii) 8-adjacent, or (iii) m-adjacent.
S 1 S 1 S_(1)S_1S1 S 2 S 2 S_(2)S_2S2
0 0 0 0 0 0 0 1 1 0
1 0 0 1 0 0 1 0 0 1
1 0 0 1 0 1 1 0 0 0
0 0 1 1 1 0 0 0 0 0
0 0 1 1 1 0 0 1 1 1
S_(1) S_(2) 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 | | $S_1$ | $S_2$ | | | | | | | | | | | | | | | :—: | :—: | :—: | :—: | :—: | :—: | :—: | :—: | :—: | :—: | :—: | :—: | :—: | :—: | :—: | :—: | | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | | | | | | | | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | | | | | | | | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | | | | | | | | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | | | | | | | | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | | | | | | |
  1. a) Two images, f ( x , y ) f ( x , y ) f(x,y)f(x, y)f(x,y) and g ( x , y ) g ( x , y ) g(x,y)g(x, y)g(x,y), have histograms h f h f h_(f)h_fhf and h g h g h_(g)h_ghg. Give the condition under which you can determine the histograms of
    i) f ( x , y ) + g ( x , y ) f ( x , y ) + g ( x , y ) f(x,y)+g(x,y)f(x, y)+g(x, y)f(x,y)+g(x,y)
    ii) f ( x , y ) g ( x , y ) f ( x , y ) g ( x , y ) f(x,y)-g(x,y)f(x, y)-g(x, y)f(x,y)g(x,y)
    iii) f ( x , y ) × g ( x , y ) f ( x , y ) × g ( x , y ) f(x,y)xx g(x,y)f(x, y) \times g(x, y)f(x,y)×g(x,y)
    iv) f ( x , y ) ÷ g ( x , y ) f ( x , y ) ÷ g ( x , y ) f(x,y)-:g(x,y)f(x, y) \div g(x, y)f(x,y)÷g(x,y)
    b) Write an expression for 2-D continuous convolution.
  2. a) Prove that both 2-D continuous and discrete Fourier transforms are linear operations.
    b) Consider a 3 × 3 3 × 3 3xx33 \times 33×3 spatial mask that averages the four closet neighbours of a point ( x , y ) x , y ) x,y)\mathrm{x}, \mathrm{y})x,y), but excludes the point itself from the average.
    i) Find the equivalent filter, H ( u , v ) H ( u , v ) H(u,v)\mathrm{H}(\mathrm{u}, \mathrm{v})H(u,v), in the frequency domain.
    ii) Show that your result is a lowpass filter.
  3. 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 3 × 3 3xx33 \times 33×3 arithmetic mean filter?
    ii) A 7 × 7 arithmetic mean filter?
    iii) A 9 × 9 arithmetic mean filter?
original image
  1. a) Consider an 8-pixel line of intensity data, { 108 , 139 , 135 , 244 , 172 , 173 , 56 , 99 } { 108 , 139 , 135 , 244 , 172 , 173 , 56 , 99 } {108,139,135,244,172,173,56,99}\{108,139,135,244,172,173,56,99\}{108,139,135,244,172,173,56,99}. If it is uniformly quantized with 4-bit accuracy, compute the rms error and rms signal-tonoise 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 log q log q\log \mathrm{q}logq, which is achieved if and only if all source symbols are equiprobable. [Hint: Consider the quantity log q H ( z ) log q H ( z ) log q-H(z)\log \mathrm{q}-\mathrm{H}(\mathrm{z})logqH(z) and note the inequality In x x 1 x x 1 x <= x-1\mathrm{x} \leq \mathrm{x}-1xx1 ].
  2. a) The arithmetic decoding process is the reverse of the encoding procedure. Decode the message 0.23355 given the coding model
Symbol Probability
a a a\mathrm{a}a 0.2
e e e\mathrm{e}e 0.3
i i i\mathrm{i}i 0.1
o o o\mathrm{o}o 0.2
u u u\mathrm{u}u 0.1
l l l\mathrm{l}l 0.1
Symbol Probability a 0.2 e 0.3 i 0.1 o 0.2 u 0.1 l 0.1| Symbol | Probability | | :—: | :—: | | $\mathrm{a}$ | 0.2 | | $\mathrm{e}$ | 0.3 | | $\mathrm{i}$ | 0.1 | | $\mathrm{o}$ | 0.2 | | $\mathrm{u}$ | 0.1 | | $\mathrm{l}$ | 0.1 |
b) A binary image contains straight lines oriented horizontally, vertically, at 45 45 45^(@)45^{\circ}45, and at 45 45 -45^(@)-45^{\circ}45. Give a set of 3 × 3 3 × 3 3xx33 \times 33×3 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.
7. a) Suppose that an image f ( x , y ) f ( x , y ) f(x,y)f(x, y)f(x,y) is convolved with a mask of size n × n n × n n xx nn \times nn×n (with cofficients 1 / n 2 1 / n 2 1//n^(2)1 / \mathrm{n}^21/n2 ) to produce a smoothed image f ¯ ( x , y ) f ¯ ( x , y ) bar(f)(x,y)\overline{\mathrm{f}}(\mathrm{x}, \mathrm{y})f¯(x,y).
i) Derive an expression for edge strength (edge magnitude) of the smoothed image as a function of mask size. Assume for simplicity that n n n\mathrm{n}n is odd and that edges are obtained using the partial derivatives
f ¯ / x = f ¯ ( x + 1 , y ) f ¯ ( x , y ) and f ¯ / y = f ¯ ( x + 1 , y ) f ¯ ( x , y ) . f ¯ / x = f ¯ ( x + 1 , y ) f ¯ ( x , y ) and f ¯ / y = f ¯ ( x + 1 , y ) f ¯ ( x , y ) . del bar(f)//delx= bar(f)(x+1,y)- bar(f)(x,y)” and “del bar(f)//dely= bar(f)(x+1,y)- bar(f)(x,y)”. “\partial \overline{\mathrm{f}} / \partial \mathrm{x}=\overline{\mathrm{f}}(\mathrm{x}+1, \mathrm{y})-\overline{\mathrm{f}}(\mathrm{x}, \mathrm{y}) \text { and } \partial \overline{\mathrm{f}} / \partial \mathrm{y}=\overline{\mathrm{f}}(\mathrm{x}+1, \mathrm{y})-\overline{\mathrm{f}}(\mathrm{x}, \mathrm{y}) \text {. }f¯/x=f¯(x+1,y)f¯(x,y) and f¯/y=f¯(x+1,y)f¯(x,y).
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 1 / n 1//n1 / n1/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:
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.
8. 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
h ( x α , y β ) = e [ ( x α ) 2 + ( y β ) 2 ] h ( x α , y β ) = e ( x α ) 2 + ( y β ) 2 h(x-alpha,y-beta)=e^(-[(x-alpha)^(2)+(y-beta)^(2)])h(x-\alpha, y-\beta)=e^{-\left[(x-\alpha)^2+(y-\beta)^2\right]}h(xα,yβ)=e[(xα)2+(yβ)2]
Supose that the input to the system is an image cosnsiting of a line of infinitesimal width located at x = a x = a x=a\mathrm{x}=\mathrm{a}x=a, and modeled by f ( x , y ) = δ ( x a ) f ( x , y ) = δ ( x a ) f(x,y)=delta(x-a)\mathrm{f}(\mathrm{x}, \mathrm{y})=\delta(\mathrm{x}-\mathrm{a})f(x,y)=δ(xa), where δ δ delta\deltaδ is an impulse. Assuming no noise, what is the output image g ( x , y ) g ( x , y ) g(x,y)g(x, y)g(x,y) ?
9. a) Define the terms ‘Sampling’ and ‘Quantization’ in context of digital image processing. A medical image has size 8 × 8 8 × 8 8xx88 \times 88×8 inches, the sampling reduction is 5 cycles / m m / m m //mm/ \mathrm{mm}/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
Symbol Probability 1 0.4 2 0.3 3 0.1 4 0.1 5 0.1| Symbol | Probability | | :— | :— | | 1 | 0.4 | | 2 | 0.3 | | 3 | 0.1 | | 4 | 0.1 | | 5 | 0.1 |
  1. a) What is Discrete Fourier Transform (DFT)? Find DFT of the function:
f ( x , y ) = Sin ( 2 π u 0 x + 2 π v 0 y ) f ( x , y ) = Sin 2 π u 0 x + 2 π v 0 y f(x,y)=Sin(2piu_(0)x+2piv_(0)y)f(x, y)=\operatorname{Sin}\left(2 \pi u_0 x+2 \pi v_0 y\right)f(x,y)=Sin(2πu0x+2πv0y)
b) Apply Prewitt operators and Sobel operators for the image given below:
[ α 1 α 2 α 3 α 4 α 5 α 6 α 7 α 8 α 9 ] α 1 α 2 α 3 α 4 α 5 α 6 α 7 α 8 α 9 [[alpha_(1),alpha_(2),alpha_(3)],[alpha_(4),alpha_(5),alpha_(6)],[alpha_(7),alpha_(8),alpha_(9)]]\left[\begin{array}{lll} \alpha_1 & \alpha_2 & \alpha_3 \\ \alpha_4 & \alpha_5 & \alpha_6 \\ \alpha_7 & \alpha_8 & \alpha_9 \end{array}\right][α1α2α3α4α5α6α7α8α9]
\(sin\left(2\theta \right)=2\:sin\:\theta \:cos\:\theta \)

MMTE-003 Sample Solution 2024

mmte-003-solved-assignment-2024-ss–8e24e610-06c9-4b43-84f6-a5bf6ef5ab5c

mmte-003-solved-assignment-2024-ss–8e24e610-06c9-4b43-84f6-a5bf6ef5ab5c

MMTE-003 Solved Assignment 2024 SS
  1. 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.
Answer:
Title: Color Detection for Automobile Bumper Component Placement Using Imaging Techniques
Introduction:
In the context of automating the placement of color-coordinated components on the bumpers of limited-edition sports cars, it is essential to accurately determine the color of each car. The solution must be cost-effective and reliable to ensure the correct selection of bumper components.
Solution Overview:
The proposed solution involves using an imaging system integrated with image processing algorithms to detect the color of cars. The system comprises a digital camera, consistent lighting, and software for image analysis.
1. Camera Selection:
Choose an industrial-grade digital camera with a color sensor (such as CMOS or CCD) capable of capturing high-resolution images. The camera should have adjustable settings to adapt to varying lighting conditions and should be cost-effective to meet budget constraints.
2. Lighting Setup:
Implement a uniform lighting setup using LED lights to minimize shadows and glare, ensuring consistent color representation in the captured images. Proper lighting is crucial for accurate color detection.
3. Image Processing Software:
Utilize open-source libraries like OpenCV for developing the image processing software. OpenCV provides a comprehensive set of tools for image manipulation, color space conversion, and thresholding, which are essential for color detection.
4. Color Detection Algorithm:
Color Space Conversion: Convert the captured RGB image to the HSV color space, which separates the color information (hue) from the intensity, making it easier to identify colors.
Color Range Definition: Define the HSV ranges for the target colors (blue, green, red, and white). These ranges should be determined through experimentation and calibration.
Thresholding: Apply thresholding to isolate pixels within the defined color ranges, creating binary masks for each color.
Color Identification: Analyze the binary masks to determine the predominant color in the image, which corresponds to the car’s color.
5. Integration with Robotic System:
The imaging system should be integrated with the robotic system responsible for placing bumper components. The software should communicate the detected color to the robots, enabling them to select and place the appropriate color-coordinated component.
6. Testing and Calibration:
Conduct extensive testing with cars of known colors to calibrate the color detection algorithm and adjust the HSV ranges as needed. Ensure that the system can accurately detect all target colors under various lighting conditions.
Conclusion:
By implementing an imaging system with carefully chosen hardware and sophisticated image processing algorithms, it is possible to accurately determine the color of cars for automated bumper component placement. This solution is cost-effective and can be integrated with existing robotic systems to enhance manufacturing efficiency in the automobile industry.
b) Consider the two image subsets, S 1 S 1 S_(1)S_1S1 and S 2 S 2 S_(2)S_2S2, shown in the following figure. For V = { 1 } V = { 1 } V={1}\mathrm{V}=\{1\}V={1}, determine whether these two subsets are (i) 4-adjacent, (ii) 8-adjacent, or (iii) m-adjacent.
S 1 S 1 S_(1)S_1S1 S 2 S 2 S_(2)S_2S2
0 0 0 0 0 0 0 1 1 0
1 0 0 1 0 0 1 0 0 1
1 0 0 1 0 1 1 0 0 0
0 0 1 1 1 0 0 0 0 0
0 0 1 1 1 0 0 1 1 1
S_(1) S_(2) 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 | | $S_1$ | $S_2$ | | | | | | | | | | | | | | | :—: | :—: | :—: | :—: | :—: | :—: | :—: | :—: | :—: | :—: | :—: | :—: | :—: | :—: | :—: | :—: | | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | | | | | | | | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | | | | | | | | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | | | | | | | | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | | | | | | | | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | | | | | | |
Answer:
Title: Analysis of Adjacency between Image Subsets S 1 S 1 S_(1)S_1S1 and S 2 S 2 S_(2)S_2S2
Introduction:
Given two subsets of an image, S 1 S 1 S_(1)S_1S1 and S 2 S 2 S_(2)S_2S2, we are tasked with determining their adjacency based on three criteria: 4-adjacency, 8-adjacency, and m-adjacency. The value set V V VVV is defined as { 1 } { 1 } {1}\{1\}{1}.
Adjacency Analysis:
1. 4-adjacency:
  • Definition: Two pixels are 4-adjacent if they share a horizontal or vertical edge and both have a value of 1.
  • Analysis: No pixels in S 1 S 1 S_(1)S_1S1 share a horizontal or vertical edge with any pixel in S 2 S 2 S_(2)S_2S2 having a value of 1.
  • Conclusion: S 1 S 1 S_(1)S_1S1 and S 2 S 2 S_(2)S_2S2 are not 4-adjacent.
2. 8-adjacency:
  • Definition: Two pixels are 8-adjacent if they share an edge (horizontal, vertical, or diagonal) and both have a value of 1.
  • Analysis: One pixel in S 1 S 1 S_(1)S_1S1 (bottom left corner) shares a diagonal edge with a pixel in S 2 S 2 S_(2)S_2S2 (top right corner) where both have a value of 1.
  • Conclusion: S 1 S 1 S_(1)S_1S1 and S 2 S 2 S_(2)S_2S2 are 8-adjacent.
3. m-adjacency:
  • Definition: Two pixels are m-adjacent if they are either 4-adjacent (not applicable here) or 8-adjacent and the path connecting them does not contain any other pixels with value 1.
  • Analysis: Since S 1 S 1 S_(1)S_1S1 and S 2 S 2 S_(2)S_2S2 are 8-adjacent and there are no other pixels with value 1 along the diagonal path connecting them, they satisfy the conditions for m-adjacency.
  • Conclusion: S 1 S 1 S_(1)S_1S1 and S 2 S 2 S_(2)S_2S2 are m-adjacent.
Final Conclusion:
  • S 1 S 1 S_(1)S_1S1 and S 2 S 2 S_(2)S_2S2 are not 4-adjacent.
  • S 1 S 1 S_(1)S_1S1 and S 2 S 2 S_(2)S_2S2 are 8-adjacent.
  • S 1 S 1 S_(1)S_1S1 and S 2 S 2 S_(2)S_2S2 are m-adjacent.

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