IGNOU MMTE003 Solved Assignment 2024  M.Sc. MACS
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IGNOU MMTE003 Assignment Question Paper 2024
mmte003solvedassignment2024ff79897dd25e4830beb3d263cf85ddfe
 a) An automobile manufacturer is automating the placement of certain components on the bumpers of a limitededition 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_1 and${S}_{1}$ ${S}_{2}$ ${S}_{2}$ S_(2) S_2 , shown in the following figure. For${S}_{2}$ $\mathrm{V}=\{1\}$ $\mathrm{V}=\{1\}$ V={1} \mathrm{V}=\{1\} , determine whether these two subsets are (i) 4adjacent, (ii) 8adjacent, or (iii) madjacent.$\mathrm{V}=\{1\}$
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 
 a) Two images,
$f(x,y)$ $f(x,y)$ f(x,y) f(x, y) and$f(x,y)$ $g(x,y)$ $g(x,y)$ g(x,y) g(x, y) , have histograms$g(x,y)$ ${h}_{f}$ ${h}_{f}$ h_(f) h_f and${h}_{f}$ ${h}_{g}$ ${h}_{g}$ h_(g) h_g . Give the condition under which you can determine the histograms of${h}_{g}$
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)$f(x,y)\times g(x,y)$ $f(x,y)\times g(x,y)$ f(x,y)xx g(x,y) f(x, y) \times g(x, y) $f(x,y)\times g(x,y)$
iv)$f(x,y)\xf7g(x,y)$ $f(x,y)\xf7g(x,y)$ f(x,y):g(x,y) f(x, y) \div g(x, y) $f(x,y)\xf7g(x,y)$
b) Write an expression for 2D continuous convolution.  a) Prove that both 2D continuous and discrete Fourier transforms are linear operations.
b) Consider a$3\times 3$ $3\times 3$ 3xx3 3 \times 3 spatial mask that averages the four closet neighbours of a point ($3\times 3$ $\mathrm{x},\mathrm{y})$ $\mathrm{x},\mathrm{y})$ x,y) \mathrm{x}, \mathrm{y}) , but excludes the point itself from the average.$\mathrm{x},\mathrm{y})$
i) Find the equivalent filter,$\mathrm{H}(\mathrm{u},\mathrm{v})$ $\mathrm{H}(\mathrm{u},\mathrm{v})$ H(u,v) \mathrm{H}(\mathrm{u}, \mathrm{v}) , in the frequency domain.$\mathrm{H}(\mathrm{u},\mathrm{v})$
ii) Show that your result is a lowpass filter.  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$3\times 3$ $3\times 3$ 3xx3 3 \times 3 arithmetic mean filter?$3\times 3$
ii) A 7 × 7 arithmetic mean filter?
iii) A 9 × 9 arithmetic mean filter?
 a) Consider an 8pixel 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\} . If it is uniformly quantized with 4bit accuracy, compute the rms error and rms signaltonoise ratios for the quantized data.$\{108,139,135,244,172,173,56,99\}$
b) Prove that, for a zeromemory source with q symbols, the maximum value of the entropy is$\mathrm{log}\mathrm{q}$ $\mathrm{log}\mathrm{q}$ log q \log \mathrm{q} , which is achieved if and only if all source symbols are equiprobable. [Hint: Consider the quantity$\mathrm{log}\mathrm{q}$ $\mathrm{log}\mathrm{q}\mathrm{H}(\mathrm{z})$ $\mathrm{log}\mathrm{q}\mathrm{H}(\mathrm{z})$ log qH(z) \log \mathrm{q}\mathrm{H}(\mathrm{z}) and note the inequality In$\mathrm{log}\mathrm{q}\mathrm{H}(\mathrm{z})$ $\mathrm{x}\le \mathrm{x}1$ $\mathrm{x}\le \mathrm{x}1$ x <= x1 \mathrm{x} \leq \mathrm{x}1 ].$\mathrm{x}\le \mathrm{x}1$  a) The arithmetic decoding process is the reverse of the encoding procedure. Decode the message 0.23355 given the coding model
Symbol  Probability 
0.2  
0.3  
0.1  
0.2  
0.1  
0.1 
7. a) Suppose that an image
i) Derive an expression for edge strength (edge magnitude) of the smoothed image as a function of mask size. Assume for simplicity that
b) Explain how the MPP algorithm behaves under the following conditions:
i) 1pixel wide, 1pixel deep indentations.
ii) 1pixel wide, 2 or more pixel deep indentations.
iii) 1pixel wide, 1pixel longprotrusions.
iv) 1pixel wide, npixel 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, positioninvariant image degradation system with impulse response
9. a) Define the terms ‘Sampling’ and ‘Quantization’ in context of digital image processing. A medical image has size
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 
 a) What is Discrete Fourier Transform (DFT)? Find DFT of the function:
MMTE003 Sample Solution 2024
mmte003solvedassignment2024ss–8e24e61006c94b4384f6a5bf6ef5ab5c
 a) An automobile manufacturer is automating the placement of certain components on the bumpers of a limitededition 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.
In the context of automating the placement of colorcoordinated components on the bumpers of limitededition sports cars, it is essential to accurately determine the color of each car. The solution must be costeffective and reliable to ensure the correct selection of bumper components.
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.
Choose an industrialgrade digital camera with a color sensor (such as CMOS or CCD) capable of capturing highresolution images. The camera should have adjustable settings to adapt to varying lighting conditions and should be costeffective to meet budget constraints.
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.
Utilize opensource 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.
– 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.
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 colorcoordinated component.
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.
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 costeffective and can be integrated with existing robotic systems to enhance manufacturing efficiency in the automobile industry.
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 
Given two subsets of an image,
 Definition: Two pixels are 4adjacent 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_1 share a horizontal or vertical edge with any pixel in${S}_{1}$ ${S}_{2}$ ${S}_{2}$ S_(2) S_2 having a value of 1.${S}_{2}$  Conclusion:
${S}_{1}$ ${S}_{1}$ S_(1) S_1 and${S}_{1}$ ${S}_{2}$ ${S}_{2}$ S_(2) S_2 are not 4adjacent.${S}_{2}$
 Definition: Two pixels are 8adjacent 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_1 (bottom left corner) shares a diagonal edge with a pixel in${S}_{1}$ ${S}_{2}$ ${S}_{2}$ S_(2) S_2 (top right corner) where both have a value of 1.${S}_{2}$  Conclusion:
${S}_{1}$ ${S}_{1}$ S_(1) S_1 and${S}_{1}$ ${S}_{2}$ ${S}_{2}$ S_(2) S_2 are 8adjacent.${S}_{2}$
 Definition: Two pixels are madjacent if they are either 4adjacent (not applicable here) or 8adjacent and the path connecting them does not contain any other pixels with value 1.
 Analysis: Since
${S}_{1}$ ${S}_{1}$ S_(1) S_1 and${S}_{1}$ ${S}_{2}$ ${S}_{2}$ S_(2) S_2 are 8adjacent and there are no other pixels with value 1 along the diagonal path connecting them, they satisfy the conditions for madjacency.${S}_{2}$  Conclusion:
${S}_{1}$ ${S}_{1}$ S_(1) S_1 and${S}_{1}$ ${S}_{2}$ ${S}_{2}$ S_(2) S_2 are madjacent.${S}_{2}$
${S}_{1}$ ${S}_{1}$ S_(1) S_1 and${S}_{1}$ ${S}_{2}$ ${S}_{2}$ S_(2) S_2 are not 4adjacent.${S}_{2}$ ${S}_{1}$ ${S}_{1}$ S_(1) S_1 and${S}_{1}$ ${S}_{2}$ ${S}_{2}$ S_(2) S_2 are 8adjacent.${S}_{2}$ ${S}_{1}$ ${S}_{1}$ S_(1) S_1 and${S}_{1}$ ${S}_{2}$ ${S}_{2}$ S_(2) S_2 are madjacent.${S}_{2}$
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