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

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$$S_1$S_(1)S_1$S_1$ and $S_2$$S_2$S_(2)S_2$S_2$, shown in the following figure. For $\mathrm{V}=\{1\}$$\mathrm{V}=\{1\}$V={1}\mathrm{V}=\{1\}$\mathrm{V}=\{1\}$, determine whether these two subsets are (i) 4-adjacent, (ii) 8-adjacent, or (iii) m-adjacent.

2. 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$$h_f$h_(f)h_f$h_f$ and $h_g$$h_g$h_(g)h_g$h_g$. 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)\times g(x,y)$$f(x,y)\times g(x,y)$f(x,y)xx g(x,y)f(x, y) \times g(x, y)$f(x,y)\times g(x,y)$
   iv) $f(x,y)÷g(x,y)$$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.
3. a) Prove that both 2-D continuous and discrete Fourier transforms are linear operations.
   b) Consider a $3\times 3$$3\times 3$3xx33 \times 3$3\times 3$ spatial mask that averages the four closet neighbours of a point ( $\mathrm{x},\mathrm{y})$$\mathrm{x},\mathrm{y})$x,y)\mathrm{x}, \mathrm{y})$\mathrm{x},\mathrm{y})$, but excludes the point itself from the average.
   i) Find the equivalent filter, $\mathrm{H}(\mathrm{u},\mathrm{v})$$\mathrm{H}(\mathrm{u},\mathrm{v})$H(u,v)\mathrm{H}(\mathrm{u}, \mathrm{v})$\mathrm{H}(\mathrm{u},\mathrm{v})$, in the frequency domain.
   ii) Show that your result is a lowpass filter.
4. The white bars in the test pattern shown are 7 pixels wide and 210 pixels high. The separation between bars is 17 pixels. What would this image look like after application of
   i) A $3\times 3$$3\times 3$3xx33 \times 3$3\times 3$ arithmetic mean filter?
   ii) A 7 × 7 arithmetic mean filter?
   iii) A 9 × 9 arithmetic mean filter?

5. a) Consider an 8-pixel line of intensity data, $\{108,139,135,244,172,173,56,99\}$$\{108,139,135,244,172,173,56,99\}${108,139,135,244,172,173,56,99}\{108,139,135,244,172,173,56,99\}$\{108,139,135,244,172,173,56,99\}$. If it is uniformly quantized with 4-bit accuracy, compute the rms error and rms signal-tonoise ratios for the quantized data.
   b) Prove that, for a zero-memory source with q symbols, the maximum value of the entropy is $\log \mathrm{q}$$\log \mathrm{q}$log q\log \mathrm{q}$\log \mathrm{q}$, which is achieved if and only if all source symbols are equiprobable. [Hint: Consider the quantity $\log \mathrm{q}-\mathrm{H}(\mathrm{z})$$\log \mathrm{q}-\mathrm{H}(\mathrm{z})$log q-H(z)\log \mathrm{q}-\mathrm{H}(\mathrm{z})$\log \mathrm{q}-\mathrm{H}(\mathrm{z})$ and note the inequality In $\mathrm{x}\le \mathrm{x}-1$$\mathrm{x}\le \mathrm{x}-1$x <= x-1\mathrm{x} \leq \mathrm{x}-1$\mathrm{x}\le \mathrm{x}-1$ ].
6. a) The arithmetic decoding process is the reverse of the encoding procedure. Decode the message 0.23355 given the coding model

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