Solve your IGNOU Doubts

Question:

What is Discrete Fourier Transform (DFT)? Find DFT of the function: $f(x,y)=Sin(2\pi u_0x+2\pi v_0y)$

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Question:

Let C1 and C2 be two binary codes with generator matrices

$G_1=\begin{bmatrix} 1 &0 & 0 & 1\\ 0 & 1 & 0&0 \\0 & 0 &1 &1 \end{bmatrix},$ $G_2=\begin{bmatrix} 1 & 0 & 0&1 \\ 0 & 1 & 1 & 0 \end{bmatrix},$

respectively.

a) Find the minimum distance of both the codes.

b) Find the generator matrix of the c

Image ignouassignments-ignouacademy-com--p-solve-37061

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Question:

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

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Question:

a) Which of the following binary codes are linear?

Image ignouassignments-ignouacademy-com--p-doubts-21344

Justify your answer.

b) Find the minimum distance for each of the codes.

c) For each of the linear codes, find the degree, a generator matrix and a parity check matrix.

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Question:

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

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Question:

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

h( $(x-\alpha ,y-\beta )=e^{-[(x-\alpha )^{2}+(y-\beta )^{2}]}$

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

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Question:

1) Which of the following statements are true and which are false? Justify your answer with a short proof or a counterexample. (

i) If the weight of each element in the generating matrix of a linear code is at least r, the mininum distance of the code is at least r.

ii) There is no linear self orthogonal code of odd length.

iii) There is no 3-cyclotomic coset modulo 121 of size 25.

iv) There is no duadic code of length 15 over F $F_{2.}$

v) There is no LDPC code with parameters n = 16, c = 3 and r = 5.

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Question:

a) Devise an efficient algorithm that takes advantage of symmetry properties to display a sine function.

b) Prove that the reflection along the line y = −x is equivalent to reflection along the y-axis followed by a counter-clockwise rotation by 90◦ .

c) Shear a square whose opposite vertices are at (1,1) and (2,2) by i) 2 units along the x-axis and reference line y = 0

ii) 4 units along the y-axis and reference line x = 0.

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Question:

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

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Question:

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.

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Question:

a) If the origin is taken as the centre of projection, then what will be the perspective projection when the projection plane passes through the point P(4,5,3) and has normal vector (1,2,−1).

b) Write a program that produces different views of a cuboid, that is, how the cuboid looks from the top, from the front or from the right.

c) Write a code to continuously rotate a pentagon about a corner point in the anti-clockwise direction.

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Question:

Suppose that an image )y,x(f is convolved with a mask of size n × n (with cofficients 1/n2 ) to produce a smoothed image ).y,x(f (5) 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

$\partial \bar{f}/\partial x= \bar{f}(x+1,y)- \bar{f}(x,y)$ and $\partial \bar{f}/\partial y= \bar{f}(x+1,y)- \bar{f}(x,y).$

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. In other words, edge strength is inversely proportional to the size of the smoothing mask.

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Question:

a) What is the difference between a parallel projection and a perspective projection? Explain with examples.

b) What will be the perspective projection of a unit cube on the plane x = y if it is viewed from the point (1,2,0)? Justify your answer.

c) Transform the scene in the world coordinate system to the viewing coordinate system with viewpoint at (1,1,2). The view plane normal vector is(−4,2,5) and the view up vector is (1,4,0).

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Question:

a) Write a boundary fill procedure to fill an 8-connected region.

b) Let W be the window having two diagonally opposite corners at (10, 2) and (30, 15). Trace the Cohen-Sutherland line clipping algorithm for the line segment joining the points (0,0) and (15, 30).

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Question:

a) Transform the quadrilateral ABCD with vertices A(1,0),B(4,−1),C(5,3) and D(−1,5) under a translation by the point (4, 5) followed by a counter-clockwise rotation by an angle of 45◦

.b) If you perform an x-direction shear transformation, and then a y-direction shear transformation, will the result be the same as the one which is obtained when it is simultaneous shear in both the directions? Justify your answer.

c) Let W be a window with corners (0,0),(8,0),(8,4) and (0,4). Clip a triangle with vertices (1,1),(10,2) and (5,9) against the window W by tracing Liang Barskey line clipping algorithm

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Question:

a) Consider a polygon with vertices at (5, 20), (12, 5), (15, 15), (25, 5), (30, 25), and (15, 30). Prepare a sorted edge list, and then make the active edge list for the

scanlines y = 5,10,15,20,25,30.

b) Develop and implement the flood fill algorithm.

c) Prove or disprove: "Multiplication of transformation matrices for two successive rotations is commutative."

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Question:

a) Explain what do you understand by the terms persistence, refresh rate, resolution, aspect ratio, horizontal and vertical retrace.

b) Compute the pixel positions along the line path of the lien joining the points A and B(10,8).

c) Using the midpoint method and symmetry in account, develop an efficient method

for scan converting the curve $y^{2}=4x$ n the interval [0, 10].

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Question:

A binary image contains straight lines oriented horizontally, vertically, at 45⁰ , and at – 45o . Give a set of 3 × 3masks 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.

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Question:

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

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Question:

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-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, 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

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