Solve your IGNOU Doubts

Question:

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 7 × 7 arithmetic mean filter?

iii) A 9 × 9 arithmetic mean filter? Image ignouassignments-ignouacademy-com--p-your-20850

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Question:

Consider a 3 × 3 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.

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Question:

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

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Question:

Write an expression for 2-D continuous convolution.

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Question:

a) Two images, f (x,y) and g (x,y), have histograms $h_f$ and $h_g.$ 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) $f(x,y)\times g(x,y)$

iv) $f(x,y)\div g(x,y)$

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Question:

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. Image ignouassignments-ignouacademy-com--p-your-11829

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Question:

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.

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Question:

(a) Find the values of n for which Qn is Eulerian.

(b) Using Fleury’s algorithm, find an Eulerian circuit in the following graph. Image ignouassignments-ignouacademy-com--p-doubts-60478

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Question:

(a) What is the maximum possible flow that can pass through the following network? Define such a flow. Image ignouassignments-ignouacademy-com--p-doubts-95832

(b) State and prove the K¨onig Eg´arvary Theorem.
(c) Let G be a graph having no isolated vertex and no induced subgraph with exactly two edges. Show that G is a complete graph.

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Question:

(a) Verify Euler’s formula for the following plane graph. Image ignouassignments-ignouacademy-com--p-doubts-85807

(b) Check whether the line graph of C5 × K2 is planar or not.
(c) What is the minimum possible thickness of a 4-connected triangle-free graph on 8 vertices? Also draw such a graph.
(d) Define the parameters α(G) and β(G) for a graph G. Also, show that
α(G) + β(G) = n(G).

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Question:

(a) Find the number of spanning trees of the following graph. Image ignouassignments-ignouacademy-com--p-doubts-82562

(b) Solve the Chinese Postman Problem for the graph given in Q. 3(b).
(c) Give an example of a 4-critical graph different from a complete graph. Justify the choice of your example. (d) State and prove the Handshaking Lemma for planar graphs.

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Question:

(a) Let G be a connected n-vertex graph. Prove that G has exactly one cycle iff G has exactly n edges

(b) Find a minimum-weigh spanning tree in the following graph

Image ignouassignments-ignouacademy-com--p-your-66505

(d) Find the chromatic and edge-chromatic numbers of the following graph.

Image ignouassignments-ignouacademy-com--p-your-36302

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Question:

The maximum subsequence sum problem is defined as follows: If $a^{_{1}},a_{2},...., a_{n}$ are in Z, find the maximum value $\sum_{K=i}^{J}=a_{i, }$ for all $i,J, 1\leq i\leq j\leq$ See Answer →

Question:

(a) The complement of the Petersen graph is 2-connected. Prove or disprove

(b) Consider a graph G. Let x, y ∈ V (G) be such that x ↔ y. Show that for all z ∈ V (G), |d(x, z) − d(y, z)| ≤ 1

Image ignouassignments-ignouacademy-com--p-your-53104

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Question:

i) There exists no 9-vertex graph with three vertices of degree 3, four vertices of degree 2 and two vertices of degree 1.

ii) $C_6\vee P_4$ has a cycle of length at least 7.

iii) The diameter of a graph cannot exceed its girth.

iv) Every Hamiltonian graph is Eulerian.

v) Every 3-connected graph is 3-edge-connected.

vi) If G is an Eulerian graph, then so is L(G).

vii) . $X{'}(C_3\times K_2)=3.$

vii) $_X(G)> \omega (G)+1.$

.ix) The minimum size of a $k$ -chromatic graph is $\binom{k}{2}$

x) The 6-dimensional hypercube $Q_6$ has no perfect matching.

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Question:

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Question:

The following data on diagnosis of coronary heart disease (where 0 indicating absence and 1 indicating presence), serum cholesterol (in mg/dl), resting blood pressure (in mmHg) and weight (in kg) were obtained for 80 patients to explore the relationship of coronary heart disease with cholesterol and weight.

S. No.	Serum Cholesterol (mg/dl)	Weight (kg)	Number of Patients having CHD	Total Number of Patients
1	420	60	10	20
2	450	68	15	30
3	400	54	4	15
4	510	74	2	10
5	480	62	1	5

(i) Fit a multiple logistic model for the dependence of coronary heart disease on the average serum cholesterol and weight considering
$\hat{\beta }_{0}^{0}=4.279,\hat{\beta }_{1}^{0}=-0.035$ and $\hat{\beta }_{2}^{0}=0.172$ the initial values of the parameters (solve only for one Iteration).
(ii) Test the significance of the fitted model using Hosmer-Lemeshow test at 5% level of significance.