Ques 1.

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.

Ques 2.

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.                                                                                                      

Ques 3.

a) Two images, f (x,y) and g (x,y), have histograms  and  Give the condition under which you can determine the histograms of

i) 

ii) 

iii) 

iv) 

Ques 4.

Write an expression for 2-D continuous convolution.

Ques 5.

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

Ques 6.

Consider a 3 × 3 spatial mask that averages the four closet neighbours of a point  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.

Ques 7.

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?

Ques 8.

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 

Ques 9.

The arithmetic decoding process is the reverse of the encoding procedure. Decode the message 0.23355 given the coding model

Ques 10.

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.

Ques 11.

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

 and 

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.

Ques 12.

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. 

Ques 13.

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 

Ques 14.

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

h(

Supose that the input to the system is an image cosnsiting of a line of infinitesimal width located at x = a, and modeled by   where δ is an impulse. Assuming no noise, what is the output image g

Ques 15.

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.

Ques 16.

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:

Ques 17.

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

Ques 18.

Apply Prewitt operators and Sobel operators for the image given below: