Code: T-14                                Subject: IMAGE PROCESSING & COMPUTER GRAPHICS

Time: 3 Hours                                                                                                     Max. Marks: 100

NOTE: There are 11 Questions in all.

· Question 1 is compulsory and carries 16 marks. Answer to Q.1 (A) must be written in the space provided for it in the answer book supplied and nowhere else.

· Answer any THREE Questions each from Part I and Part II. Each of these questions carries 14 marks.

· Any required data not explicitly given, may be suitably assumed and stated.

Q.1      

   (A)     Choose the correct or best alternative in the following:                                         (2 x 4)

a. Projection that preserves relative proportions of objects

(A)  Perspective                                  (B)  Orthographic

(C) Isometric                                     (D)  Parallel

             b.   Size of  image at 240 pixels per inch

(A)  2.5 by 2 inches.                            (B)  1.5 by 2 inches.

(C)  2.67 by 2 inches.                          (D)  3 by 2 inches.

             c.   Low spatial resolution results in

(A) False contouring.                          (B)  Checker board effect

(C)  Moire Patterns                             (D)  none of the above.

             d.   mask is a

(A)   line detection mask.                     (B)   point detection mask.

(C)  Laplacian mask.                           (D)  Gaussain mask.

(B)     Write brief notes on the following :-                                                                       (2 x 4)

(i) Vanishing point.                                                                                   

(ii) Horizontal Retrace.             

(iii) Quantization.                          

(iv) Lossy compression.

PART I

Answer any THREE Questions. Each question carries 14 marks.

Q.2     a.   With a neat diagram explain the construction and working principle of CRT.        (8)

             b.   The American standard video system uses 525 horizontal lines with an aspect ratio of 4:3.  The frame rate is 30 frames / second.  Calculate the time available for each scan line.  If the time required for vertical retrace for each field is 21 lines and the horizontal retrace takes 17% of the time allowed for one scan line, calculate the time available to access and display a pixel.                                                   (6)

Q.3     a.   Explain the DDA algorithm for drawing lines.                                                      (6)

             b.   Calculate the pixel positions for drawing a line segment between (0, 0) and    (-8, -4) in the third quadrant using DDA algorithm. What is the problem in this algorithm?                                               (8)

Q.4     a.   Explain with an example the sequence of transformations required to convert a square to a parallelogram by stretching it along the diagonal.  Derive the composite transformation matrix for this operation.         (8)

b.   Find the mirror reflection of the triangle P (10, 50), Q (40, 60) and R (10, 80) about the line 2y = 2x + 4.                                                              (6)

Q.5     a.   What are parallel projections?  Explain orthographic and oblique projection with suitable figures and transformation matrix for each of them. (8)

             b.   Explain scaling of the size of a 3D object with respect to origin and with respect to a selected fixed position with suitable figures and transformation matrix.                                                                   (6)

  Q.6     a.   Describe the sequence of transformations to align a viewing system with world coordinate axes with suitable example figures.                                   (8)

b. Write and explain the Z-buffer algorithm for hidden surface detection.                 (6)

PART II

Answer any THREE Questions. Each question carries 14 marks.

Q.7     a.   Explain the concepts of image sampling and quantization with suitable diagrams.  Explain how digital images are represented.                                   (8)

b. What is the purpose of a color model? Explain the HSI color model and write the equations for converting colors from RGB to HSI.                     (6)

Q.8     a.   What is a histogram?  Draw the histogram for different types of images.  Briefly explain the histogram equalization technique for image enhancement.                                                                                (8)

     b.   An image has the gray level pdf p(r) shown in Fig.1.  It is desired to transform the gray levels of this image so that they will have the specified p(z) shown.  Assume continuous quantities and find the transformation in terms of r and z that will accomplish this.                                                                            (6)

Q.9     a.   What is convolution and correlation?  Write the convolution and correlation theorems in frequency domain.  Prove the convolution theorem.  Mention the differences between these two operations with their applications.                                        (8)

             b.   Explain the filtering in the frequency domain.  Indicate the differences between ideal, Butterworth and Gaussian filters in frequency domain.    (6)

Q.10           a.                                                        Write short notes on Threshold coding and Zonal coding techniques for coding the transform coefficients.  Clearly indicate the differences between these two coding strategies.                                                            (8)

             b.  A zero memory information source with source alphabet A = {X, Y, Z} has symbol probabilities P(X)= 0.1, P(Y) = 0.2 and P(Z) = 0.7.   If the symbols are coded with Huffman code, find the average length and efficiency of the resultant code.                                                                           (6)

Q.11     a.   Explain the optimal global thresholding segmentation algorithm with necessary equations.                 (8)

             b.   For the edge models shown in Fig.2 sketch the profile of a horizontal line, its gradient and Laplacian. (6)