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

Time: 3 Hours                                                                                                     Max. Marks: 100

NOTE: There are 9 Questions in all.

· Question 1 is compulsory and carries 20 marks. Answer to Q. 1. must be written in the space provided for it in the answer book supplied and nowhere else.

· Out of the remaining EIGHT Questions answer any FIVE Questions. Each question carries 16 marks.

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

Q.1       Choose the correct or best alternative in the following:                                         (2x10)

a. The method used for displaying color pictures with raster scan monitors is

(A)  shadow mask method.                  (B)  refreshing method.

(C)   raster method.                             (D)  none of the above.

b. This is used to grasp a virtual object.

(A)  mouse.                                         (B)  data glove.

(C)  joystick..                                      (D)  light pen.

             c.   The transformation matrix that defines shearing is given by

(A) (B)

(C) (D)

             d.   If P (x, y, z, w) are the homogeneous coordinates of a point in the three dimensional projective plane, the corresponding three dimensional Cartesian point P(x, y, z) is

(A) (wx, wy, wz)                                (B)  (x/w, y/w, z/w)

(C)  (x+w,y+w, z+w)                          (D)  (x-w, y-w, z-w)

             e.   An orthographic projection is obtained from oblique projection when the projection angle is

(A) (B) 

(C)  (D)

             f.    The number of bits required to store a digitised image of size 512512 with a resolution of 8 levels for a pixel is

(A) 262144                                         (B) 2097152

(C)  786432                                        (D)  87381

             g.   If the components of the image histogram cover a narrow range and centered toward the middle of the gray scale, then the image is a

(A) High contrast image                       (B)  Low contrast image

(C)  Dark image                                  (D)  Bright image

             h.   Imaging file formats GIF, TIFF and PDF use this compression technique.

(A) Huffman coding.                           (B) LZW coding.

(C) Bit plane coding.                            (D) JPEG.

             i.    Which is used to determine whether an edge pixel lies on the dark or light side of an edge?

(A) Sign of first derivative                   (B) Magnitude of first derivative.

(C) Magnitude of second derivative.     (D) Sign of second derivative.

             j.    Quadtrees are a convenient representation for

(A)  Line detection.                              (B)  Edge linking.

(C)  Region splitting and Merging.        (D) Thresholding.

Answer any FIVE Questions out of EIGHT Questions.

Each question carries 16 marks.

Q.2     a.   Let R be the rectangular window whose lower left hand corner is at L(-3, 1) and upper right hand corner is at R(2,6). Find the region codes for the points A(-4, 2), B(-1, 7), C(-1, 5), D(3, 8), E(-2, 3), F(1, 2), G(1, -2), H(3, 3),      I(-4, 7) and J(-2, 10). Find whether the line segments AB, CD, EF, GH and IJ require clipping or not.                                                                                                 (10)

             b.   What is visible surface detection? How are these algorithms classified? Explain back face detection algorithm with suitable figures.                             (6)

Q.3     a.   Explain the steps required to plot a line whose slope is between and  using Bresenhem’s algorithm with an example.                                  (8)

             b.   Illustrate the steps to draw a circle of radis r = 10 with the origin as the centre using the midpoint circle algorithm.                                            (8)

Q.4     a.   Find the composite transformation matrix for the general pivot point rotation about any selected point (x, y).  Explain with the help of an example.                                                                  (8)

b.   Magnify the triangle with vertices A(0, 0), B(1, 1) and C(5, 2) to twice its size while keeping C(5, 2) fixed.                                                            (8)

Q.5     a.   Explain three dimensional rotation with respect to different axes giving the transformation matrix for each of the case.                                              (8)

     b.   Describe in detail the steps required to transform world coordinates to viewing coordinates.                                                                       (8)

  Q.6     a. Describe different image acquisition techniques with suitable diagrams and explain the image formation model.                                                                                                               (8)

             b.   Given the following histogram of an original image, perform the histogram equalization technique and obtain the transformation function and the enhanced histogram.                                                     (8)

Grey Value	Number of pixels
0	20
10	15
20	10
30	5
40	0

Q.7     a.   State and prove the following properties of Fourier transform

(i) Translation

(ii) Average value

(iii) Distributivity

(iv) Periodicity                                                                                 (8)

b.   Explain the Fast Fourier Transform algorithm with necessary equations and compare its complexity with that of the direct Discrete Fourier Transform.                                                                            (8)

Q.8     a.   Encode the pixel values {1, 1, 2, 1, 2, 1, 3, 2, 1, 1, 3, 2, 1, 1, 4, 1, 1, 1} using the LZW algorithm. Starting with the dictionary given below clearly indicate the final dictionary contents and the encoded sequence.                                                           (8)

Dictionary Location	Entry
1	1
2	2
3	3
4	4

             b.   Explain transform coding of images clearly explaining transform selection, subimage size selection and bit allocation.                                            (8)

Q.9     a.   Explain the Hough transform technique for linking points by determining if they lie on a curve of specified shape.                                                 (10)

b.   Consider an 8 8 image shown in the figure below. Draw the quadtree and determine the quadtree representation.                                     (6)