1. CMSC5711
Revision 3
CMSC5711 revision 3 ver.x67.8c

2. CMSC5711, Revision3, Q1:(20 %) A 3D point M is at [X,Y,Z]T=[1,1,5]T meters in the world coordinate system. Intrinsic parameters (Mint) and characteristics:
The horizontal focal length in meters is Fx=5mm. And the vertical focal length in meters is Fy=5mm, and the image centre is at (Ox ,Oy)=(0,0).
The image centre is at the centre of the image plane.
You may assume the camera coordinates are the same as the world coordinates.
The point M is at the (500,500) pixel position. Estimate the horizontal pixel width sx and vertical pixel width sy in meters.
Calculate the horizontal and vertical focal lengths (fx, fy) in pixels.
Discuss the purpose of having parameters Ox and Oy of a camera.
If you are using a similar camera, all the above parameters are the same but Ox and Oy are different. Based on this new camera, the image point of M is not at (500,500) pixels but at (530,490) pixels instead. Calculate O’x and O’y in pixels of the new camera.
M is being rotated around a point P=[0.5, 0.6, 0.7] T in meters first, the rotation angles are (1, 2, 1.5) in degrees (remember to convert degrees into radians before use). Then, it is translated by T= [0.1,0.2,0.3]T meters . Find the new 3-D position (M’) of M in pixels.Note: 1, 2, 3 are in radians. Assume the image centre is at (O’x , O’y) find the 2-D image position (in pixels) of M’.
CMSC5711 revision 3 ver.x67.8c

3. Q2 (15%) Convolution , edge mask and edge detection
An image S and a mask m are shown below
Find the convolution result of S and m, the result include all partially overlapping cases.
Show the matrix of a normalized 3 x 3 smoothing convolution mask that you know.
What is the problem of using a second order edge detection method?
CMSC5711 revision 3 ver.x67.8c

4. Q3:(15 %) An original gray level image has resolution M=50 rows and N=50 columns. The gray level resolution (L) of each pixel is 8 (gray level from 0 to 7). R(k) is the gray level of index k, N(k) is the number of pixels that have gray level R(k). Pr(R(k)) is the probability of the pixels in the image having gray level R(k). After histogram normalization, S(k) is the normalized gray level of index k. A table to help you to perform histogram equalization is shown below.
Find the value of Y in the table.
Discuss the relation between pixel resolution (bits per pixel) and the result of histogram normalization in image processing.
For the following table (you may copy it to your answer book first), fill in the blanks.
Discuss how to use histogram equalization to make a colour picture looks better.
r(k)
N(k)
Pr(r(k))
S(k)
Round off (S(k))
r(0)
 0.0056
r(1)
 0.0228
r(2)
 0.0940
r(3)
 0.2460
r(4)
 0.3248
r(5)
 0.2000
r(6)
 0.0808
r(7)  Y
CMSC5711 revision 3 ver.x67.8c

5. Q4
(10 %) In a stereo system with 2 parallel cameras (the principal axis are in parallel) as shown below, derive Z in terms of left image position x’l, right image position x’r, baseline b and focal length f.
CMSC5711 revision 3 ver.x67.8c

6. Q5 (15 %) Corner feature calculation. Horizontal gradient I/x of A
Discuss the Harris algorithm to find corner features in an image.
An image window A has 3x3 image horizontal and vertical gradient images shown below. Calculate E.
Discuss how to check if this window has a corner feature or not. There is no need to find the actual Eigen values involved, just describe the procedure.
Horizontal gradient I/x of A
Vertical gradient I/y of A 2 4 1 7 6 1 2 5 3
CMSC5711 revision 3 ver.x67.8c

7. #The VRML code starts from here, # is used for commenting in VRML.
#(table (i)) 3-D points)
# format used for each line: X,Y,Z positions in 3-D and point index p
0 0 1, # point p0
1 0 1, # point p1
1 1 1, # point p2
0 1 1, # point p3
0 0 0, # point p4
1 0 0, # point p5
1 1 0, # point p6
0 1 0, # point p7
#(table (ii)) Triangles
# format used for each line: point index1, point index2, , point index3, -1 (end of line code)
# the triangles are using the anticlockwise format
, #first line of table ii, triangle 1, using point 0, 1, 2, -1 is end of line code.
: (missing part a: 3 lines of VRML code of table ii)
 #(table iii) 2-D points in the image
0 0, # first line of table iii, #0 point 0
: (missing part b: 7 lines of VRML code of table iii)
 #(table (iv)) Triangles
, # first line of table iv
: (missing part c: 3 lines of VRML code of table iv)
Write the missing parts: a,b,c (underlined) in the above VRML program.
Q6: (15 %) 3-D display using VRML ((Virtual Reality Modelling Language) files.
In writing the VRML file, one has to write 4 tables(i), (ii), (iii) and (iv). The VRML code, the VRML 3-D display, the 3-D object and the 2D texture image are shown below.
CMSC5711 revision 3 ver.x67.8c

8. CMSC5711 revision 3 ver.x67.8c