ENT492-ROBOT VISION
SESSION 2008/09
TUTORIAL 2
2.1 The gray level of the object and the background pixels are distributed according to the
probability density function
 1 2

a  ( x  b) 2 , b  a  x  a  b
p( x)   3a 3

0, otherwise

With a=1, b=5 for background and a=2, b=7 for the object, sketch the two distributions
and determine the range of possible. If the object pixels are 4/5 of the total number of
pixels, determine the threshold.


2.2 Use any convolution mask to obtain the edge of the following image for a value of
threshold of 6 and 8.
2.3 Consider the binary image given below:
(i)
Determine the boundary of the object using edge detection
(ii)
Determine the area, aspect ratio and the centroid of the image
Assume the object is white (1s) and background is black (0s)
2.4 Suppose that an image has the gray level probability density functions as shown,
where p1 ( z ) and p2 ( z) corresponds to the object and background respectively. Find the
threshold between the object and the background if the probability of the object is twice
than the background.
1
p1 ( z)
p2 ( z )
3
8
13
z
2.5 Find the 4-directional chain code, difference code and shape number for the image
shown. Repeat this for 8-directional.
2.6 Obtain the chain code, difference code and shape number for 4-directional and 8directonal converters for the following images.
2.7 Consider the following three pattern classes:
T
T
T
T
w1 : 1.2 0.7 , 1 1 , 1.1 1.2 , 0.7 1.1 ,
w2

: 3.2
: 5.3
2.7 , 3 3 , 3 3.2 , 2.8
T
T
T

3.1 
T

w3
1.2 , 4.8 0.9 , 4.9 1.1 , 5 0.8
(i) Find 1 ,  2 , and  3 , the mean pattern vectors of the three classes.
T
T
T
T
(ii) Determine the decision functions z1 ( x), z 2 ( x) and z3 ( x)
(iii) Determine the class member of an unknown pattern
T
vector x  6 2