<p>Safe and Secure Inc. is a company that specializes in electronic security systems. You are part of their
research and development team and are developing a product that identifies people based on the stromal
pattern of the iris in their eye and permits or denies access based upon this identification.
The stromal pattern in the iris is determined randomly during embryonic gestation and is unique to each
individual; even identical twins have different iris patterns. In addition, it changes very little as we age. This
makes it attractive for biometric identification. Indeed, iris recognition systems have been used for passport
free immigration at Schiphol Airport in the Netherlands and in the United Arab Emirates since 2001.
Commercially available iris recognition systems work, essentially, as follows. Digital photographs of the
irises of the individuals to be identified are carefully centered and scaled and stored in a database. When
a person needs to be identified, a photograph of their iris is taken and it is compared with those in the
database. If a match is found, the person is positively identified. The algorithms used to encode and
compare the images of irises are very sophisticated and this makes these systems quite costly. Safe and
Secure Inc. has developed a device in which only partial information about the iris images is stored. This
means that the algorithm used to compare two images can be much more primitive. If it works, the hope
is that it would be cheaper but still viable for, say, small companies that have areas to which they need to
restrict access to only a handful of people.
The device Safe and Secure Inc. has developed works as follows. A person looks through a peephole. This
locates their eye precisely and controls the ambient light reaching their eye which in turn controls the size
of the pupil. The device takes a digital photograph of their iris using a 500 by 500 grid and calculates the
integral of the intensity function through 10 different lines through the image producing a vector of length
10. The lines are shown in the picture below.
column, c
row, r
50 100 150 200 250 300 350 400 450 500
50
100
150
200
250
300
350
400
450
500
More specifically, the lines are:
1. r = 125 (from c = 1 to c = 500),
2. r = 250 (from c = 1 to c = 500),
3. r = 375 (from c = 1 to c = 500),
4. c = 125 (from r = 1 to r = 500),
5. c = 250 (from r = 1 to r = 500),
6, c = 375 (from r = 1 to r = 500),
7. The sub-diagonal stretching from r = 250 and c = 1 to r = 1 and c = 250,
8. The sub-diagonal stretching from r = 1 and c = 251 to r = 250 and c = 500,
9. The sub-diagonal stretching from r = 251 and c = 1 to r = 500 and c = 250,
10. The sub-diagonal stretching from r = 500 and c = 251 to r = 251 and c = 500.
Only the values of these 10 integrals and not the whole image are stored. People that are to be allowed
access to the company’s restricted area will look into the device and the corresponding vector of length 10
will be stored in a database. When a person wants to gain access to the restricted area they will be required
to look into the device. The device will calculate the corresponding vector of length 10 and compare it with
those in the database. If a match is found the person will be admitted, otherwise they will be denied entry.
Whether or not this system will work depends on how two different vectors of length 10 are to be compared.
In particular, when the same person looks into the device on two different occasions the corresponding vectors
1
that are obtained will be close but not exactly the same. So the question is, what does it mean for two
vectors to be close to each other and how close do they need to be in order to conclude that they are coming
from the same person?
Your job is to determine if this system could work and, if so, how the distance between two vectors should
be measured and how close two vectors need to be in order to conclude that they come from the same person.
To do this you have been provided with the following:
• The vectors associated with six different people (the control set). Each person looked into the device
three times so you have three vectors for each person. The vectors are called ind1a, ind1b, ind1c,
ind2a, ind2b, ind2c, ...ind6a, ind6b, ind6c. The vector ind1a is the vector obtained from
the first image of the first individual, ind1b is the vector obtained from the second image of the first
individual etc.
• The digital image of the iris of the first person in the control set that produced the vector ind1a.
This is a 500 by 500 matrix called iris1a.
• The images of seven people (the test set) some of whom may be in the control set and some of whom
may not. These are 500 by 500 matrices called iris1, iris2, ...iris7 .
The vectors and images can be downloaded from blackboard. They are in the file called irisdata*.mat
where * is either 1, 2, 3, 4, or 5 depending on which class you are in. Be sure to use the correct file. If you
use the wrong file you may get no credit for this assignment. If you would like to actually see the images of
the eyes corresponding to the matrices iris1a, iris1, iris2, . . . iris7, then use the m-file script lookat
that can also be downloaded from blackboard.
What you need to do:
To determine if the system could work and, if so, how the distance between two vectors should be measured
you should do the following:
a) Explore at least two different ways of measuring the distance between vectors. For each way you
should determine how close two vectors should be in order to conclude that they come from the same
person and you should write a function m-file whose input is a vector and whose output is 1 if that
vector corresponds to someone in the control set and 0 otherwise.
b) Write a function m-file whose input is a 500 by 500 image and whose output is the corresponding
vector of length 10. You can test your m-file on irisdata1a since the corresponding vector is ind1a.
c) Use your m-file in part b) to find the vector corresponding to each image iris1, ...iris7. Then,
for each method you explored in a), determine which of these seven people belong to the control set
and which do not. See if you get the same results with each method.
What you need to turn in for the assignment:
Write up your findings as a report to the project director. The report should be typed and should include
the following:
1. An introduction explaining the issue being addressed.
2. A description of at least two different methods that could be used to measure the distance between
two vectors. In each case show how you determined how close two vectors need to be in order
to conclude that they come from the same person. Show all the work you did to determine this
including any Matlab code you used.
3. Show the m-files you wrote (one for each method) to determine if a given vector belongs to someone
in the control set or not.
4. Show the m-file you wrote that takes an image and finds the corresponding vector of length 10
associated with it.
5. Show the vectors associated with the seven people in the test set and for each method your conclusion
as to whether or not each person was in the control set.
6. A conclusion as to whether or not the system could work.
Attach the cover sheet posted on blackboard to the front of your report. For students in those classes that
meet in the mathematics instructional computer lab on Tuesdays, the report is due on Tuesday Nov 14 in
discussion sections. For all other students the report is due on Thursday Nov 16 in discussion sections.
Disclaimer: The iris images in this project were computer generated and are not real images.</p>