1 Introduction There are three fundamental principles of There are - - PDF document

1

Fingerprint Identification

By: Travis R. Gault

Overview

Introduction Features of interest Feature Encoding Implementations in Industry Conclusions Lab Overview Steps for Classroom Implementation References Introduction Features of interest Feature Encoding Implementations in Industry Conclusions Lab Overview Steps for Classroom Implementation References

Introduction

Fingerprints have been used for centuries for

identification purposes

Much like irises, each fingerprint is unique to

individuals

Even identical twins have different

fingerprints

Fingerprints have been used for centuries for

identification purposes

Much like irises, each fingerprint is unique to

individuals

Even identical twins have different

fingerprints

2

Introduction

There are three fundamental principles of

fingerprints [3].

• 1. A fingerprint is an individual characteristic and no

two fingers have identical ridge characteristics

• 2. A fingerprint will remain unchanged during an

individual’s lifetime.

• 3. Fingerprints have general ridge patterns, making

it possible to systematically classify them.

There are three fundamental principles of

fingerprints [3].

• 1. A fingerprint is an individual characteristic and no

two fingers have identical ridge characteristics

• 2. A fingerprint will remain unchanged during an

individual’s lifetime.

• 3. Fingerprints have general ridge patterns, making

it possible to systematically classify them.

Features of Interest

Global Features - are the characteristics that any human can see with the naked eye

Basic Ridge Patterns Pattern Area Delta Type Lines Ridge Count

Local Features - or “Minutia Points” are the unique characteristics of fingerprint ridges that are used for positive identification. It’s possible to have the same global features, but the local features remain unique. Global Features - are the characteristics that any human can see with the naked eye

Basic Ridge Patterns Pattern Area Delta Type Lines Ridge Count

Local Features - or “Minutia Points” are the unique characteristics of fingerprint ridges that are used for positive identification. It’s possible to have the same global features, but the local features remain unique.

Features of Interest

Pattern Area - is the part of the fingerprint that contains all the global features. However, some local features may be found outside the pattern area.

Images taken from [1].

Pattern Area - is the part of the fingerprint that contains all the global features. However, some local features may be found outside the pattern area.

Images taken from [1].

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Features of Interest

Core Point - is the approximate center of the fingerprint, and is used as the reference point for reading/classifying the print. More specifically it is defined as the topmost point on the innermost upwardly curving ridgeline The figure below, taken from [2], shows some fingerprints and their core point locations Core Point - is the approximate center of the fingerprint, and is used as the reference point for reading/classifying the print. More specifically it is defined as the topmost point on the innermost upwardly curving ridgeline The figure below, taken from [2], shows some fingerprints and their core point locations

Features of Interest

Type Lines - are the two innermost ridges

that start parallel, diverge, and tend to surround the pattern area.

Type Lines - are the two innermost ridges

that start parallel, diverge, and tend to surround the pattern area.

Type Lines

Features of Interest

Delta - is the point on the first bifurcation,

abrupt ending ridge, meeting of two ridges, dot, fragmentary ridge, or any point on a ridge at or nearest the center of divergence of two type lines, located at or directly in front of their point of divergence.

Delta - is the point on the first bifurcation,

abrupt ending ridge, meeting of two ridges, dot, fragmentary ridge, or any point on a ridge at or nearest the center of divergence of two type lines, located at or directly in front of their point of divergence.

4

Features of Interest

Ridge Count - is the number of ridges

between the delta and the core.

This is done by drawing an imaginary line

from the Delta to the Core and each ridge that touches this line is counted.

Ridge Count - is the number of ridges

between the delta and the core.

This is done by drawing an imaginary line

from the Delta to the Core and each ridge that touches this line is counted.

Features of Interest

In the figure below, taken from [4], the circle

is the core, the triangle is the delta, the square is a minutiae-ridge ending and the diamond is a minutiae-ridge bifurcation. The

• range line is the ridge count line.

In the figure below, taken from [4], the circle

is the core, the triangle is the delta, the square is a minutiae-ridge ending and the diamond is a minutiae-ridge bifurcation. The

• range line is the ridge count line.

Features of Interest

Local Features

Ridge Ending - ridge ends Ridge Bifurcation - divides into branches Ridge Divergence - diverging of two parallel lines Dot or Island - small ridge Enclosure - divides and reunites Short Ridge - like a dot/island, but larger

Image taken from [5]. Local Features

Ridge Ending - ridge ends Ridge Bifurcation - divides into branches Ridge Divergence - diverging of two parallel lines Dot or Island - small ridge Enclosure - divides and reunites Short Ridge - like a dot/island, but larger

Image taken from [5].

5

Features of Interest

Basic Ridge Patterns

Loop - is the most common (~ 65% of all prints) Arch - more open curve than a loop Whorl - ridge that makes a complete circle (~ 30%

• f all prints)

Basic Ridge Patterns

Loop - is the most common (~ 65% of all prints) Arch - more open curve than a loop Whorl - ridge that makes a complete circle (~ 30%

• f all prints)

Feature E ncoding

Manual Human experts use a combination of visual, textural, minutiae cues and experience for verification Still used in the final stages of law enforcement applications Image based Utilizes only visual appearance. Requires the complete image to be stored (large template sizes) Taken from [5]. Manual Human experts use a combination of visual, textural, minutiae cues and experience for verification Still used in the final stages of law enforcement applications Image based Utilizes only visual appearance. Requires the complete image to be stored (large template sizes) Taken from [5].

Feature E ncoding

Texture based Treats the fingerprint as an oriented texture image Less accurate than minutiae based matchers since most regions in the fingerprints carry low textural content Minutiae based Uses the relative position of the minutiae points The most popular and accurate approach for verification Resembles manual approach very closely. From a software perspective, the minutia are also used to align the images for database comparisons. Texture based Treats the fingerprint as an oriented texture image Less accurate than minutiae based matchers since most regions in the fingerprints carry low textural content Minutiae based Uses the relative position of the minutiae points The most popular and accurate approach for verification Resembles manual approach very closely. From a software perspective, the minutia are also used to align the images for database comparisons.

6

Feature E ncoding

Image Based Matching Using Optical Correlation Advantages

Image itself is used as the template Requires only low resolution images Fast

Disadvantages

Image itself is used as the template Requires accurate alignment of the two prints Not robust to changes in scale, orientation and position

Taken from [5] Image Based Matching Using Optical Correlation Advantages

Image itself is used as the template Requires only low resolution images Fast

Disadvantages

Image itself is used as the template Requires accurate alignment of the two prints Not robust to changes in scale, orientation and position

Taken from [5]

Feature E ncoding

• Texture Based Matching
• Advantages

Uses texture information (lost in optical and minutiae based schemes) Performs well with poor quality prints Features are statistically independent from minutiae and can be combined with minutiae matchers for higher accuracy

• Disadvantages

Requires accurate alignment of the two prints Varies with translation, orientation and non- linear distortion Less accurate than minutiae based matchers

• Taken from [5]
• Texture Based Matching
• Advantages

Uses texture information (lost in optical and minutiae based schemes) Performs well with poor quality prints Features are statistically independent from minutiae and can be combined with minutiae matchers for higher accuracy

• Disadvantages

Requires accurate alignment of the two prints Varies with translation, orientation and non- linear distortion Less accurate than minutiae based matchers

• Taken from [5]

Feature E ncoding

• Minutiae Based Matching
• Advantages

Invariant to translation, rotation and scale changes Very accurate

• Disadvantages

Error prone in low quality images Not robust to non-linear distortion Does not use visual and textural cues Taken from [5].

• Minutiae Based Matching
• Advantages

Invariant to translation, rotation and scale changes Very accurate

• Disadvantages

Error prone in low quality images Not robust to non-linear distortion Does not use visual and textural cues Taken from [5].

7

Feature E ncoding

In simple terms, we’re

looking for areas where ridges stop or intersect another ridge.

This data is stored and used

for comparisons to other templates

Image taken from [5]. In simple terms, we’re

looking for areas where ridges stop or intersect another ridge.

This data is stored and used

for comparisons to other templates

Image taken from [5].

Implementations

Binarization Approach

Used by: MINDTCT fingerprint minutiae detection system NIST uses this in a lot of implementations NBIS - NIST Biometric Image Software Done directionally or with template matching to detect minutiae

Adaptive Flow Orientation Technique

Binarization is done by peak detection But this leads to false positive in areas of poor contrast

Direct Gray Scale Ridge Following

Based on ridge pursuit Has low computational complexity Cannot handle poor contrast prints and images with poor ridge structure Relies on a good orientation map for ridge pursuit

Modified from [5]. Binarization Approach

Used by: MINDTCT fingerprint minutiae detection system NIST uses this in a lot of implementations NBIS - NIST Biometric Image Software Done directionally or with template matching to detect minutiae

Adaptive Flow Orientation Technique

Binarization is done by peak detection But this leads to false positive in areas of poor contrast

Direct Gray Scale Ridge Following

Based on ridge pursuit Has low computational complexity Cannot handle poor contrast prints and images with poor ridge structure Relies on a good orientation map for ridge pursuit

Modified from [5].

Implementations

Images taken from [5]. Images taken from [5].

Binarization Thinning Minutia Detection Acquisition

8

Implementations

The biometrics lab

setup uses the Binarization approach.

Additionally, a variety

• f software is freely

available on the web for C+ + , C# , Java, and VB implementations.

The biometrics lab

setup uses the Binarization approach.

Additionally, a variety

• f software is freely

available on the web for C+ + , C# , Java, and VB implementations.

Implementations

How successful is Fingerprint Matching? Typical False Rejection Rates range between

0.03% -1.4% [1,6]

Typical False Acceptance Rates are around

0.01% -0.001% [1,6].

These rates depend on the manufacturer and

the algorithm used

Comparatively, iris FRR is about 0.001% and

FAR is about 1 in billions (basically 0).

How successful is Fingerprint Matching? Typical False Rejection Rates range between

0.03% -1.4% [1,6]

Typical False Acceptance Rates are around

0.01% -0.001% [1,6].

These rates depend on the manufacturer and

the algorithm used

Comparatively, iris FRR is about 0.001% and

FAR is about 1 in billions (basically 0).

Conclusions

Fingerprinting is still a viable means for biometric identification, especially in law enforcement, where fingerprints may be left behind. Fingerprints also offer a cheaper solution for day-to- day activities than iris recognition Fingerprints are not as good for high-security implementation More work needs to be done to develop better methods to compensate for the variations in fingerprint recording when identifying local features Fingerprinting is still a viable means for biometric identification, especially in law enforcement, where fingerprints may be left behind. Fingerprints also offer a cheaper solution for day-to- day activities than iris recognition Fingerprints are not as good for high-security implementation More work needs to be done to develop better methods to compensate for the variations in fingerprint recording when identifying local features

9

Lab Overview

Each classmate will submit their right thumbprint twice

One set of thumbprints will serve as a gallery One set of thumbprints will serve as a test gallery, along with two additional random prints

Students will use MATLAB and code examples provided to encode fingerprint minutiae Students will test each print from the test gallery and shall report on the FAR and FRR. Students must also include technical documentation as well as a small research segment into the field of fingerprint analysis. Each classmate will submit their right thumbprint twice

One set of thumbprints will serve as a gallery One set of thumbprints will serve as a test gallery, along with two additional random prints

Students will use MATLAB and code examples provided to encode fingerprint minutiae Students will test each print from the test gallery and shall report on the FAR and FRR. Students must also include technical documentation as well as a small research segment into the field of fingerprint analysis.

Lab Overview

This lab will be officially distributed on Tues.,

• Nov. 12, and will be due no later than Noon

in the CVIP Lab on Dec. 8.

Students must submit all code and supporting

files with the report.

Students must arrange to demo their work. This lab will be officially distributed on Tues.,

• Nov. 12, and will be due no later than Noon

in the CVIP Lab on Dec. 8.

Students must submit all code and supporting

files with the report.

Students must arrange to demo their work.

Steps for Implemetation

6 Steps:

Preprocessing Binarization Thinning Minutiae identification Minutiae alignment Database comparisons

6 Steps:

Preprocessing Binarization Thinning Minutiae identification Minutiae alignment Database comparisons

10

Preprocessing

Unless you have a very high quality fingerprint reader, you’ll need to enhance the image after cropping There are two goals:

Increase the contrast in the image Bridge empty spots in ridges

Techniques

Histogram equalization (histeq) Gamma correction Gabor Filter (gaborfilter)

Download from: http://www.mathworks.com/matlabcentral/fileexchange/5237

Unless you have a very high quality fingerprint reader, you’ll need to enhance the image after cropping There are two goals:

Increase the contrast in the image Bridge empty spots in ridges

Techniques

Histogram equalization (histeq) Gamma correction Gabor Filter (gaborfilter)

Download from: http://www.mathworks.com/matlabcentral/fileexchange/5237

Histogram E qualization

The histogram equalization technique is used to improve global image contrast. However, the disadvantage is that it may have the incorrect effect by increasing background noise while decreasing the signal of interest. The implementation of this will depend on the images rendered by your input device. The histogram equalization technique is used to improve global image contrast. However, the disadvantage is that it may have the incorrect effect by increasing background noise while decreasing the signal of interest. The implementation of this will depend on the images rendered by your input device.

Gabor Filter

“The Gabor filter is basically a Gaussian (with variances Sx and Sy along x and y-axes respectively) modulated by a complex sinusoid (with center frequencies U and V along x and y-axes respectively).” [9] This will help bridge the empty spots along ridges. “The Gabor filter is basically a Gaussian (with variances Sx and Sy along x and y-axes respectively) modulated by a complex sinusoid (with center frequencies U and V along x and y-axes respectively).” [9] This will help bridge the empty spots along ridges.

11

Binarization

Next, convert the 8-bit grayscale images to 1-bit images

Select a window block size (say 32x32) Find the average of the values in the block Set values greater than the average equal 1, else 0

Next, convert the 8-bit grayscale images to 1-bit images

Select a window block size (say 32x32) Find the average of the values in the block Set values greater than the average equal 1, else 0

Thinning

Next, we must convert the binary image to a set of lines. This process is called thinning. MATLAB’s morphological toolbox facilitates this bwmorph( bin_img, ‘thin’, ‘inf’) Next, we must convert the binary image to a set of lines. This process is called thinning. MATLAB’s morphological toolbox facilitates this bwmorph( bin_img, ‘thin’, ‘inf’)

Minutiae Detection

We are primarily interested in two types of minutia

Termination Points – where a ridge ends Bifurcation Points – where a ridge splits

Now, consider a 3x3 window in the thinned image (see right). We are interested in figures that look like the top row or rotated versions. We are not interested in images like the bottom row We are primarily interested in two types of minutia

Termination Points – where a ridge ends Bifurcation Points – where a ridge splits

Now, consider a 3x3 window in the thinned image (see right). We are interested in figures that look like the top row or rotated versions. We are not interested in images like the bottom row

1 1 1 1

Bifurcation

1 1

Termination

1 1 1

Not Interested

1 1 1

Not Interested

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Minutiae Detection

How do you tell the difference between valid and invalid windows?

Windows with the center value set equal to 0 are

• f no interest to us.

How do you tell the difference between valid and invalid windows?

Windows with the center value set equal to 0 are

• f no interest to us.

1 1 1

Not Interested

1 1 1

Not Interested

Minutiae Detection

How do you distinguish between bifurcation and termination points?

Sum the entries and subtract 1. If the answer is 3, then it’s a bifurcation point, If the answer is 1, then it’s a termination point

How do you distinguish between bifurcation and termination points?

Sum the entries and subtract 1. If the answer is 3, then it’s a bifurcation point, If the answer is 1, then it’s a termination point

1 1 1 1

Bifurcation

1 1

Termination

1 1 1

Not Interested

1

Not Interested

Minutiae Detection

This is an example

• f detecting the

termination points from a thinned image taken with the lab’s finger print reader. Done using MATLAB This is an example

• f detecting the

termination points from a thinned image taken with the lab’s finger print reader. Done using MATLAB

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Minutiae Detection

This is an example

• f detecting the

bifurcation points from a thinned image taken with the lab’s finger print reader. Done using MATLAB This is an example

• f detecting the

bifurcation points from a thinned image taken with the lab’s finger print reader. Done using MATLAB

Minutiae Detection

This is a composite

• f both the

bifurcation and termination points along with the

• riginal thinned

image. This is a composite

• f both the

bifurcation and termination points along with the

• riginal thinned

image.

Minutiae Detection

After identifying the minutiae as on the previous slides, there are a lot of spurious minutiae that need to be removed This can be done removing minutiae that occur with an arbitrary Euclidian distance from one another. We need to check the following points’ distances:

Termination-Termination Termination-Bifurcation (and vice versa) Bifurcation-Bifurcation

Coordinates separated by a smaller distance than specified shall be removed After identifying the minutiae as on the previous slides, there are a lot of spurious minutiae that need to be removed This can be done removing minutiae that occur with an arbitrary Euclidian distance from one another. We need to check the following points’ distances:

Termination-Termination Termination-Bifurcation (and vice versa) Bifurcation-Bifurcation

Coordinates separated by a smaller distance than specified shall be removed

14

Minutiae Detection Next Time

On Tuesday:

ROI selection Minutiae Orientation/Alignment Gallery comparison Fingerprint project distributed Fingerprint acquisition (CVIP Lab)

On Tuesday:

ROI selection Minutiae Orientation/Alignment Gallery comparison Fingerprint project distributed Fingerprint acquisition (CVIP Lab)

ROI Selection

The ROI selection is determined using MATLAB’s morpho- logical toolbox by running the thinned image is through imclose(), imerode() and imfill(). The results are shown below. The ROI selection is determined using MATLAB’s morpho- logical toolbox by running the thinned image is through imclose(), imerode() and imfill(). The results are shown below.

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ROI Selection

The next step is to mask out coordinates outside the ROI. Graphically, the results are shown below. The next step is to mask out coordinates outside the ROI. Graphically, the results are shown below.

Termination Orientation

Consider a 5x5 square centered about a termination point. We know the angle of each border point w.r.t. the center point. When the termination point intersects the border, we then know a rough estimate of the angle. Consider a 5x5 square centered about a termination point. We know the angle of each border point w.r.t. the center point. When the termination point intersects the border, we then know a rough estimate of the angle.

• 135
• 150

180 150 135

• 45
• 60
• 90
• 120
• 30

X 30 45 60 90 120

Termination Orientation

Example

Let the red blocks represent a termination ridge From this, we determine the angle to be 120 degrees

Example

Let the red blocks represent a termination ridge From this, we determine the angle to be 120 degrees

• 135
• 150

180 150 135

• 45
• 60
• 90
• 120
• 30

X 30 45 60 90 120

16

Termination Orientation

Example

Let the red blocks represent a termination ridge From this, we have two possible angles: 120 or 135 degrees. We must choose which to use. In my code, I use the angle representing the smallest distance from the center. In this case 135.

Example

Let the red blocks represent a termination ridge From this, we have two possible angles: 120 or 135 degrees. We must choose which to use. In my code, I use the angle representing the smallest distance from the center. In this case 135.

• 135
• 150

180 150 135

• 45
• 60
• 90
• 120
• 30

X 30 45 60 90 120

Termination Orientation

Example

Let the red blocks represent a termination ridge From this, we have no possible angles, which indicates noise. In this case, we remove the point from the list of termination minutia.

Example

Let the red blocks represent a termination ridge From this, we have no possible angles, which indicates noise. In this case, we remove the point from the list of termination minutia.

• 135
• 150

180 150 135

• 45
• 60
• 90
• 120
• 30

X 30 45 60 90 120

Bifurcation Orientation

Example

Let the red blocks represent a bifurcation ridge and an unknown ridge. We must determine all three angles, and exclude the angles from the unknown ridge. To do this, apply bwlabel(). One region will be labeled with 1’s, the other with 2’s. Select the correct region that by choosing the label assigned to X

Example

Let the red blocks represent a bifurcation ridge and an unknown ridge. We must determine all three angles, and exclude the angles from the unknown ridge. To do this, apply bwlabel(). One region will be labeled with 1’s, the other with 2’s. Select the correct region that by choosing the label assigned to X

• 135
• 150

180 150 135

• 45
• 60
• 90
• 120
• 30

X 30 45 60 90 120

17

Bifurcation Orientation

Example

Remove X and apply bwlabel() again. In the second figure, red = 1, green = 2, blue = 3 Perform a similar

• peration to determine

the three angles by analyzing each label (1,2,3). Handle multiple angles for each label as with termination points or similarly

Example

Remove X and apply bwlabel() again. In the second figure, red = 1, green = 2, blue = 3 Perform a similar

• peration to determine

the three angles by analyzing each label (1,2,3). Handle multiple angles for each label as with termination points or similarly

• 135
• 150

180 150 135

• 45
• 60
• 90
• 120
• 30

X 30 45 60 90 120

• 135
• 150

180 150 135

• 45
• 60
• 90
• 120
• 30

X 30 45 60 90 120

Orientation Results

The results of finding the termination and bifurcation points is on the right. The results of finding the termination and bifurcation points is on the right.

Gallery Comparisons

General Steps

• 1. Select any one minutia from image A and B. This will

serve as the origin in each image.

• 2. Use the orientation and location information from the

minutia in image A to transform all minutia in image B, about it’s origin.

• 3. Perform a similarity comparison between the minutia in A

to the transformed minutia in B. There are a large variety of algorithms and types available You will investigate and select algorithm to use in the project

• 4. Repeat for all minutia in B.
• 5. Select a new image A to compare against B if the

similarity score is insufficient.

General Steps

• 1. Select any one minutia from image A and B. This will

serve as the origin in each image.

• 2. Use the orientation and location information from the

minutia in image A to transform all minutia in image B, about it’s origin.

• 3. Perform a similarity comparison between the minutia in A

to the transformed minutia in B. There are a large variety of algorithms and types available You will investigate and select algorithm to use in the project

• 4. Repeat for all minutia in B.
• 5. Select a new image A to compare against B if the

similarity score is insufficient.

18

Gallery Comparisons

Graphically, this is what we are doing w.r.t. rotating the coordinates. Image taken from [8]. Graphically, this is what we are doing w.r.t. rotating the coordinates. Image taken from [8].

θ

D E F D E F

X-axis Y-axis X'-axis Y'-axis

y x

θ

D E F D E F

θ

D E F D E F D E F D E F

X-axis Y-axis X'-axis Y'-axis

y x

References

1. “DigitalPersonaTM White Paper: Guide to Fingerprint Identification.” Voice Recognition Systems. www.talktoyourcomputer.com 2. “Frequently Asked Questions.” SecuGen Biometrics Solutions. http://www.secugen.com/support/faqs.htm 3. “Fingerprint Techniques Manual.” New Mexico Department of Health, Division

• f Health Improvement.

4. Liu, L.; Dai, T.; Hsin-Chu. “Ridge Orientation Estimation and Verification Algorithm for Fingerprint Enhancement.” Journal of Universal Knowledge

• Management. Vol. 12, Issue 10. Pgs. 1426-1438.

5. Chikkerur, S. “Online Fingerprint Verification.” Center for Unified Biometrics and Sensors. University at Buffalo. 6. “Security Issues.” Affirmative Technologies. http://www.affirmativeusa.com/security_issues.htm 7. “FingerPrint Demo.” MathWorks. http://www.mathworks.com/matlabcentral/fx_files/16728/1/content/FingerPri nt/html/fingerprint.html 1. “DigitalPersonaTM White Paper: Guide to Fingerprint Identification.” Voice Recognition Systems. www.talktoyourcomputer.com 2. “Frequently Asked Questions.” SecuGen Biometrics Solutions. http://www.secugen.com/support/faqs.htm 3. “Fingerprint Techniques Manual.” New Mexico Department of Health, Division

• f Health Improvement.

4. Liu, L.; Dai, T.; Hsin-Chu. “Ridge Orientation Estimation and Verification Algorithm for Fingerprint Enhancement.” Journal of Universal Knowledge

• Management. Vol. 12, Issue 10. Pgs. 1426-1438.

5. Chikkerur, S. “Online Fingerprint Verification.” Center for Unified Biometrics and Sensors. University at Buffalo. 6. “Security Issues.” Affirmative Technologies. http://www.affirmativeusa.com/security_issues.htm 7. “FingerPrint Demo.” MathWorks. http://www.mathworks.com/matlabcentral/fx_files/16728/1/content/FingerPri nt/html/fingerprint.html

References

8. Zhili, W. “Fingerprint Recognition.” Department of Computer Science. BS

• Thesis. Hong Kong Baptist University.

http://www.comp.hkbu.edu.hk/~ vincent/resPaper.htm 9. “2D Gabor Filter (Ver 1,2,3).” MathWorks. http://www.mathworks.com/matlabcentral/fileexchange/5237 10. Kenner, F. “FingerPrint Demo”. Mathworks. http://www.mathworks.com/matlabcentral/fx_files/16728/1/content/FingerPri nt/html/fingerprint.html 8. Zhili, W. “Fingerprint Recognition.” Department of Computer Science. BS

• Thesis. Hong Kong Baptist University.

http://www.comp.hkbu.edu.hk/~ vincent/resPaper.htm 9. “2D Gabor Filter (Ver 1,2,3).” MathWorks. http://www.mathworks.com/matlabcentral/fileexchange/5237 10. Kenner, F. “FingerPrint Demo”. Mathworks. http://www.mathworks.com/matlabcentral/fx_files/16728/1/content/FingerPri nt/html/fingerprint.html