1. Online Signature as a Behavioral Biometric
Berrin Yanıkoğlu

2. Problem
Given a signature and a claimed identity, decide on whether to accept or reject the signature.
Signature is a behavioral biometric such as gait and voice, as opposed to physiological biometrics such as fingerprint and iris.
Advantages:
No need to remember pins or carry tokens/cards
Well accepted socially and legally
Already used in a number of applications (e.g., points of sales)
Acquisition hardware already integrated in devices (Tablet PC, PDA, …)
Changeable
Disadvantages:
May be forged

3. Signature Verification
Static (offline)
Image of the signature is the input
Applications: bank check clearing
3/8/2002
Dear John,
Best regards,
Dynamic (online):
Pressure-sensitive tablets used to capture the image and dynamic properties of the signature
More unique, more difficult to forge
Applications: credit card processing, added security to laptops/PDAs...

4. Signature Verification - Jan 2010 - B. Yanikoglu
Input
x,y
Time Stamp
Pressure
Pen Inclination
Curvature
Acceleration
Signature Verification - Jan B. Yanikoglu

5. Sample Vector Representation
(x1 y1 p1 t1)
(x2 y2 p2 t2)
S =
(xN yN pN tN)
where xi and yi are the coordinates and pi and ti are the pressure and timestamp at point i.
There may be more features which are measured or extracted.

6. Genuine and Forgery Signatures

7. Genuine Signature Variations
Common variations in genuine signatures:
Size
Pen thickness
Extra/missing/longer/shorter strokes
Rotation
Relative position of strokes
Easier to handle
Difficult to handle

8. Genuine vs Forgeries Main difficulty in signature verification:
Forgeries Genuine
Main difficulty in signature verification:
high intra-class and low inter-class variations

9. Genuine vs Forgeries
Reference set (all genuine):
Queries:

10. Genuine vs Forgeries
Reference set (all genuine):
Queries:
Forgery

11. Genuine vs Forgeries
Reference set (all genuine):
Queries:
Forgery

12. Genuine vs Forgeries Reference set (all genuine): Queries: Forgery

13. Genuine vs Forgeries Reference set (all genuine): Queries: Forgery

14. Genuine vs Forgeries Reference set (all genuine): Queries: Forgery

15. Genuine vs Forgeries Reference set (all genuine): Queries: Forgery

16. Genuine vs Forgeries Reference set (all genuine): Queries: Genuine
Forgery
Genuine
Forgery

17. Matching and Verification

18. Matching/Verification
Need a similarity/distance measure.
signatures are of varying length
distance measure should be insensitive to intra-class variations
in shape or timing
Then we can accept a signature as genuine if the distance is small; reject otherwise x

19. Euclidian distance?
Dynamic Time Warping

20. Fourier Coefficients in Online Signature Verification
7.5% EER in SUSIG database

21. Local Features Spatial features (at each trajectory point):
x, y coordinates w.r.t the center of the signature
x & y offset btw. two consecutive points
sine & cosine of the angle with x axis
curvature
grey values in the 9x9 neighbourhood
...
Dynamic features (at each trajectory point):
absolute speed: (pi – pi-1)/ (ti – ti-1) distance per sample pts
relative speed (absolute speed normalized by the average signing speed) acceleration
pressure
pen tilt

22. A Dynamic Programming Approach
Dynamic Time Warping
A Dynamic Programming Approach

23. Dynamic time warping
Goal: find the best non-linear alignment between two sequences, such that the total alignment cost is minimized.
Method: Dynamic time warping is an algorithm for measuring similarity between two sequences which may vary in time/speed/length.

24. Dynamic Programming
Dynamic Time Warping used here is a special case of Dynamic Programming which is
a powerful optimization technique for certain problems
where there are overlapping subproblems and optimal structure.
Dynamic Programming uses the solutions to subproblems in the globally optimal solution.
Many application areas:
String edit distance
Viterbi algorithm in Hidden Markov Models
Longest common subsequence
...

25. Dynamic Programming Example: Sequence Alignment
...
For the following sequences:
S1: ABCDFGGGXYZ
S2: ABCDDFFGXYZ
what is the `best` alignment?
Depend on costs associated with insertion, deletion and substitution.
ABCD. F. GGGXYZ
ABCDDF FG . . XYZ
4 insertion/deletions
ABCDFGGGXYZ
ABCDDF FGXYZ
3 substitutions
Notice how different paths on the grid correspond to different alignments.
There are exponentially many paths and enumerating each of them to compute the cost is infeasible! This is where Dynamic Programming principle come into play.

26. Dynamic Programming Example: Sequence AlignmentF
F D D D C B A
We need to fill the cost matrix on
the right, according to the formulas
below and keep a back pointer to
the cell that gave the minimum value:
Cost [0,0]=0
Cost [i,0]=i*InsertionCost
Cost [0,j]=j*DeletionCost
0,0
A B C D E F G G G
Euclidian dist.

27. Dynamic Programming Example: Sequence AlignmentF
D D D C B A
Note that:
1) Cost[i,j] stores the minimum
cost of all the paths starting from
(0,0) and ending at (i,j).
2) Cost[i,j] is independent from
the rest of the alignment (from i,j to N,M).
Hence, we can compute it once for all the
alternative paths!
0,0
A B C D E F G G G
3) We won`t know until the end whether the optimal alignment (global solution) passes through i,j or any other grid locations.

28. Dynamic time warping for Online Signatures
Signature alignment is basically done the same as sequence alignment:
instead of letters at each index, we compare local features such as normalized x,y coordinates
decide whether an insertion, deletion or matching with penalty (diagonal move) would result in a minimum cost
we typically use the same cost for insertion and deletion, but they should be adjusted compared to the matching cost such that the path does not always degenerate to a sequence of Delete followed by Inserts.

29. User-based score distribution of genuine and forgery users
Common (EER)
Threshold
User-based score distribution of genuine and forgery users

30. User-based score distribution of genuine and forgery users
Common (EER)
Threshold
User-based score distribution of genuine and forgery users
Especially applicable for voice, signature ... biometrics
Need for user-based score normalization
There is a lot of research in this area.

31. Verification

32. Verification xTemplate x3
Compare the test signature (Y) to the reference signatures (Xi)
belonging to the claimed identity, obtaining: Y x4 x3 x1 x2 x5
xTemplate Y
dmin
dtemplate
dmax
Calculated Distances:
Maximum Distance to Ref. Set
Minimum Distance to Ref. Set
Distance to Template Sig. …
Typically, the distance to the nearest reference signature or the distance to a template signature, is used and are both reasonable choices.

33. Our System’s Performance
2013 First Place in SigWiComp2013
All tasks: Online (Japanese signatures) and Offline (Japanese and Dutch signatures)
2011 1st place in ESRA2011 Online Signature Evaluation Campaign on Task1-DS3
2011 Winner of the SigComp2011 Offline Signature Verification (on Chinese database; 3rd place in Dutch database)
Winner of the 4NSIGCOMP2010 Forensic Signature Verification
Winner of the First International Signature Verification Competition (SVC 2004)
Interpro Computing Awards – R&D Prize Finalist (Online Signature Verification System)