1. Online Signature Verification
Based on Dynamic Regression
Signature Verification 11/06/2003

2. Signature verification ->Basic Procedure
1. Template generation
In real application, the number of given genuine signatures is very few (usually less than 6) and no forgery is provided.
2. Matching based on the template.
Input one signature, output a confidence(0%-100%) that the signature is genuine.

3. Signature verification ->1. Template generation
The challenges are:
1).Very limited signatures for training.
Usually we can not expect more than 6 genuine signatures for training for each subject. This is unlike handwriting recognition.
2). Decide the consistent features.
There are over 100 features for signature[2], such as Width, Height, Duration, Orientation, X positions, Y positions, Speed, Curvature, Pressure, so on.

4. Signature verification ->1. Template generation
We have following experience:
1). The most reliable feature is the shape of the signature.
2). The second reliable feature is the speed of writing.
3). No other features are consistent.
To represent shape and speed, each signature is a 3-D sequence: Sigi=[Xi, Yi, Vi], where Vi is the sequence of speed magnitude. Then we use Dynamic Regression to match two signatures and return a Confidence of similarity (0%-100%).

5. Template Generation Features we choose Sequence of X & Y Genuine Sig.
X positions
Y positions

6. Template Generation Features comparison X from genuine sig.
X from forgery sig.
Genuine sig.
Forgery sig.

7. Template Generation More features
X, Y positions are not enough. We need spatial features that describe the shape of the signature curve. Torques, Curvature-ellipse are candidates
Torques of genuine sig.
Torques of forgery sig.
Now we can distinguish them !

8. Template Generation More features: Curvature Ellipse
S1 of Curvature Ellipse (genuine)
S1 of Curvature Ellipse (forgery)
S2 of Curvature Ellipse (genuine)
S2 of Curvature Ellipse (forgery)

9. Template Generation
Curve Matching & Segmentation

10. Signature verification ->2. Matching
Traditional Simple Regression
Similarity: 91%
Similarity: 31%

11. Signature verification ->2. Matching
Traditional Simple Regression
Advantages: Invariant to scale and translation; Similarity (Goodness- of-fit) makes sense.
Disadvantages: One-one alignment, brittle.
One-One alignment
Dynamic alignment

12. Signature verification ->2. Matching
Dynamic Regression
( y2 is matched x2, x3, so we extend it to be two points in Y sequence.)
The DTW warping path in the n-by-m matrix is the path which has minimum average cumulative cost. The unmarked area is the constrain that path is allowed to go.

13. Signature verification ->Demo System
Enroll two or more genuine signatures

14. Signature verification ->Demo System
Verifying signature. Similarity is output and Accept/Reject is recommended

15. Signature verification ->Remarks
Segmentation?
Signature is an art of drawing, not limited to some kind language. Segments by Perceptually Important Points[7] are by no means consistent during genuine signature of one subject.

16. Signature verification ->Remarks
User-dependent distance threshold?
Distance (Euclidean, DTW, etc.) for similarity measure is so embarrassing. In real applications, users tends to ask: how similar is the two signatures? Or, what is the confidence that this signature is genuine? It is nature and friendly to answer: their similarity confidence is 90%! (instead of saying their distance of dissimilarity is 5.8). Our demo system shows that the answer by Dynamic Regression really makes sense.

17. References
[1] Rejean Plamondon, Guy Lorette. Automatic Signature Verification and Writer identification-the state of the art. Pattern Recognition, Vol.22, No.2, pp , 1989.
[2] F. Leclerc and R. Plamondon. Automatic signature verification: the state of the art International Journal of Pattern Recognition and Artificial Intelligence, 8(3): , 1994.
[3] Luan L. Lee, Toby Berger, Erez Aviczer. Reliable On-line Human Signature Verifications Systems. IEEE trans. On Pattern Analysis and Machine Intelligence, Vol. 18, No.6, June 1996.
[4] R. Plamondon. The Design of On-line Signature Verification System: From Theory to Practice. Int’l J. Pattern Recognition and Artificial Intelligence, vol. 8, no. 3, pp , 1994.
[5] Mario E. Munich, Pietro Perona. Visual Identification by Signature Tracking. IEEE Trans. On Pattern Analysis and Machine Intelligence, Vol. 25, No. 2, pp , February 2003.

18. References
[6] Vishvjit S. Nalwa. Automatic On-line Signature Verification. Proceedings of the IEEE, Vol. 85, No. 2, pp , February 1997.
[7] Jean-Jules Brault and Rejean Plamondon. Segmenting Hanwritten Signatures at Their Perceptually Important Points. IEEE Trans. On Pattern Analysis and Machine Intelligence, Vol, 15, No. 9, pp , September 1993.
[8] Taik H. Rhee, Sung J. Cho, Jin H. Kim. On-line Signature Verification Using Model-Guided Segmentation and Discriminative Feature Selection for Skilled Forgeries. Sixth International Conference on Document Analysis and
Recognition (ICDAR '01), September, Seattle, Washington, 2001.
[9] Thomas B. Sebastian, Philip N. Klein, Bejamin B. Kimia. On Aligning Curves. IEEE Trans. On Pattern Analysis and Machine Intelligence, Vol. 25, No. 1, January 2003.
[10] A.K. Jain, Friederike D. Griess and Scott D. Connell. On-line Signature Verification. Pattern Recognition, vol. 35, no. 12, pp , Dec 2002.

19. References
[11] K. Huang and H. Yan, “On-Line Signature Verification Based on Dynamic segmentation and Global and Local Matching,” Optical Eng., vol. 34, no. 12, pp , 1995.
[12] G. Lorette and R. Plamondon, “Dynamic Approaches to Hand-written Signature Verification,” Computer Processing of Hand-writing, pp , 1990.
[13] R. Martens and L. Claesen, “On-Line Signature Verification by Dynamic Time-Warping,” Proc. 13th Int’l Conf. Pattern Recognition, pp , 1996.
[14] B. Wirtz, “Stroke-Based Time Warping for Signature Verification,” Proc. Int’l Conf. Document Analysis and Recognition, pp , 1995.