Quality-driven and real-time iris recognition from close-up eye videos

Abstract

This paper deals with the computation of robust iris templates from video sequences. The main contribution is to propose (i) optimal tracking and robust detection of the pupil, (ii) smart selection of iris images to be enrolled, and (iii) multi-thread and quality-driven decomposition of tasks to reach real-time processing. The evaluation of the system was done on the multiple biometric grand challenge dataset. Especially, we conducted a systematic study regarding the fragile bit rate and the number of merged images, using classical criteria. We reached an equal error rate value of 0.2 % that reflects high performance on this database with respect to previous studies.

Appendix: Proof of Eqs. (5) and (6)

Let them prove by recurrence:

• For $p=0$, the proof is trivial (${\varvec{F}}'_0 = {\varvec{F}}$ and $\varvec{Q}'_0 = \varvec{Q}'$)

• Let assume  (5) and (6) true for $p-1$. Then,

  $$\begin{aligned} {\varvec{t}}_{n+p}&= {\varvec{F}}'_{p-1} {\varvec{t}}_n + \varvec{\omega }_{n,p-1} \end{aligned}$$

  (7)

  where $\varvec{\omega }_{n,p - 1}$ follow the Gaussian law $\mathcal {N}(0, Q'_{p-1})$. Let them prove for $p$:

Proof

$$\begin{aligned} {\varvec{t}}_{n + p + 1}&= {\varvec{F}}{\varvec{F}}'_{p-1} {\varvec{t}}_n+ {\varvec{F}}\underbrace{\varvec{\omega }_{n,p-1}}_{\sim \mathcal {N}(0, Q'_{p-1})} + \underbrace{\varvec{\omega }_{n + p + 1}}_{\sim \mathcal {N}(0, Q)} \\&= {\varvec{F}}^{p + 1} {\varvec{t}}_{n} + \underbrace{{\varvec{F}}\varvec{\omega }_{n,p-1}}_{\sim \mathcal {N}(0, {\varvec{F}}Q'_p {\varvec{F}}^T)} + \underbrace{\varvec{\omega }_{n + p + 1}}_{\sim \mathcal {N}(0, Q)} \\&= {\varvec{F}}'_{p} {\varvec{t}}_{n} + \underbrace{{\varvec{F}}\varvec{\omega }_{n,p-1}}_{\sim \mathcal {N}(0, {\varvec{F}}\left[ \sum _{r = 0}^{p - 1} {\varvec{F}}^r \varvec{Q}\left[ {\varvec{F}}^r\right] ^T\right] {\varvec{F}}^T)} + \underbrace{\varvec{\omega }_{n + p + 1}}_{\sim \mathcal {N}(0, Q)} \\&= {\varvec{F}}'_{p} {\varvec{t}}_{n} + \underbrace{{\varvec{F}}\varvec{\omega }_{n,p-1}}_{\sim \mathcal {N}(0, \sum _{r = 1}^{p} {\varvec{F}}^r \varvec{Q}\left[ {\varvec{F}}^r \right] ^T)} + \underbrace{\varvec{\omega }_{n + p + 1}}_{\sim \mathcal {N}(0, Q)} \\&= {\varvec{F}}'_{p} {\varvec{t}}_{n} + \underbrace{{\varvec{F}}\varvec{\omega }_{n,p-1} + \varvec{\omega }_{n + p + 1}}_{\sim \mathcal {N}(0, \sum _{r = 0}^{p} {\varvec{F}}^r \varvec{Q}\left[ {\varvec{F}}^r\right] ^T )} \\&= {\varvec{F}}'_{p} {\varvec{t}}_{n} + \underbrace{\varvec{\omega }_{n,p + 1}}_{\sim \mathcal {N}(0, Q'_{p})} \end{aligned}$$