10.6. Concluding Remarks

This chapter has introduced and reviewed different fusion techniques for multicue biometric authentication systems. The pros and cons of fusing biometric data at different levels have been discussed. A novel multisample fusion technique, which is general and applicable to both face and speaker recognition systems, was then proposed to fuse the scores obtained from speaker or face models. This is evident by promising experimental results using the HTIMIT corpus, NIST2001 speaker recognition benchmark test, and XM2VTSDB audio-visual database. The technique is also amenable to the fusion of AV data. It was found that error rate reduction of up to 83% can be achieved when the multisample fusion technique is applied to fuse the scores derived from speaker models and face models.

Problems

  1. This exercise highlights the motivation of adoptng data-dependent fusion weights for a multicue biometric system. Assume that the audio and visual scores of an audio-visual biometric authentication system range from 0 to 10 (the larger the score, the more likely the claimant is a genuine user) and that the decision threshold is set to 8.0. Suppose that in a verification session, the scores of a claimant from the audio and visual channels are equal to 6.0 and 9.0, respectively. Denote the fusion weight for the audio channel as β, the fused score is s = 6β + 9(1 − β).

    1. Determine the decision (accept/reject) if the fusion weights for the audio channel and visual channel are both 0.5 (i.e., β = 0.5).

    2. Assume that an acoustic noise detector picks up a high level of background noise during the verification session. The system automatically reduces the contribution of the audio channel by lowering the corresponding fusion weight to 0.2 and raising the visual channel's fusion weight to 0.8 (i.e., β = 0.2). Will the claimant be accepted or rejected?

    3. Assume that the noise detector indicates a low level of background noise but a light-intensity sensor gives an unusually low reading during the verification session. The biometric system responds to this situation by lowering the visual channel's fusion weight to 0.2 and raising the audio channel's fusion weight to 0.8 (i.e., β = 0.8). Determine the decision of the system.

    4. Determine the range of fusion weights for which the claimant is acceptable (i.e., the fused score exceeds the threshold).

  2. Show that when in Eq. 10.4.7 tends to infinity, multisample fusion reduces to equal-weight fusion.

  3. Assume that the client scores sc,a from the audio channel of an audio-visual biometric authentication system follow a Gaussian distribution with mean μc,a and variance , and the impostor scores from the audio channel follow a Gaussian distribution with mean μi,a and variance . Similarly, the corresponding score statistics from the visual channel are μc,v, , μi,v, and ,. Assume also that the audio and visual scores are fused by the following formulae:


    where β ∊ [0, 1] is a fusion weight and sc and si are the fused client scores and fused impostor scores, respectively.

    1. Show that the variances of the fused client scores and fused impostor scores are


      State your assumption on the statistic dependence of the scores from the two channels.

    2. Hence, show that the variances of the fused scores satisfy


    3. Show that the fusion weight that minimizes σc is given by


    4. Hence, explain why fusion of independent audio and visual scores helps increase the separation between the fused client scores and the fused impostor scores.

  4. Matlab Exercise. Create two Gaussian distributions with means 0.8 and 1.2 and variances equal to 1.0 to simulate the score distributions of two client utterances. Similarly, create two Gaussian distributions with means −1.3 and −0.7 and variances that are equal to 2.0 to simulate the score distributions of two impostor utterances. Write a Matlab program to implement Eqs. 10.4.3 through 10.4.7.

    1. Create a plot similar to Figure 10.8(c) by computing the differences between the fused client scores and the fused impostor scores for different values of prior score .

    2. Sort the two client score sequences in opposite order. Similarly, sort the two impostor score sequences in opposite order. Use the Matlab program to compute the score dispersion between the fused client scores and the fused impostor scores. Plot the score dispersion against the prior score .

    3. Repeat (a) and (b) for different values of prior variance .

  5. Repeat Problem 4 by replacing the Gaussian distributions with uniform distributions.

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