Total Variance

It is not possible to calculate the redundancy in the model directly. However, a measure of the total variance within a given model can be produced. Models with a smaller total variance have a closer fit to the data and thus are likely to have less redundancy. Total variation smoothly varies with the number and magnitude of the Eigenvalues. This is a simple measure that is sufficient for comparing models. Alternative metrics, such as

0 20 40 60 80 100 120 140 The number of training samples

0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035

The rms reconstruction error at vertex positions (meters)

Figure 4.14: Graph of generality

the model volume or the largest displacement for a given probability, have undesirable properties. For example, the volume is reduced when an additional small eigenvalue is added to the model. Also, if the largest displacement is used, all dimensions smaller than the largest eigenvalue are ignored. Variance can thus be calculated using the equation:

variance(e) =

l

X

k=0

e_k

where e represents the model’s eigenvalues. As with generality, the error in these values has been calculated using 10-fold cross validation. Figure 4.15 shows the results. The graph of generality has a much faster rate of convergence than that of variance. This may be explained by errors within the registration process increasing the variance of the model without significantly improving its generality.

4.5 Conclusions

This work demonstrates the first complete Morphable Model of the head that is explic-itly designed to recreate both the face and ear shape accurately. This approach includes the identification of a key set of ear feature points to enable accurate registration. In ad-dition, it improves the robustness of existing Morphable Model construction techniques by using classifiers trained to detect occluding and high noise areas. It also provides a framework for evaluating the quality of the registration of training scans, and metrics to assess the resulting model quality. These metrics are used to indicate the improvement in the generalisation capabilities of the model as the training set size is increased. The

0 20 40 60 80 100 120 140 The number of training samples

0 1 2 3 4 5 6 7 8

The total variance (meters squared)

Figure 4.15: Graph of total variance

evaluation shows that the described technique extracts a consistent shape for a given individual and that within the error margins of the registration process, 160 training samples are close to achieving convergence of the model.

Further work in this area will involve the use of the evaluation framework to examine other Morphable Model techniques, such as the correlated correspondence algorithm of Anguelov et al. [5] and the non-rigid iterated closest point algorithm developed by Amberg et al. [4]. The framework can also be expanded to evaluate the utility of the model in inferring identity from partial data such as detected features within 2D images.

There is also scope for creating an improved surface classifier, through additional dis-tance constraints, and providing improved speed and precision using support vector machines or boosting techniques. If this classifier could be combined with an auto-matic feature point detection process, fully automated model construction from rela-tively unconstrained training data would be possible. This offers the potential for more widespread application of Morphable Models within object recognition.

To complete the construction of the Morphable Model, the surface texture variation also needs to be calculated. First the surface textures associated with each range scan are extracted. These are calculated by mapping the colour values of the range points onto the uv-map of the fitted mesh. The resulting variation in appearance is then modelled by applying PCA to the extracted textures. One difficulty, however, is that the range scans are recorded with uncalibrated lighting. This is in contrast to the original Morphable Model technique developed by Blanz and Vetter [17] which used uniformly lit 3D scans.

By using uniformly lit textures the effect of varying light direction can be simulated using a rendering algorithm. Further work is needed to investigate whether it is possible

to reconstruct uniformly lit textures by applying a shape from shading technique to the unconstrained textures. When combined with the shape modelling approach described in this chapter, such a lighting normalisation algorithm would enable the construction of complete Morphable Models from largely unconstrained range scans.

Conclusions and Discussion

The work described in this thesis examined the hypothesis that

The constraints on the use of ear-based biometric systems can be relaxed significantly through the introduction of robust recognition algorithms.

It began by clarifying the main obstacles to achieving unconstrained recognition and after examining the existing approaches to addressing these issues, proposed two new techniques. This chapter provides a critical analysis of these techniques followed by a discussion of possible future work.

5.1 SIFT Based Ear Recognition

The first new technique presented was a robust and automated 2D ear registration and recognition algorithm. By taking a SIFT point based approach it provides the first reliable solution to identifying the position and rotation of ears even when they are occluded. The evaluation of the technique demonstrated that the approach is practical for small datasets and relatively controlled pose and lighting conditions. A detailed evaluation, however, highlighted a sensitivity to pose variation with recognition rates dropping significantly beyond 20 degrees and falling to zero at 40 degrees or more.

Another limitation is that the time taken to recognise a new ear is directly proportional to the size of the gallery. This means that the approach is only practical when applied to verification, or when recognition is across small datasets. Recent developments in internet scale image matching could be applied to this technique to make it practical for large scale datasets. However, the additional issue of pose variation requires a new approach.

81