3D Face --> Surface Space Analysis

In this section we analyse the surface spaces produced when various facial surface representations are used with the fishersurface method. We begin by testing the variety of fishersurface systems introduced by Heseltine et al [1] on test set A, showing the range of error rates produced when using various surface representations (Figure 3). Continuing this line of research we persist with the same surface representations, referring the reader to previous work [1, 9] for implementation details, while in this
paper we focus on the effect and methodologies of combining multiple systems, rather than the surface representations themselves. Figure 3 clearly shows the choice of surface representation has a significant impact on the effectiveness of the fishersurface approach, with horizontal gradient
representations providing the lowest EER (point at which false acceptance rate equals
false rejection rate).

However, the superiority of the horizontal gradient representations does not suggest that the vertical gradient and curvature representations are no use whatsoever. Although discriminatory information provided by these representations may not be as robust and distinguishing, they may contain a degree of information not available in horizontal gradients and could therefore still make a positive contribution to a combined surface space. We measure the discriminating ability of surface space dimensions by applying Fisher’s Linear Discriminant (FLD) (as used by Gordon [14]) to individual components
(single dimensions) of each surface space. We calculate the discriminant dn, describing
the discriminating power of a given dimension n, between c people in test set A.



Where _i is the set of all class i face-key vector elements in dimension n, and m and mi the mean and class mean of nth dimension elements in test set A. Applying equation 3 to the assortment of surface space systems listed in Figure 3, we see a wide range of discriminant values across the individual surface space dimensions (Figure 4).




Figure 4: Top ten discriminant values of all fishersurface dimensions

It is clear that although some surface representations do not perform well in the face recognition tests, producing high EERs, some face-key components do contain highly discriminatory information. For example, we see that the min and max curvature representations contain one dimension with a higher discriminant than any horizontal gradient and curve type dimension, yet the EERs are significantly higher. We hypothesise that the reason for these highly discriminating anomalies, in an otherwise ineffective subspace, is that a certain surface representation may be particularly suited to a single discriminating factor, such as nose shape or jaw structure, but is not effective when used as a more general classifier. Therefore, if we were able to isolate these few useful qualities from the more specialised subspaces, they could be used to make a positive contribution to a generally more effective surface space, reducing error rates further.