8.5 Experimental Results: Recognition of Identity

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Figure 8.5. Examples of the following expressions: (a) neutral, (b) happy, (c) angry, and (d) scream. (e) The recognition rates obtained when matching: i) happy and neutral faces, ii) angry and neutral faces, and iii) cream and neutral faces. Note that when we incorporate the information of the DF process in our model (i.e. f ), the results improve and the matching process becomes less sensitive to the differences in facial expression. Equation (8.1) indicates a simple Euclidean distance, and Eq. (8.2) the weighted measure given in Eq. (8.2). Adapted from Martinez [66].

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As sample images we will use the neutral faces (Figure 8.5a). As test images (i.e., images to be matched with the sample ones), we will use the happy, angry, and scream faces (Figure 8.5b d). For each of the test images, we will select the sample image that best matches it, as given by Eq. (8.2). If the retrieved image belongs to the same person (class) as the one in the testing image, we will say that our recognition was successful. Figure 8.5e shows the percentage of successful identi cations. We have detailed the recognition rates for each of the facial expression images to show the dependency between the recognition of identity and facial expression. We have also shown, in this gure, what would happen if the DF process was damaged or absent. This is represented by omitting the value of f in Eq. (8.2). The results of such damage as predicted by our model are obtained with Eq. (8.1) in Figure 8.5e [66]. 8.5.1.2 Computation Time

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As expressions increasingly diverge, the time required for the recognition of identity also increases. To calculate the time required to compute the motion eld for each of the expressions, we need to determine (i) the number of coarse-to- ne (pyramid) levels required to compute the largest motions of the image and (ii) the number of iterations necessary to correctly calculate the minimum of the nonconvex function at each level of the pyramid. For each of the facial expressions in the AR database (i.e., happy, angry, and scream) as well as for the neutral expression image, we have calculated the minimum number of iterations and levels of the pyramid required as follows. For each expression, we computed the motion elds, f , using levels of the pyramid that range from 1 to 4 . The results obtained when using h + 1 levels of the pyramid were compared to results obtained when only using h levels. If the similarity in magnitude (as computed

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A Biologically Inspired Model

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Figure 8.6. Shown here are the mean delays (computational time, CT) required to compute the motion elds, f , for each facial expression group.

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by SM /mo ) and angle (SA ) between the two (h and h + 1) was below a threshold of one pixel, we determined that h levels suf ce for the computation of the motion in that image; otherwise h + 1 levels were necessary. This chosen value is referred to as H. To determine the number of iterations required at each level of the pyramid, we compared the results obtained when using g + 1 and g iterations. Again, if the comparison was below a threshold, we selected g; otherwise we selected g + 1. We will refer to this value as G. In this case, the threshold was 0.1 and g was tested for the range of values from 10 to 50. Now, we combine the two selected values into a single measure as CT = G H; that is, computational time equals the number of iterations necessary at each level multiplied by the number of levels needed. The results (mean across samples) are: Neutral faces: H = 1, G = 10, and CT = 10, Happy faces: H = 3, G = 26, and CT = 78, Angry faces: H = 2.4, G = 20, and CT = 48, Scream faces: H = 4, G = 33, and CT = 152. These results are plotted in the graphical representation of Figure 8.6. These results do not include the time necessary to compute Eq. (8.2); but since in our current implementation of the model this time is always constant, we can omit it for simplicity.

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