I CP Fusion Techniques for 3D Face Recognition

I CP Fusion Techniques for 3D Face Recognition Robert McKeon University of Notre Dame Notre Dame, Indiana, USA rmckeon@nd.edu Patrick Flynn University of Notre Dame Notre Dame, Indiana, USA flynn@nd.edu Abstract The 3D shape of the face has been shown to be a viable and robust biometric for security applications. Many state of the art techniques use Iterative Closest Point (ICP) to match one or more face regions to comparable regions stored in an enrollment database. In this paper, we propose and explore several optimizations of the ICPbased matching technique relating to the processing of multiple regions and the fusion of region matching scores obtained from ICP alignment. Some of these optimizations yielded improved recognition results. The optimizations explored included: (i) the symmetric use of probe and enabling score fusion; (ii) gallery and probe region matching score normalization; (iii) region selection based on face data centroid rather than the nose tip, and (iv) region weighting. As a result of these optimizations, the rank-one recognition rate for a canonical matching experiment improved from 96.4% to 98.6%, and the True Accept Rate (TAR) at 0.1% False Accept Rate (FAR) improved from 90.4% to 98.5%. I. Introduction The security of knowledge and buildings is increasingly important in many areas; access to the same must be restricted to authorized personnel in such situations. Researchers have explored the field of biometrics to establish identity and thus decide on access rights, and many biometric signatures like iris and fingerprint are well-known. Iris and fingerprint recognition require significant subject cooperation, so researchers have also investigated face recognition, which requires less subject cooperation. Due to a relative lack of sensitivity to lighting variations, 3D face recognition has a unique advantage over 2D face recognition; the information captured is the shape of the face and not the color. 3D face images are commonly acquired using structured light sensors and/or stereo vision techniques [13]. The Iterative Closest Point (ICP) [1] algorithm has proven to be a workhorse solution for a host of geometric alignment problems, including the alignment of two 3D samplings of the face obtained from a 3D sensor. ICP aligns two 3D point clouds by minimizing the average error between the nearestneighbors. ICP aligns a data point cloud to a model point cloud. The main disadvantage to this technique is the need for an expensive nearest-point search at each iteration (this search can be accelerated through use of hierarchical data structures). In most 3D face recognition systems, the comparison of an enrolled gallery face to an unlabeled probe face yields a matching score typically based on the alignment error calculated by an ICP-based technique [2]. Thus, lower scores are better and the best match identifies the matching gallery image and conveys an identity claim. Principal component analysis has also been used to match aligned 3D faces [4, 5, 7]. Faltemier el al. [2] used a simple ensemble of 38 face regions to significantly improve face recognition using ICP as a matching metric. In this paper, we find that the ICP face recognition approach can be improved in both processing time and recognition performance. The goal of this paper is to exploit both areas to improve 3D face recognition using three recognition metrics: rank-one recognition performance, the True Accept Rate (TAR) at 0.1% False Accept Rate (FAR), and an examination of the Receiver Operating Characteristic (ROC). The paper is organized as follows. We examine prior work in the area in Section 2. In section 3, we will show a variety of methods we used to improve face recognition. Section 4 shows the results achieved from these improvements, and Section 5 provides a summary and outlines potential future areas of research. II. Literature Review Faltemier et al. [2] conducted recognition experiments using the testing partition of the FRGC 2.0 3D face image dataset, which has 4007 3D face images of 466 unique subjects. They fused the match results of multiple face region alignments in order to improve performance over full face performance. They achieved 97.2% rank-one recognition where the earliest image acquired was used as the gallery. They achieved a TAR of 94.8% at a 0.1% FAR for the first semester images as gallery images and the second semester images as probes. This result remains,

to our knowledge, one of best-published performance on the FRGC 2.0 testing partition. Russ et al. [4] used a form of PCA for facial recognition by first aligning each face to a reference model using ICP. PCA was performed based on the corresponding reference face points to each gallery face, and they experimented on the neutral expression probes of FRGC 2.0 achieving 96.0% TAR at 0.1% FAR. Boehnen et al. [5] developed face signatures to compare 3D faces quickly using the reference face technique for alignment. They compare these signatures using a combination of a nearest neighbor technique and a normal vector search. They achieved 95.5% rank one identification merging 8 facial regions on the FRGC 2.0 dataset, which is an improvement over 92.9% for 8 regions as seen by Faltemier et al. [2]. Al- Osaimi et al. [7] used PCA on a set of 2.5D face images in order to avoid some of the pitfalls of ICP such as the possibility that ICP does not converge to a correct answer. They achieved 95.4% TAR at 0.1% FAR and 93.7% rankone recognition for the neutral expression images of the FRGC 2.0 dataset. Faltemier et al. [2] achieved 99.2% rank-one on the same neutral expression subset. Colbry et al. [6] used region selection to narrow the search space for 3D recognition. They selected the region around the nose and eyes to reduce the number of feature points, but this caused a decrease in recognition performance. They achieved 98.2% rank-one recognition on a data set of 325 face scans. Chua et al. [8] aim to find the regions on the face that deform (such as like the nose, the eye sockets, and the forehead), which were identified using surface curvature. Their data set was only six face images on which they achieved 100% rank-one recognition, but it is not a fair comparison to the size of the FRGC set. Mian et al. [14] used a 3D spherical face representation in a modified ICP algorithm for face recognition. They used the nose and eye-forehead regions and fused these two region scores together. On the FRGC 2.0 dataset, they achieved 98.5% TAR at 0.1% FAR. III. Methods Previous research on face recognition has focused on finding new algorithms to recognize faces better, but the main research in using ICP for face recognition has not looked at improving the ICP strategy beyond employing multiple regions. Faltemier et al. [2] improved the ICP strategy by using multiple regions. We looked at a variety of improvements based on observations made during our ICP-based 3D face image matching experiments. We conclude that some of these improvements should always be implemented, some improvements require further development, and some experiments suggested additional possible improvements. Among the modifications we considered are score fusion, probe normalization, gallery normalization, improved region selection, and weighting regions. 3.1 The Basic I CP Method To compute a match score for two face image meshes (or two face image regions segmented from the face mesh), we used the Iterative Closest Point (ICP) algorithm [1] to align the meshes, using the alignment Err or E 2 as the match score (lower is better). ICP employs two geometric sets: a fixed model shape M and a data shape D to which a transformation T is applied to perform the alignment; In the execution of ICP, D is aligned iteratively to M T 0 is obtained through some heuristic procedure. At each subsequent iteration i, the nearest neighbor points for each point in T i-1 D are found using search of a previously constructed k-d tree [12]. Using these correspondences an updated transformation matrix T i is calculated. T i is composed of a 3D rotation and a 3D translation. The RMS alignment error E 2 i for the iteration is then calculated using Equation 1, in which d p closest to p when transformed by T i : E 2 i pm p T d 2 M i p is the data shape point 2 Iteration continues until E i does not change significantly between iterations or until some other stopping criterion is met. The final value of E 2 i is reported as the matching score. A value of zero would imply a perfect alignment of identically sampled shapes. For notational convenience, we will denote the matching error obtained via equation (1) from an ICP invocation with a data shape D and a model shape M as ICP(M,D) or E 2. 3.2 Dual I C P Invocation and Score F usion Techniques In face recognition, it is not always obvious whether the probe face p or the gallery face g should serve as the model shape M and the data shape D in the ICP formulation. Ideally, the data shape should be a subset of the model shape in terms of geometric coverage. In some cases, this assumption is not true with either assignment of g or p to M or D. Thus, we invoke ICP twice, obtaining two matching scores ICP(p,g) and ICP(g,p) as implemented by McKeon and Flynn [3]. These two scores are fused using the product and minimum rules, yielding two matching scores used henceforth: (1)

E 2 min(p,g) = min(icp(p,g), ICP(g,p)) (2) E 2 prod(p,g) = ICP(p,g)ICP(g,p) (3) In Section 4.2, we demonstrate improvements in performance due to the use of E 2 min and E 2 prod. E 2 pk L E 2 jk j1 L 1 where L is the total number of images in the gallery (8) 3.3 Techniques In order to fuse matching scores from multiple regions effectively, we found it necessary to perform normalization. The distributions of the match scores obtained from different facial image regions differ significantly. We examined two techniques to normalize the set of match scores for a vector V p = [ E 2 *(p,g 1 E 2 *(p,g k )] of k gallery matches to a single probe match: -- these vectors, the * indicates the score fusion technique used. - E 2 minmax) transforms all the values in a vector to be in the range [0, 1]. For a vector V p, the normalization yields an output vector V p,minmax : V p,minmax = [(E 2 *(p,g 1 )-min(v p ))/(max(v p ) min(v p (E 2 *(p,g k ) min(v p )) /(max(v p ) min(v p )) ] (4) Z-score normalization (E 2 z) transforms all the values in a vector to have an average of zero and unit variance: V p,z = [(E 2 *(p,g 1 )-mean(v p ))/(std(v p 2 *(p,g k ) mean(v p )) /(std(v p )) ] (5) We also examined the application of these normalization techniques to vectors V g = [E 2 *(p 1 E 2 *(p K,g)] of probe matches to a single gallery match. The same normalization techniques may be applied to the vector V g, yielding output vectors V g,m and V g,z, but these did not improve performance. Instead, we normalized each V g to make the average of V g equal to one. E 2 pk (Equation 6) was normalized by the mean of all E jk 2 (Equation 7) as shown in (Equation 8), resulting in (V gn for the vector V g ) for a probe p and a gallery image G k. E 2 kk is excluded from the calculation of the mean because it equals 0 due to being an exact match. E 2 pk = ICP(P,G k ) (6) where P is a probe image, and G k is a gallery image. E 2 jk = ICP(G j,g k ) (7) where G j is the j th gallery image, and G k is a gallery image. 3.4 Nose-centered Regions vs. Centroid-Centered Regions 3D face recognition performance can be improved through use of ensemble matching strategies using local face region matches instead of whole face matches. In such methods, the initial selection of regions for matching depends on a registration step, which is itself often performed using the results of a whole-face ICP alignment to a canonical face model. We find the nose tip using the curvature-based technique described by Faltemier et al. [2], and then form a series of regions centered either at the nose tip or at the centroid of the face data and cropped from the face data using a set of cropping spheres of various radii combined with offsets in the X and Y axes. The face regions cropped using the nose tip as a cropping origin are denoted R n,i, where n denotes the nose-centered crop and i refers to the region number. Similarly, the face regions cropped around the data centroid are denoted R c,i. In our experience, the data centroid is typically located strategies are depicted graphically in Figure 3.1. (a) (b) (c) Figure 3.1: (a) A face with the nose-tip and the face centroid identified. The vector b connects the centroid and the nose tip. (b) A family R n,i of nose-centered cropped regions. (b) A family R c,i of centroid-centered cropped regions. 3.5 Matching using Weighted Ensemble Scores Previous researchers have found facial region ensembles outperform full face recognition. Faltemier et al. [2] fused match score results from multiple nose centered cropped regions to form a final match score. Boehnen et al. [5] cropped regions with a variety of shapes

shape. We used the same face regions as Faltemier et al. [2], with a Sequential Forward Search (SFS) [11] to find the region ensemble with the best performance. We formed the ensemble using as SFS as employed by Liwicki and Bunke [10]. An ensemble S k with k elements was selected from the initial set of all regions S 0 = {R 1, R 2, R 3 n } as follows: 1. Find the best performing region R* in S 0 based on TAR at 0.1% FAR, remove R* from S 0, and set S 1 to be the singleton {R*}. 2. For -1 do: a. Find the region R* in S 0 that maximizes TAR at 0.1% FAR when added to S k-1 b. Set S k = S k-1 { R* } c. Set S 0 = S 0 { R* } d. Form the E 2 k,sfs : E 2 k,sfs S k R j k Previous region merging schemes like Faltemier et al. [2] also used SFS. However, a region can only be added to match score with respect to the other regions. We did this match score by an integer found using a modified SFS process. The SFS Weighted (SFSW) starts with S k = {( 1,R 1 ), ( 2,R 2 n,r n )} containing a weight i for each region R i, all initialized at 0, and selectively incremented at each iteration k as follows: 1. Find the region R* whose addition to the initial set S 1 maximizes TAR at 0.1% FAR, set the corresponding to 1. 2. For -1 do: a. Find the region R* which, if its weight is incremented, maximizes TAR at 0.1% FAR b. Increment the corresponding to R*, and add (*) to S if necessary. 3. Form E 2 k,sfsw as a weighted sum of per-region match scores : E 2 k,sfsw = 1 R 1 + 2 R 2 + 3 R 3 n R n I V. j 0 Experimental Results We used the training partition of the FRGC v2 3D face database [9] for our recognition experiments. This partition contains 4007 3D face images. We excluded the subjects that have only one image in the data set, yielding a total of 3950 images. For the rank-one recognition experiments, this set was divided into 466 gallery images and 3484 probe images. The gallery images were acquired prior to the probe images. For the TAR @ 0.1% FAR and the ROC curve experiments, this set was divided into the first semester of acquisition (1628 gallery images) and the second semester of acquisition (1727 probe images). The gallery images were acquired prior to the probe images. Both probe sets contain both neutral and non-neutral expressions. The 38 regions used in Faltimier et al. [2] were used for both R n and R c and formed into an ensemble using either SFS or SFSW. Table 4.1: Experimental Variables Experimental Variables Number of Variables { E 2, E 2 min, E 2 prod } 3 { E 2 minmax, E 2 z } 2 { E 2, } 2 { R n, R c, R n R c } 3 { SFS, SFSW } 2 Total Number of Experiments: 72 Table 4.2: Experiment Descriptions Matching Experiment Comments score 1. Baseline E 2 SFS 2. Minimum ICP Score 3. Product ICP Score 4. Probe Min-max 5. Probe Z-score 6. Gallery 7. Nosecentered regions vs Centroidcentered regions 8. Weighted Region Ensembles 9. Optimal Number of Regions E 2 min E 2 prod E 2 minmax E 2 z R n vs. R c R n vs. R n R c SFS vs. SFSW N/A Selected regions using the nose or the centroid as the offset Allowed regions to be weighted differently Explored when adding more regions to ensemble degrades performance As a baseline, we employ the performance results of an implementation that uses ICP(g,p) or E 2 as a matching score, employing none of the optimizations described above. We found that the use of E 2 min or E 2 prod as the matching score improves performance as do both probe score normalization and gallery score normalization.

Weighting region match scores also improves performance. The use of centroid-centered cropping regions did not by itself improve performance, but performance was improved when regions obtained by centroid-centered cropping and nose-centered cropping were combined. We also found that some regions cannot improve an ensemble. Table 4.1 lists the experimental variables, and Table 4.2 lists a short description of each experiment. This baseline matcher differed slightly from Faltimier et al. [2] in performance for rank-one recognition (some match ranks were different), but we were unable to identify which part of the process deviated from their stated process. The TAR @ 0.1% FAR values were also different because we used a summation scheme, and they used a Confidence Voting scheme to merge regions. 4.1 Biometric Evaluation Metrics The two typical biometric tasks are identification and verification. Both tasks compare an incoming probe template to an existing database of gallery templates. Identification tasks compare the probe against every template of interest in the gallery and return the identity of the best match. A verification task compares the probe only against templates that match the identity claim presented with the probe. In our experiments, recognition performance is typically quantified using the rank-one recognition rate, and verification performance is quantified by the True Accept Rate (TAR) at 0.1% False Accept Rate (FAR), or graphically by the Receiver Operating Characteristic (ROC) curve, which can also be examined to determine improved performance. For rank-one recognition, match ranks were computed from ensembles of regions using a modified Borda Count [2]. The original Borda Count (BC) is the sum of the match ranks for regions in the ensemble. The gallery match g for a probe with the largest Borda Count will be the rank-one match. The modified Borda Count (MBC) first proposed by Faltemier et al. [2] adds a quadratic weight to the first N b matches and forms a weighted sum. As before, the match with the largest modified Borda count is considered correct. We found the ROC curve and the TAR at 0.1% FAR by summing the region match scores (E 2, E 2 min, or E 2 prod) to give a final match score from which the ROC was calculated. We used SFS [10, 11] to find the region ensemble with the best performance expect when specified. 4.2 E 2 min and E 2 prod We found that both E 2 min and E 2 prod were superior to E 2 with respect to both identification and verification experiments. Table 4.3 shows the rank-one performance and the TAR at 0.1% FAR. Figure 4.1 presents the ROC curves for identification experiments using E 2, E 2 min and E 2 prod and SFS for region selection. Using SFS, the best performing ensembles contained between 10 and 20 regions. Table 4.3: E 2, E 2 min and E 2 prod performance Rank-one correct match rate 96.4% 97.4% 97.4% TAR @ 0.1% FAR 90.5% 93.2% 92.6% To determine the statistical significance of these results, we ran 30 experiments using 500 random probes for each system, and we used a one-tailed t-test to test a null hypothesis that the mean recognition performance (rankone recognition or TAR at 0.1% FAR) of the alternative technique (E 2 min, etc.) is better than the default. A p-value below 0.05 will indicate rejection of the null hypothesis. E 2 min and E 2 prod compared to E 2 have p-values of 1.67 x 10-2 and 1.67 x 10-2 respectively for rank-one recognition rates and p-values of 8.89 x 10-22 and 4.69 x 10-16 respectively for TAR at 0.1% FAR. Thus, we rejected the null hypothesis that E 2 min is equivalent to E 2, and also rejected the null hypothesis that E 2 prod is equivalent to E 2. However, we accepted the null hypothesis that E 2 prod and E 2 min demonstrated the same performance for rank-one recognition (p-value of 0.50) but rejected the null hypothesis for TAR at 0.1% FAR (p-value of 8.16 x 10-4 ). True Accept Rate (TAR) 100.0% 98.0% 96.0% 94.0% 92.0% 90.0% 88.0% 86.0% 84.0% 82.0% 80.0% 78.0% 76.0% 74.0% 0.001% 0.010% 0.100% 1.000% 10.000% 100.000% False Accept Rate (FAR) Err- pg Err- min Err- prod Figure 4.1: The ROC curve for E 2, E 2 min and E 2 prod. 4.3 Both probe normalization (E 2 minmax, E 2 z) and gallery

normalization () improved recognition. For probe score normalization, E 2 minmax and E 2 z both improved recognition, but E 2 minmax outperformed E 2 z. Rank-one correct recognition rates were not affected by any probe score normalization because the ranking of a region does not change when using probe score normalization. We also found using followed by probe score normalization, results in a significant performance gain. Table 4.4 summarizes TAR at 0.1% FAR results for E 2 minmax, E 2 z and. Figure 4.2 presents the ROC curves of E 2 compared to E 2 min with min-max probe score normalization and gallery score normalization. E 2 minmax and E 2 z have p-values as compared to E 2 of 1.85 x 10-26 and 1.32 x 10-40 for TAR at 0.1% FAR, so both rejected the null hypothesis of equal average performance. Table 4.5 shows the p-values for the probe normalization and gallery normalization experiments. We rejected the null hypothesis that was statistically equal to E 2. Table 4.4: TAR at 0.1% FAR for probe and gallery normalization E 2 Probe 2 E 90.5% 93.2% 92.6% E 2 minmax 94.2% 96.2% 95.9% E 2 z 75.5% 74.3% 75.8% E 2 91.7% 94.1% 93.9% E 2 minmax 96.9% 97.8% 97.7% E 2 z 81.0% 78.1% 79.0% Table 4.5: p-values for TAR at 0.1% FAR results of probe and gallery normalization (bold indicates statistical significance, p- value<0.05) p-values E 2 vs. { E 2 minmax, E 2 z } E 2 vs. Probe E 2 minmax 1.85E-26 1.07E-34 1.99E-34 E 2 z 1.32E-40 2.34E-38 3.35E-36 E 2 2.15E-08 2.83E-27 1.13E-26 E 2 minmax 2.11E-34 2.34E-35 1.83E-35 E 2 z 6.48E-30 9.93E-34 5.23E-34 True Accept Rate (TAR) 100.0% 98.0% 96.0% 94.0% 92.0% 90.0% 88.0% 86.0% 84.0% 82.0% 80.0% 78.0% 76.0% 74.0% Err- pg 0.001% 0.010% 0.100% 1.000% 10.000% 100.000% False Accept Rate (FAR) Err- min, gallery normalization, Min- max probe normalization Figure 4.2: ROC of original E 2 and E 2 min with gallery score normalization and Min-max probe score normalization. 4.4 Centroid-centered vs. Nose-centered The ensemble with R c R n for E 2 min and E 2 prod as show in Table 4.4. R c does improve the raw scores for rank-one recognition. However, building an ensemble using R n R c does improve performance as seen in Table 4.6. Table 4.6: Rank-one Recognition for R n, R n, and R n R c Region Selection E 2 R c 97.8% 97.7% 97.7% R n 96.4% 97.4% 97.4% R n R c 98.2% 98.1% 98.1% R n 96.6% 97.9% 97.8% R c 97.5% 97.2% 97.2% R n R c 98.4% 98.2% 98.3% R c does not perform as well when looking at the TAR at 0.1% FAR as seen in Table 4.7. Figure 4.3 shows the ROC curves for a few of these methods. From the ROC curve, one can see that R n R c performs the best, and more performance is gained using Min-max probe score normalization and gallery score normalization. Table 4.8 shows the results of hypothesis testing on this set of experiments. Overall, R n R c combinations exhibited significantly better performance. 4.5 Weighted Regions We formed region ensembles using SFSW as opposed to

SFS. This resulted a significant improvement as seen in Table 4.9 for rank-one recognition. Table 4.10 shows the results for TAR at 0.1% FAR. Figure 4.4 shows the ROC curve for a few selections. To properly build any ensemble using SFS or SFSW, training data is required. These experiments show that ensembles could be built using either SFS or SFSW to achieve the best performance, but SFSW improves the lower end of the ROC curve slightly. The p-values for the weighted experiments are shown in Table 4.11, and the SFSW results all rejected the null hypothesis of equal average performance to the SFS results. Table 4.7: TAR @ 0.1% FAR for R n, R n, and R n R c Region Selection E 2 R c 85.5% 87.8% 87.3% R n 90.5% 93.2% 92.6% E 2 minmax R n R c 91.5% 93.1% 92.7% R n 96.9% 97.8% 97.7% R c 92.6% 93.7% 93.1% R n R c 97.8% 98.1% 97.9% Table 4.8: p-values for TAR @ 0.1% FAR results comparing R n, R n, and R n R c True Accept Rate (TAR) Region Selection R n vs. R c R n R c vs. R n R n vs. R n with E 2 minmax and R c vs. R c with E 2 minmax and R n R c vs. R n R c with E 2 minmax and 100.0% 98.0% 96.0% 94.0% 92.0% 90.0% 88.0% 86.0% 84.0% 82.0% 80.0% 78.0% 76.0% 74.0% 72.0% 70.0% 7.78E-26 1.09E-31 2.93E-29 9.32E-28 3.27E-32 3.54E-30 2.11E-34 2.34E-35 1.83E-35 2.70E-32 2.00E-35 2.94E-34 8.73E-42 6.26E-40 3.19E-40 0.001% 0.010% 0.100% 1.000% 10.000% 100.000% False Accept Rate (FAR) Figure 4.3: The ROC curves for a few normalization experiments. R- nc, Err- pg R- nc, Min- max normalized, Gallery normalized R- cc, Err- pg (R- nc, R- cc), Err- pg (R- nc, R- cc), Min- max normalized Gallery normalized Table 4.9: Rank-one Recognition on Weighted Region Ensembles E 2 Region Selection R n SFS 96.4% 97.4% 97.4% R n R c SFS 98.2% 98.1% 98.1% R n SFSW 96.7% 97.6% 97.6% R n R c SFSW 98.3% 98.4% 98.4% R n SFS 96.6% 97.9% 97.8% R n R c SFS 98.4% 98.2% 98.3% R n SFSW 97.2% 98.0% 98.1% R n R c SFSW 98.6% 98.4% 98.5% Table 4.10: TAR @ 0.1% FAR on Weighted Region Ensembles True Accept Rate (TAR) E 2 E 2 minmax Region Selection R n SFS 90.5% 93.2% 92.6% R n R c SFS 91.5% 93.1% 92.7% R n SFSW 91.3% 93.6% 93.4% R n R c SFSW 92.8% 94.2% 93.7% R n SFS 96.9% 97.8% 97.7% R n R c SFS 97.8% 98.1% 97.9% R n SFSW 97.2% 98.1% 97.9% R n R c SFSW 98.1% 98.5% 98.2% Table 4.11: p-values for TAR @ 0.1% FAR results using Weighted Region Ensembles Region Selection R n SFS vs. R n SFSW 4.18E-04 7.53E-03 7.42E-06 R n R c SFS vs. R n R c SFSW 2.49E-11 5.33E-07 4.75E-06 100.0% 98.0% 96.0% 94.0% 92.0% 90.0% 88.0% 86.0% 84.0% 82.0% 80.0% 78.0% 76.0% 74.0% 72.0% 0.001% 0.010% 0.100% 1.000% 10.000% 100.000% False Accept Rate (FAR) R- nc, Err- pg Weighted R- nc, Err- min Weighted, Min- max normalization, Gallery (R- nc, R- cc), Err- pg Weighted (R- nc, R- cc), Err- min Weighted, Min- max normalization, Gallery Figure 4.4: The ROC curves for a few weighted region experiments.

4.6 Number of regions in the ensemble Using SFS, we found that more regions do not necessarily improve results. In most cases, there is a peak in performance, after which the performance decreases. This is true except in the case of SFSW because only a few regions have a greater than 0. However, this actually requires training to determine for each region, but we used all the test data to train the SFS for the ensemble as did other researchers [2, 5]. Figure 4.5 shows the rank-one as a function of the number of regions added on the R n using SFS and SFSW. Figure 4.5: The rank-one recognition as compared to the number of regions added to the ensemble. V. Conclusion Through our experiments, we have shown that 3D face recognition could be improved through region selection, ensemble creation, normalization, and post-processing the raw ICP scores. We found E 2 min and E 2 prod are very helpful in post-processing the raw ICP scores, and their success has expanded the understanding of the inter-workings of ICP. Probe and gallery normalization were very successful especially when combined. Forming region ensembles using SFSW was not significantly better than SFS. We found more regions in an ensemble do not always provide improved recognition. We also found by picking regions based on the face centroid, we can improve an ensemble particularly when a region ensemble for face recognition is drawn from a pool of nose-centered regions and centroid-centered regions. Future work will aim to improve the ICP match score itself by cropping out outlier points and will improve the ICP running time using a reference face and a reduced number of points of the face region. V I. References [1] 14, no. 2, pp. 239-256, 1992. [2] Profile Signatures for Robust 3D Feature De IEEE International Conference on Automatic Face and Gesture Recognition, Amsterdam, The Netherlands. September 2008. [3] Timothy Faltemier, Kevin W. Bowyer and Patrick J. Flynn, IEEE Transactions on Information Forensics and Security, vol. 3, iss. 1, pp.62-73, 2008. [4] -Dimensional Facial Imaging using a Static Light Screen and a Dynamic Proceedings of the 3D Data Processing, Visualization, and Transmission (3DPVT), 2008. Pages 175 182. [5] Proceedings of the Computer Vision and Pattern Recognition, New York, pp. 1391-1398, 2006. [6] C. Boehnen, T. s for Proceedings of the International Conference on Biometrics 2009, Alghero, Italy. [7] The Proceedings of the Society of Photographic Instrumentation Engineers Conference on Defense & Security, 2008. [8] F.R. Al- local and global geometrical cues for 3D face recognition", Pattern Recognition Letters, pp. 1030-1040, 2008. [9] C.S. Chua, F. Han, Fourth IEEE International Conference on Automatic Face and Gesture Recognition, Page 233, 2000. [10] P.J. Phillips, P.J. Flynn, T. Scruggs, and K.W. Bowyer. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) 2005. Vol 1, pp. 947-954. [11] search 15(11):11191125. 1994. [12] Proceedings of the Third Int. Conf. on Pattern recognition, pages 71-75, Coronado, CA, 1976. [13] J. Bentle 18, pp. 509517, 1975. [14] the Fifth IEEE International Conference on 3-D Digital Imaging and Modeling (3DIM). Pages 310-317, 2005. [15] Multimodal 2D-3D Hybrid Approach to Automatic Face Transactions on Pattern Analysis and Machine Intelligence, vol. 29, no. 1, November 2007.