1. 1 A Multimodal Approach for Face Modeling and Recognition 指導老師 : 萬書言 老師 學生 : 何炳杰

2. 2 Outline Abstract Introduction 3-D Face Recognition Based On Ridge Images And Iterative Closest Points 2-D Face Recognition Based On Attributed Graphs Fusing The Information From 2-D And 3-D Experiments And Results

3. 3 Abstract 1/3 In this paper, we present a fully automated multimodal (3-D and 2-D) face recognition system. For the 3-D modality, we model the facial image as a 3-D binary ridge image that contains the ridge lines on the face. We use the principal curvature max to extract the locations of the ridge lines around the important facial regions on the range image (i.e., the eyes, the nose, and the mouth.)

4. 4 Abstract 2/3 For the 2-D modality, we model the face by an attributed relational graph (ARG). Each node of the graph corresponds to a facial feature point. At each facial feature point, a set of attributes is extracted by applying Gabor wavelets to the 2-D image and assigned to the node of the graph.

5. 5 Abstract 3/3 Finally, we fuse the matching results of the 3-D and the 2-D modalities at the score level to improve the overall performance of the system.

6. 6 Introduction 1/5 In this paper, we present a multimodal face recognition system that fuses results from both 3-D and 2-D face recognition. The 2-D and the 3-D modeling data in our system is independent of each other, this system can be employed in different scenarios of face recognition, such as 2-D or 3-D face recognition individually, or multimodal face recognition.

7. 7 Introduction 2/5 Fig. 1 illustrates a general block diagram of our system. 3-D binary ridge image ARG

8. 8 Introduction 3/5 For the 3-D modality: (i) we use the principal curvature to extract the locations of the ridge lines around the important facial regions in the range image (i.e. the eyes, nose, and mouth). (ii) we represent the face image as a 3-D binary ridge image that contains the ridge lines on the face. (iii) In the matching phase, instead of using the entire surface of the face, we only match the ridge lines. (By (iii) This reduces the computations during the matching process. )

9. 9 Introduction 4/5 For 2-D modality, we build an attributed relational graph using nodes at certain labeled facial points. In order to automatically extract the locations of facial points, we use an improved version of active shape model (ASM). At each node of the graph, we compute the response of 40 Gabor filters in eight orientations and five wavelengths. The similarity between the ARG models is employed for 2-D face recognition.

10. 10 Introduction 5/5 The similarity between the ARG models is employed for 2-D face recognition. In summary, the main contributions of this paper are: presenting a fully automated algorithm for 3-D face recognition based on the ridge lines of the face; developing a fully automated algorithm for 2-D face recognition based on attributed relational graph models. presenting and comparing two methods for the fusion of the 2-D and 3-D face recognition based on the Dempster– Shafer (DS) theory of evidence and the weighted sum of scores technique; evaluating the performance of the system using the FRGC2.0 database.

11. 11 3-D Face Recognition Based On Ridge Images And Iterative Closest Points 1/3 A. Ridge Images( 山脊影像 ) Our goal is to extract and use the points lying on ridge lines as the feature points on the surface. For facial range images, these are points on the lines around the eyes, the nose, and the mouth. In the literature [13], ridges are defined as the points at which the principal curvature of the surface attains a local positive maximum. Intuitively, valleys are the points that illustrate the drainage patterns and are referred to as ridges when looked at from the opposite side.

12. 12 圖. 2 顯示了一個例子，一山脊圖像得到了 的 Kmax 閾值。這是一張三維二值影像 顯示臉部表面上山脊線的位置。

13. 13 3-D Face Recognition Based On Ridge Images And Iterative Closest Points 2/3 B. Ridge Image Matching In this work, we use a fast ICP variant [33]. The difference in the ICP that we used in this paper and the ICP in [33] is in the phase of feature point selection. We do not rely on random sampling of the points and we use all of the feature points in the 3-D ridge image during the matching process. Although random sampling of the points speeds up the matching process, it has a major effect on the accuracy of the final results. … 作者的觀點

14. 14 3-D Face Recognition Based On Ridge Images And Iterative Closest Points 3/3 Before matching the ridge images, we initially align the ridge images using three extracted facial landmarks (i.e., the two inner corners of the eyes and the tip of the nose). We use a fully automated technique to extract these facial landmarks, based on Gaussian curvature.

15. 15 As shown in Fig. 3 Fig. 3, the surface that either has a peak or a pit shape has a positive Gaussian curvature value.

16. 16 As shown in Fig. 4 Fig. 4 shows a sample range image with the three extracted facial landmarks 眼窩 鼻尖 / 頭

17. 17 2-D Face Recognition Based On Attributed Graphs 1/14 Elastic bunch graph matching (EBGM) represented a facial image by a labeled graph called bunch graph. Where edges are labeled with distance information and nodes are labeled with wavelet responses bundled in jets. In addition, bunch graphs are treated as combinatorial entities in which, for each fiducial point, a set of jets from different sample faces is combined, thus creating a highly adaptable model.

18. 18 2-D Face Recognition Based On Attributed Graphs 2/14 In mathematics, a geometric graph is a graph in which the vertices or edges are associated with geometric objects or configurations. A triangulation is a technique for building a geometric graph. Delaunay triangulation, a graph defined from a set of points in the plane by connecting two points with an edge whenever a circle exists containing only those two points.

19. 19 Delaunay triangulation

20. 20 2-D Face Recognition Based On Attributed Graphs 3/14 In this paper, the goal is to model 2-D facial images by attributed relational graphs.

21. 21 2-D Face Recognition Based On Attributed Graphs 4/14 A. Building the Attributed Graph An ARG [26] consists of a set of nodes, edges, and mutual relations between them. Let us denote the ARG by, where is the set of N nodes of the graph and is the set of M edges. The nodes of the graph represent the extracted facial features. R is a set of mutual relations between the three edges of each triangle in the Delaunay triangulation.

22. 22 2-D Face Recognition Based On Attributed Graphs 5/14 Mathematically, we write, where is the set of triangles in Delaunay triangulation. Recall that a Delaunay triangulation for a set of points satisfies the condition that no point in is inside the circumcircle of any triangle in.

23. 23 2-D Face Recognition Based On Attributed Graphs 6/14 Where specifies the orientation of the wavelet, is the wavelength of the sine wave, is the radius of the Gaussian, is the phase of the sine wave, and γ specifies the aspect ratio of the Gaussian. The kernels of the Gabor filters are selected at eight orientations (i.e., ) and five wavelengths (i.e., )

24. 24 2-D Face Recognition Based On Attributed Graphs 7/14 Specifically, referring to Fig. 5, the mutual relations used in this work are defined to be :

25. 25 2-D Face Recognition Based On Attributed Graphs 8/14 B. Facial Feature Extraction In this paper, we transform the color image into HSV space and assume that the three channels, (i.e., hue, saturation, and value) are statistically independent and the normalized first derivative for each channel along a profile line satisfies a multivariate Gaussian distribution.

26. 26 2-D Face Recognition Based On Attributed Graphs 9/14 The best match for a probe sample in HSV color space to a reference model is found by minimizing the distance : : is the sample profile. and : are the mean and the covariance of the profile line of the component of the Gaussian model, respectively. : is the weighting factor for the component of the model with the constraint that the

27. 27 2-D Face Recognition Based On Attributed Graphs 10/14 C. Feature Selection The number of feature points affects the performance of the graph representation for face recognition. In this work, we initially extracted 75 feature points and we then used a standard template to add more features at certain positions on the face, such as the cheek and the points on the ridge of the nose.

28. 28 2-D Face Recognition Based On Attributed Graphs 11/14 By using the standard template (Fig. 6), the total number of the feature point candidates represented by the nodes of the ARG model was increased to 111 points.

29. 29 2-D Face Recognition Based On Attributed Graphs 12/14 Fig. 7 shows a sample face in the gallery along with the candidate points for building the ARG model.

30. 30 2-D Face Recognition Based On Attributed Graphs 13/14 D. Recognition Assume that the ARG models of two faces and are given. The dissimilarity between these two ARGs is defined by and are functions that measure the differences between the nodes of the graph and the mutual relations of the corresponding triangles from the Delaunay triangulation, respectively. The and are weighting factors.

31. 31 2-D Face Recognition Based On Attributed Graphs 14/14 The similarity measure is defined as : is the magnitude of the set of 40 complex coefficients of the Gabor filter response, obtained at the node of the graph.

32. 32 Fusing The Information From 2-D And 3-D 1/4 The Tanh-estimators score normalization is efficient and robust and is defined as and : are the scores before normalization and after normalization. The and are the mean and standard deviation estimates, respectively.

33. 33 Fusing The Information From 2-D And 3-D 2/4 Hampel estimators are based on the following influence function: where sign( ) = +1 if >=0 ; otherwise,sign( ) = -1. The Hampel influence function reduces the influence of the scores at the tails of the distribution (identified by a, b, and c ).

34. 34 Fusing The Information From 2-D And 3-D 3/4 B. Fusion Techniques The weighted sum score fusion technique is defined as : : is the weight of the modality with the condition and is the normalized score of the modality.

35. 35 Fusing The Information From 2-D And 3-D 4/4 In our case, the values of the weights and for the 3-D and 2-D modalities, respectively. Another fusion algorithm that we applied to combine the results of the 2-D and 3-D face recognition is the DS theory. Based on the Dempster rule of combination, the match scores obtained from two different techniques (i.e., two modalities in our work) can be fused by

36. 36 Experiments And Results 1/5 Fig. 8 shows the results of the verification experiment for neutral versus neutral facial images. As the ROC curve shows (also the second row of Table II), the 3-D modality has better performance than the 2-D modality (88.5% versus 79.80% verification at 0.1% FAR) and the best verification rate of multimodal (3-D + 2-D) fusion belongs to the DS combination rule (94.49% at 0.1% FAR).

37. 37 Table II

38. 38 Experiments And Results 2/5 Fig. 9 shows the verification rate of the multimodal (3-D + 2-D) fusion, at 0.1% FAR, with respect to different weights for each modality. Since there are only two modalities, then and the x axis of Fig. 9 is.

39. 39 Experiments And Results 3/5 As the figure shows, the optimum weights that produce the maximum fusion performance are 0.7 and 0.3, respectively, for and.

40. 40 Experiments And Results 4/5 Fig. 10 shows for various numbers of subjects enrolled in the database the average rank-one identification rate.

41. 41 Experiments And Results 5/5 Fig. 11 shows the cumulative match characteristic (CMC) curve for the recognition, based on ridge images, of faces with expressions using the FRGC v2.0 database.

42. 42 Thank you !