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Elastic Shape Models for Face Analysis Using Curvilinear Coordinates:
We study the problem of analyzing variability in shapes of facial surfaces. The main difficulty in this problem comes from the lack of a canonical coordinate system to compare faces. Our idea is to impose a special, yet natural, coordinate system, called a Darcyan curvilinear coordinate system, on facial surfaces. This system is intrinsic to the surfaces and it deforms with them. Here, one coordinate µ measures the distance from the tip of the nose and the other coordinate ß measures distances along level curves of µ. Using the Darcyan system, we develop tools for matching, comparing and deforming surfaces under an elastic metric. The central idea is to finnd optimal matches between level curves of µ across faces, and to use an elastic (Riemannian) metric on the space of closed curves to define and compute geodesic paths between matched curves. Together these geodesics provide optimal elastic deformations between faces and an elastic metric for comparing facial shapes.
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Geometrical Analysis of Facial Surfaces:
A quantitative analysis of shapes of facial surfaces can play an important role in biometric authentication. The main difficulty in comparing shapes of surfaces is the lack of a canonical system to represent all surfaces. This work overcomes that problem by proposing a specific coordinate system, on facial surfaces, that enables comparisons of geometries offaces. In this system, a facial surface is represented as a path on the space of closed curves, called facial curves, where each curve is a level curve of distance function from the tip of the nose. Defining H to be the space of paths on the space of closed curves, the work studies the differential geometry of H and endows it with a Riemannian. Using numerical techniques, it computes geodesic paths between elements of H that represent individual facial surfaces. This Riemannian analysis of faces is then used to: (i) find an optimal deformation from one face to another, (ii) define and compute an average face (Karcher Mean) for a given set of faces, and (iii) compute distances between faces to quantify differences in their shapes.
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3D Face Recognition Using Facial Shapes:
In addition to facial textures, or facial images, the shapes of facial surfaces can also prove to be important tools in human recognition. We study facial surfaces by representing them as indexed sets of level curves of a continuous function, such as the depth function, on these surfaces. The shapes of facial surfaces are then analyzed using the shapes of these level curves, called the facial curves. Shapes of facial curves are compared using a geometric approach. The metric for comparing facial surfaces is a composition of the metric involving individual facial curves.
Given 3D scans of facial surfaces, the goal is to develop algorithms for comparing their shapes. Human faces can not be treated as rigid objects since they undergo deformations during different facial expressions. Classical surface matching methods, based on finding best Euclidean transformations to match any two surfaces are not directly applicable here. Two facial surfaces resulting from different facial expressions of the same person, should be classified similarly. Therefore, our goal is to characterize the shape of a facial surface modulo deformations that correspond to different facial expressions. Our approach is to derive efficient mathematical representations for capturing shapes of facial surfaces, and to impose metrics that quantify dissimilarities between such shape representations.
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3D Face Recognition by Combining Facial Shapes and Textures:
In this work we develop a framework for face recognition based on 3D surface comparison and texture image. To compare 3D face, we have described a geometric approach for comparing shapes of facial surfaces via the shapes of facial curves. The basic idea is to coarsely approximate a facial surface $S$ with a finite set of level curves, called the facial curves, of the height function on $S$. Curve extraction is accomplished using range images, and metric between facial curves are computed using a method described in {klassen-srivastava-planar-shape}. A metric $d_g$ on shapes of facial surfaces is derived by accumulating distances between corresponding facial curves. Results are presented from clustering and recognition of facial surfaces according to this metric. Using the commonly used spectral representation of a texture image, i.e. filter images using Gabor filters and compute histograms as image representations, we can compare texture images by comparing their corresponding histograms using the chi-squared distance $d_t$.
Performance, of the proposed framework measured by the recognition rate based on FSU database shows better performance than 3D face recognition and texture image recognition alone. Indeed, the results obtained by combining the distances $d_g$ and $d_t$, improve the recognition rate for face recognition.
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3D Face Comaparison Using Topological Reeb Graph:
In this work, we use the three-dimensional topological shape information for human face identification. We propose a new method to represent 3D faces as a topological graph. Fine registration of surfaces is done by first automatically finding topological connected components, and then constructing its topological graph representing the important topological changes on the face. The similarity calculation between 3D faces is processed using coarse-to-fine strategy while preserving the consistency of the graph structures, which result in establishing a correspondence between the parts of faces. The contribution of this work is to show the importance of topological features (critical points) to localize the pertinent information on the surface. In topology, it corresponds to a big change of the neighbourhood. Such properties are well illustrated near nose, Nose Bridge and eyes.
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Resume and Research Interests:
Journals:
A. Srivastava, C. Samir, S. Joshi, and M. Daoudi, Elastic Shape Models for Face Analysis Using Curvilinear Coordinates, Journal of Mathematical Imaging and Vision, Submitted for Review in May 2007.
C. Samir, A. Srivastava, M. Daoudi, and E. Klassen, An Intrinsic Framework for Analysis of Facial Surfaces , Journal of International Journal of Computer Vision, Submitted for review in February 2007.
C. Samir, A. Srivastava, M. Daoudi, Automatic 3D Face Recognition Using Shapes of Facial Curves IEEE Trans. Pattern Analysis and Machine Intelligence, novembre Vol. 28, N° 11, pp. 1858-1863, 2006.
C. Samir, M. Daoudi, and A. Srivastava, A Framework of Calculus on Facial Surfaces, 14th IEEE International Conference on Image Analysis and Processing 2007, Medona, Italy.
C. Samir, M. Daoudi, and A. Srivastava, Human Identification Using Facial Curves With Extension To Joint Shape-Texture Analysis, 2nd International Conference on Computer Vision Theory and Applications, 8 - 11 March 2007, Barcelona, Spain.
C. Samir, A. Srivastava, M. Daoudi, 3D Face Recognition Using Shapes of Facial Curves, Statistical inferences on nonlinear manifolds with applications in signal and image processing, special session ICASSP 2006.
C. Samir, J.P. Vandeborre, M. Daoudi, "Automatic 3D face recognition using topological techniques", IEEE International Conference on Multimedia & Expo (ICME) 2005.
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Talks:
Poster in Geometry and Statistics of Shape Spaces (workshop), organized by David Mumford and Laurent Younes, and SAMSI (Statistical and Applied Mathematical Sciences Institute), North Carolina, USA, July 2007.
Teaching:
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