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A. M. Bronstein, M. M. Bronstein, M. Ovsjanikov
"3D features, surface descriptors, and object descriptors", chapter in 3D Imaging, Analysis, and Applications (Y. Liu and N Pears Eds.), Springer, to appear. Abstract: The computer vision and pattern recognition communities have recently witnessed a surge of feature-based methods in numerous applications including object recognition and image retrieval. Similar concepts and analogous approaches are penetrating the world of 3D shape analysis, in a variety of areas including non-rigid shape retrieval and matching. In this chapter, we present the state-of-the-art of feature-based approaches in 3D shape analysis. |
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A. M. Bronstein, M. M. Bronstein,
"Manifold intrinsic similarity", chapter in Handbook of Mathematical Methods in Imaging (O. Scherzer Ed.), Springer, 2011. Abstract: Non-rigid shapes are ubiquitous in Nature and are encountered at all levels of life, from macro to nano. The need to model such shapes and understand their behavior arises in many applications in imaging sciences, pattern recognition, computer vision, and computer graphics. Of particular importance is understanding which properties of the shape are attributed to deformations and which are invariant, i.e., remain unchanged. This chapter presents an approach to non- rigid shapes from the point of view of metric geometry. Modeling shapes as metric spaces, one can pose the problem of shape similarity as the similarity of metric spaces and harness tools from theoretical metric geometry for the computation of such a similarity. |
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A. M. Bronstein, M. M. Bronstein, R. Kimmel,
"Story of Cinderella: biometrics and isometry-invariant distances", chapter in 3D Imaging for Safety and Security (A. Koschan, M. Pollefeys, M. Abidi Eds.), Springer, 2007. Abstract: In this chapter, we address the question of what are the facial measures one could use in order to distinguish between people. Our starting point is the fact that the expressions of our face can, in most cases, be modeled as isometries, which we validate empirically. Then, based on this observation, we introduce a technique that enables us to distinguish between people based on the intrinsic geometry of their faces. We provide empirical evidence that the proposed geometric measures are invariant to facial expressions and relate our findings to the broad context of biometric methods, ranging from modern face recognition technologies to fairy tales and biblical stories. |
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A. M. Bronstein, M. M. Bronstein, R. Kimmel,
"Expression invariant face recognition: faces as isometric surfaces", chapter in Face Processing: Advanced Modeling and Methods (R. Chellappa, W. Zhao Eds.), Academic Press, 2006. Abstract: One of the hardest problems in face recognition is dealing with facial expressions. Finding an expression-invariant representation of the face could be a remedy for this problem. We suggest treating faces as deformable surfaces in the context of Riemannian geometry, and propose to approximate facial expressions as isometries of the facial surface. This way, we can define geometric invariants of a given face under different expressions. One such invariant is constructed by isometrically embedding the facial surface structure into a low-dimensional flat space. Based on this approach, we built an accurate three-dimensional face recognition system that is able to distinguish between identical twins under various facial expressions. In this chapter we show how under the near-isometric model assumption, the difficult problem of face recognition in the presence of facial expressions can be solved in a relatively simple way. |
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A. M. Bronstein, M. M. Bronstein, M. Zibulevsky,
"Bind source separation: biomedical applications", article in Wiley Encyclopedia of Biomedical Engineering (M. Akay Ed.), April 2006. Abstract: Blind source separation (BSS) refers to a wide class of methods in signal and image processing, which extract the underlying sources from a set of mixtures without almost any prior knowledge about the sources nor about the mixing process. In biomedical applications, BSS is used for the analysis of electroencephalogram (EEG), magenetoencephalogram (MEG) and electrocardiogram (ECG) signals and functional magnetic resonance (fMRI) images. |
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