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DICTA '05 Proceedings of the Digital Image Computing on Techniques and Applications
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FGR '06 Proceedings of the 7th International Conference on Automatic Face and Gesture Recognition
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ICML '06 Proceedings of the 23rd international conference on Machine learning
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CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
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CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 2
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ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 03
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The Journal of Machine Learning Research
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ICIG '09 Proceedings of the 2009 Fifth International Conference on Image and Graphics
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CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
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In this paper, two significant weaknesses of locally linear embedding (LLE) applied to computer vision are addressed: ''intrinsic dimension'' and ''eigenvector meanings''. ''Topological embedding'' and ''multi-resolution nonlinearity capture'' are introduced based on mathematical analysis of topological manifolds and LLE. The manifold topological analysis (MTA) method is described and is based on ''topological embedding''. MTA is a more robust method to determine the ''intrinsic dimension'' of a manifold with typical topology, which is important for tracking and perception understanding. The manifold multi-resolution analysis (MMA) method is based on ''multi-resolution nonlinearity capture''. MMA defines LLE eigenvectors as features for pattern recognition and dimension reduction. Both MTA and MMA are proved mathematically, and several examples are provided. Applications in 3D object recognition and 3D object viewpoint space partitioning are also described.