Affine-invariant Shape Recognition Using Grassmann Manifold
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摘要: 传统的Kendall形状空间理论仅适用于相似变换, 然而成像过程中目标发生的几何变形在更多情形时应该用仿射变换来刻画. 基于Grassmann流形理论, 本文分析了仿射不变形状空间的非线性几何结构, 提出了基于Grassmann流形的仿射不变形状识别算法. 算法首先对训练集中的每类形状分别计算形状均值和方差, 进而在形状均值附近的切空间构建多变量正态分布; 最后,根据测试形状的观测和先验形状模型求解测试形状的最大似然类, 对形状进行贝叶斯分类. MPEG 7形状数据库的实验结果表明, 与传统Kendall形状分析中的基于Procrustean度量识别算法相比, 本文识别算法具有明显优势; 真实场景中的目标识别结果进一步表明, 本文算法对仿射变形有更好的适应能力, 在复杂场景下能以较高的后验概率辨识出目标类别.
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关键词:
- 形状识别 /
- Grassmann 流形 /
- 仿射不变 /
- 形状空间 /
- 形状均值
Abstract: Traditional Kendall shape space theory is only applied to similar transform. However, geometric transforms of the object in the imaging process should be represented by affine transform at most situations. We analyze the nonlinear geometry structure of the affine invariant shape space and propose an affine-invariant shape recognition algorithm based on Grassmann manifold geometry. Firstly, we compute the mean shape and covariance for every shape class in the train sets. Then, we construct their norm probability models on the tangent space at each mean shape. Finally, we compute the maximum likelihood class according to the measured object and prior learned shape models. We use the proposed algorithm to recognize shapes in standard shape dataset and real images. Experiment results on MPEG-7 shape dataset show that our recognition algorithm outperforms the algorithm based on Procrustean metric in traditional Kendall shape space theory. Experiment results on real images also show that the proposed algorithm exhibits higher capacity to affine transform than the Procrustean metric based algorithm and can recognize object classes with higher posterior probability.-
Key words:
- Shape recognition /
- Grassmann manifold /
- affine invariant /
- shape space /
- mean shapes
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[1] Srivastava A, Damon J N, Dryden I L, Jermyn I H. Guest editors' introduction to the special section on shape analysis and its applications in image understanding. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2010, 32(4): 577-578[2] Kendall D G. Shape manifolds, procrustean metrics and complex projective spaces. Bulletin of London Mathematical Society, 1984, 16(2): 81-121[3] Zhang J, Zhang X, Krim H, Walter G G. Object representation and recognition in shape spaces. Pattern Recognition, 2003, 36(5): 1143-1154[4] Huckemann S, Hotz T, Munk A. Intrinsic MANOVA for Riemannian manifolds with an application to Kendall's space of planar shapes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2010, 32(4): 593-603[5] Han Y X, Wang B, Idesawa M, Shimai H. Recognition of multiple configurations of objects with limited data. Pattern Recognition, 2010, 43(4): 1467-1475[6] Huttenlocher D P, Ullman S. Recognizing solid objects by alignment with an image. International Journal of Computer Vision, 1990, 5(2): 195-212[7] Grenander U, Miller M I. Pattern Theory: from Representation to Inference. New York: Oxford University Press, 2007[8] Fletcher P T, Whitaker T R. Riemannian metrics on the space of solid shapes. In: Proceedings of the International Workshop on Mathematical Foundations of Computational Anatomy. Copenhagen, Denmark: MICCAI, 2006. 1-11[9] Klassen E, Srivastava A, Mio W, Joshi S. Analysis of planar shapes using geodesic paths on shape spaces. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2004, 26(3): 372-383[10] Srivastava A, Joshi S, Mio W, Liu X W. Statistical shape analysis: clustering, learning and testing. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005, 27(4): 590-602[11] Cootes T F, Taylor C J, Cooper D H, Graham J. Active shape models: their training and application. Computer Vision and Image Understanding, 1995, 61(1): 38-59[12] Wang B, Chen Y Q. An invariant shape representation: interior angle chain. International Journal of Pattern Recognition and Artificial Intelligence, 2007, 21(3): 543-559[13] Chen Xiao-Chun, Ye Mao-Dong, Ni Chen-Min. A method for shape recognition. Pattern Recognition and Artificial Intelligence, 2006, 19(6): 758-763(陈孝春, 叶懋冬, 倪臣敏. 一种形状识别的方法. 模式识别与人工智能, 2006, 19(6): 758-763)[14] Mumford D. Mathematic theories of shape: do they model perception? In: Proceedings of the Conference on Geometric Methods in Computer Vision. San Diego, USA: SPIE, 1991. 2-10[15] Latecki L J, Lakimper R, Eckhardt U. Shape descriptors for non-rigid shapes with a single closed contour. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. Hilton Head Island, USA: IEEE, 2000. 424-429[16] Spivak M. A Comprehensive Introduction to Differential Geometry. Berlin: Berkeley, 1979[17] Berger M. A Panoramic View of Riemannian Geometry. Berlin: Springer, 2003[18] Edelman A, Arias T A, Smith S T. The geometry of algorithms with orthogonality constraints. SIAM Journal on Matrix Analysis and Applications, 1999, 20(2): 303-353[19] Lin D, Yan S, Tang X. Pursuing informative projection on Grassmann manifold. In: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. New York, USA: IEEE, 2006. 1727-1734[20] Zhang L, Tse D N. Communication on the Grassmann manifold: a geometric approach to the noncoherent multiple-antenna channel. IEEE Transactions on Information Theory, 2002, 48(2): 359-383[21] Amsallem D, Farhat C. An interpolation method for adapting reduced-order models and application to aeroelasticity. AIAA Journal, 2008, 46(7): 1803-1813[22] Subbarao R, Meer P. Nonlinear mean shift over Riemannian manifolds. International Journal of Computer Vision, 2009, 84(1): 1-20[23] Absil P A, Mahoney R, Sepulchre R. Riemannian geometry of Grassmann manifolds with a view on algorithmic computation. Arta Applicandae Mathematicae, 2004, 80(2): 199-220[24] Fletcher P T, Lu C, Pizer S M, Joshi S. Principal geodesic analysis for the study of nonlinear statistics of shape. IEEE Transactions on Medical Imaging, 2004, 23(8): 995-1005[25] Baker S, Matthews I. Lucas-Kanade 20 years on: a unifying framework. International Journal of Computer Vision, 2004, 56(3): 221-255[26] Marszalek M, Schmid C. Accurate object localization with shape masks. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. Minnesota, USA: IEEE, 2007. 1-8[27] Dryden I L, Mardia K V. Statistical Shape Analysis. New York: John Wiley and Sons, 1998
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