@article {12439,
	title = {Statistical Computations on Grassmann and Stiefel Manifolds for Image and Video-Based Recognition},
	journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
	volume = {33},
	year = {2011},
	month = {2011/11//},
	pages = {2273 - 2286},
	abstract = {In this paper, we examine image and video-based recognition applications where the underlying models have a special structure-the linear subspace structure. We discuss how commonly used parametric models for videos and image sets can be described using the unified framework of Grassmann and Stiefel manifolds. We first show that the parameters of linear dynamic models are finite-dimensional linear subspaces of appropriate dimensions. Unordered image sets as samples from a finite-dimensional linear subspace naturally fall under this framework. We show that an inference over subspaces can be naturally cast as an inference problem on the Grassmann manifold. To perform recognition using subspace-based models, we need tools from the Riemannian geometry of the Grassmann manifold. This involves a study of the geometric properties of the space, appropriate definitions of Riemannian metrics, and definition of geodesics. Further, we derive statistical modeling of inter and intraclass variations that respect the geometry of the space. We apply techniques such as intrinsic and extrinsic statistics to enable maximum-likelihood classification. We also provide algorithms for unsupervised clustering derived from the geometry of the manifold. Finally, we demonstrate the improved performance of these methods in a wide variety of vision applications such as activity recognition, video-based face recognition, object recognition from image sets, and activity-based video clustering.},
	keywords = {activity based video clustering, activity recognition, computational geometry, Computational modeling, Data models, face recognition, feature representation, finite dimensional linear subspaces, geometric properties, Geometry, Grassmann Manifolds, Grassmann., HUMANS, Image and video models, image recognition, linear dynamic models, linear subspace structure, Manifolds, maximum likelihood classification, maximum likelihood estimation, Object recognition, Riemannian geometry, Riemannian metrics, SHAPE, statistical computations, statistical models, Stiefel, Stiefel Manifolds, unsupervised clustering, video based face recognition, video based recognition, video signal processing},
	isbn = {0162-8828},
	doi = {10.1109/TPAMI.2011.52},
	author = {Turaga,P. and Veeraraghavan,A. and Srivastava, A. and Chellapa, Rama}
}
@conference {15063,
	title = {An adaptive mean shift tracking method using multiscale images},
	booktitle = {Wavelet Analysis and Pattern Recognition, 2007. ICWAPR {\textquoteright}07. International Conference on},
	volume = {3},
	year = {2007},
	month = {2007/11//},
	pages = {1060 - 1066},
	abstract = {An adaptive mean shift tracking method for object tracking using multiscale images is presented in this paper. A bandwidth matrix and a Gaussian kernel are used to extend the definition of target model. The method can exactly estimate the position of the tracked object using multiscale images from Gaussian pyramid. The tracking method determines the parameters of kernel bandwidth by maximizing the lower bound of a log-likelihood function, which is derived from a kernel density estimate with the bandwidth matrix and the modified weight function. The experimental results show that it can averagely converge in 2.55 iterations per frame.},
	keywords = {adaptive mean shift tracking method, bandwidth matrix, Gaussian kernel, Gaussian processes, Image sequences, log-likelihood function, matrix algebra, maximum likelihood estimation, multiscale image, Object detection, object tracking},
	doi = {10.1109/ICWAPR.2007.4421589},
	author = {Zhuolin Jiang and Li,Shao-Fa and Gao,Dong-Fa}
}
