Statistical Computations on Grassmann and Stiefel Manifolds for Image and Video-Based Recognition

By Pavan K. Turaga, Ashok Narayanan Veeraraghavan, Anuj Srivastava, Ramalingam Chellappa. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2011

402 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/08fbe3187f31b828a38811cc8dc7ca17933b91e9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Computer Vision and Pattern Recognition

In Geometry and Topology

Citations in the corpus

Elastic functional coding of human actions: From vector-fields to latent variables (2015, background): “Subspaces such as these can be identified as points on a Grassmann manifold [26].”
High-Dimensional Stochastic Gradient Quantization for Communication-Efficient Edge Learning (2019, neutral): “To the best known of authors’ knowledge, this work represents the first attempt to consider vector quantization for stochastic gradient quantization, where advanced Grassmannian tools [15] from differential geometry are applied to facilitating the codebook design.”
Elastic Functional Coding of Riemannian Trajectories (2016, background): “Subspaces such as these can be identified as points on a Grassmann manifold [5], [40].”
Accurate 3D action recognition using learning on the Grassmann manifold (2015, methodology): “Thus, we can estimate the parameters of a probability density function such as a Gaussian and then use the exponential map to wrap these param-412 eters back onto the manifold using exponential map operator [18].”
Deep Reconstruction Models for Image Set Classification (2015, background): “Date of publication 28 Aug. 2014; date of current version 3 Mar. 2015.”
Building Deep Networks on Grassmann Manifolds (2016, background): “, 31]. For video visual recognition, linear dynamic system (i.e., linear subspace) of autoregressive and moving average model has shown its great power to model dynamics in spatio-temporal processing [12, 52, 54]. In addition, Grassmannian data also appear in image restoration [56], chromatic noise ”
Neural Aggregation Network for Video Face Recognition (2016, methodology): “For set based face recognition, many previous methods have attempted to represent the set of face images with appearance subspaces or manifolds and perform recognition via computing manifold similarity or distance [19, 2, 17, 40, 37].”
Generalized Rank Pooling for Activity Recognition (2017, background): “While, using subspaces for action recognition has been done several times in the past [21, 44], we are not aware of any work that shows these benefits on CNN features.”
Space-Time Pose Representation for 3D Human Action Recognition (2013, background): “Our proposal in this work is motivated by: (1) The fact that many features in computer vision applications lie on curved space due to the geometric nature of the problems; (2) The shape and dynamic cues are very important for modeling human activity and their effectiveness have been demonstrated in ”
Human Action Recognition by Shape Analysis of Motion Trajectories on Riemannian Manifold (2014, background): “The main considerations that motivated our 97 solution are: (1) The fact that many feature descriptors typically adopted in computer vision applications 98 lie on curved spaces due to the geometric nature of the problems; (2) The shape and dynamic cues are 99 very important for modeling human activi”
Action Recognition Using Rate-Invariant Analysis of Skeletal Shape Trajectories (2016, neutral): “In [27], Turaga et al.”
A Blur-Robust Descriptor with Applications to Face Recognition (2012, methodology): “However, in this work, we compute the distance using the geodesic since it offers scope for subsequent statistical analysis when there are variations other than blur [32].”
Projection Metric Learning on Grassmann Manifold with Application to Video based Face Recognition (2015, background): “As is mostly studied in [42, 28, 9, 32, 12, 34, 21, 22], linear subspaces with the same dimensionality reside on a special type of Riemannian manifold, i.”
Grassmannian Representation of Motion Depth for 3D Human Gesture and Action Recognition (2014, background): “This can be approximated by the finite observability matrix [15]:”