A note on the gradient of a multi-image
Computer Vision, Graphics, and Image Processing - Lectures notes in computer science, Vol. 201 (G. Goos and J. Hartmanis, Eds.)
Multidimensional Orientation Estimation with Applications to Texture Analysis and Optical Flow
IEEE Transactions on Pattern Analysis and Machine Intelligence
Pfinder: Real-Time Tracking of the Human Body
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Bayesian Computer Vision System for Modeling Human Interactions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Non-parametric Model for Background Subtraction
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part II
A Hierarchical Approach to Robust Background Subtraction using Color and Gradient Information
MOTION '02 Proceedings of the Workshop on Motion and Video Computing
Detecting Moving Shadows: Algorithms and Evaluation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Background Modeling and Subtraction of Dynamic Scenes
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices
SIAM Journal on Matrix Analysis and Applications
Bayesian Modeling of Dynamic Scenes for Object Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Bayesian Approach to Background Modeling
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Workshops - Volume 03
A Riemannian Framework for Tensor Computing
International Journal of Computer Vision
A Texture-Based Method for Modeling the Background and Detecting Moving Objects
IEEE Transactions on Pattern Analysis and Machine Intelligence
Covariance Tracking using Model Update Based on Lie Algebra
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
A Riemannian approach to graph embedding
Pattern Recognition
Efficient hierarchical method for background subtraction
Pattern Recognition
Learning and Removing Cast Shadows through a Multidistribution Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Spatio-temporal background models for outdoor surveillance
EURASIP Journal on Applied Signal Processing
Robust Foreground Detection In Video Using Pixel Layers
IEEE Transactions on Pattern Analysis and Machine Intelligence
Pedestrian Detection via Classification on Riemannian Manifolds
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scene modeling and change detection in dynamic scenes: A subspace approach
Computer Vision and Image Understanding
Background Subtraction on Distributions
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
Detection and segmentation of moving objects in complex scenes
Computer Vision and Image Understanding
A model for dynamic object segmentation with kernel density estimation based on gradient features
Image and Vision Computing
Spatiotemporal Saliency in Dynamic Scenes
IEEE Transactions on Pattern Analysis and Machine Intelligence
New Riemannian techniques for directional and tensorial image data
Pattern Recognition
Fuzzy nonparametric DTI segmentation for robust cingulum-tract extraction
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention - Volume Part I
Foreground Segmentation via Background Modeling on Riemannian Manifolds
ICPR '10 Proceedings of the 2010 20th International Conference on Pattern Recognition
Local histogram of figure/ground segmentations for dynamic background subtraction
EURASIP Journal on Advances in Signal Processing
Image segmentation in video sequences: a probabilistic approach
UAI'97 Proceedings of the Thirteenth conference on Uncertainty in artificial intelligence
Generalized Stauffer–Grimson background subtraction for dynamic scenes
Machine Vision and Applications - Special Issue on Dynamic Textures in Video
Tensor processing for texture and colour segmentation
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
Region covariance: a fast descriptor for detection and classification
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
A nonparametric Riemannian framework on tensor field with application to foreground segmentation
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
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Background modeling on tensor field has recently been proposed for foreground detection tasks. Taking into account the Riemannian structure of the tensor manifold, recent research has focused on developing parametric methods on the tensor domain, e.g. mixture of Gaussians (GMM). However, in some scenarios, simple parametric models do not accurately explain the physical processes. Kernel density estimators (KDEs) have been successful to model, on Euclidean sample spaces, the nonparametric nature of complex, time varying, and non-static backgrounds. Founded on a mathematically rigorous KDE paradigm on general Riemannian manifolds recently proposed in the literature, we define a KDE specifically to operate on the tensor manifold in order to nonparametrically reformulate the existing tensor-based algorithms. We present a mathematically sound framework for nonparametric modeling on tensor field to foreground detection. We endow the tensor manifold with two well-founded Riemannian metrics, i.e. Affine-Invariant and Log-Euclidean. Theoretical aspects are presented and the metrics are compared experimentally. By inducing a space with a null curvature, the Log-Euclidean metric considerably simplifies the scheme, from a practical point of view, while maintaining the mathematical soundness and the excellent segmentation performance. Theoretic analysis and experimental results demonstrate the promise and effectiveness of this framework.