Introduction to statistical pattern recognition (2nd ed.)
Introduction to statistical pattern recognition (2nd ed.)
A Stable and Efficient Algorithm for the Rank-One Modification of the Symmetric Eigenproblem
SIAM Journal on Matrix Analysis and Applications
On Photometric Issues in 3D Visual Recognition from aSingle 2D Image
International Journal of Computer Vision
An eigenspace update algorithm for image analysis
Graphical Models and Image Processing
Proceedings of the 1998 conference on Advances in neural information processing systems II
Acquiring the reflectance field of a human face
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Merging and Splitting Eigenspace Models
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image-based 3D photography using opacity hulls
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Relighting with the Reflected Irradiance Field: Representation, Sampling and Reconstruction
International Journal of Computer Vision
Principal Component Analysis over Continuous Subspaces and Intersection of Half-Spaces
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
EigenSegments: A Spatio-Temporal Decomposition of an Ensemble of Images
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
Probabilistic visual learning for object detection
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Mixtures of Eigenfeatures for Real-Time Structure from Texture
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Partial eigenvalue decomposition of large images using spatial temporal adaptive method
IEEE Transactions on Image Processing
A theory of locally low dimensional light transport
ACM SIGGRAPH 2007 papers
Hierarchical Tensor Approximation of Multi-Dimensional Visual Data
IEEE Transactions on Visualization and Computer Graphics
Secure and incidental distortion tolerant digital signature for image authentication
Journal of Computer Science and Technology
Precomputation-Based Rendering
Foundations and Trends® in Computer Graphics and Vision
Interactive region-based linear 3D face models
ACM SIGGRAPH 2011 papers
Computational and space complexity analysis of SubXPCA
Pattern Recognition
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Principal Component Analysis (PCA) is extensively used in computer vision and image processing. Since it provides the optimal linear subspace in a least-square sense, it has been used for dimensionality reduction and subspace analysis in various domains. However, its scalability is very limited because of its inherent computational complexity. We introduce a new framework for applying PCA to visual data which takes advantage of the spatio-temporal correlation and localized frequency variations that are typically found in such data. Instead of applying PCA to the whole volume of data (complete set of images), we partition the volume into a set of blocks and apply PCA to each block. Then, we group the subspaces corresponding to the blocks and merge them together. As a result, we not only achieve greater efficiency in the resulting representation of the visual data, but also successfully scale PCA to handle large data sets. We present a thorough analysis of the computational complexity and storage benefits of our approach. We apply our algorithm to several types of videos. We show that, in addition to its storage and speed benefits, the algorithm results in a useful representation of the visual data.