Merging and splitting eigenspace models
IEEE Transactions on Pattern Analysis and Machine IntelligencePublished 1 January 2000
Peter Hall, D. Marshall, Ralph R. Martin
Citations237
SJR quartileQ1
SJR score3.91
SNIP5.99
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
New deterministic methods that, given two eigenspace models-each representing a set of n-dimensional observations-will: merge the models to yield a representation of the union of the sets and split one model from another to represent the difference between the sets are presented.
Abstract
We present new deterministic methods that, given two eigenspace models-each representing a set of n-dimensional observations-will: 1) merge the models to yield a representation of the union of the sets and 2) split one model from another to represent the difference between the sets. As this is done, we accurately keep track of the mean. Here, we give a theoretical derivation of the methods, empirical results relating to the efficiency and accuracy of the techniques, and three general applications, including the construction of Gaussian mixture models that are dynamically updateable.
Keywords
Computer Science
Journal of the Royal Statistical Society Series B (Statistical Methodology)Maximum Likelihood from Incomplete Data Via the <i>EM</i> Algorithm
49,657 Citations1977A. P. Dempster, N. M. Laird +1 more
Digital Access to Scholarship at Harvard (DASH) (Harvard University)Maximum Likelihood from Incomplete Data via the EM Algorithm
4,523 Citations1977Dempster, Arthur P., Laird, Nan M. +1 more
Journal of the Optical Society of America ALow-dimensional procedure for the characterization of human faces
2,316 Citations1987L. Sirovich, Michael Kirby
A method is presented for the representation of faces that results in the characterization of a face, to within an error bound, by a relatively low-dimensional vector.
International Journal of Computer VisionVisual learning and recognition of 3-d objects from appearance
1,891 Citations1995Hiroshi Murase, Shree K. Nayar
A near real-time recognition system with 20 complex objects in the database has been developed and a compact representation of object appearance is proposed that is parametrized by pose and illumination.
IEEE Transactions on Pattern Analysis and Machine IntelligenceProbabilistic visual learning for object representation
1,451 Citations1997B. Moghaddam, Alex Pentland
An unsupervised technique for visual learning is presented, which is based on density estimation in high-dimensional spaces using an eigenspace decomposition and is applied to the probabilistic visual modeling, detection, recognition, and coding of human faces and nonrigid objects.
Numerische MathematikRank-one modification of the symmetric eigenproblem
490 Citations1978James R. Bunch, Christopher P. Nielsen +1 more
An algorithm is presented for computing the eigensystem of the rank-one modification of a symmetric matrix with known eIGensystem and the explicit computation of the updated eigenvectors and the treatment of multiple eigenvalues.
Training Models of Shape from Sets of Examples
455 Citations1992T.F. Cootes, Chris Taylor +2 more
IEEE Transactions on Neural NetworksModeling the manifolds of images of handwritten digits
329 Citations1997Geoffrey E. Hinton, Peter Dayan +1 more
Two new methods for modeling the manifolds of digitized images of handwritten digits of principal components analysis and factor analysis are described, based on locally linear low-dimensional approximations to the underlying data manifold.
Numerische MathematikUpdating the singular value decomposition
285 Citations1978James R. Bunch, Christopher P. Nielsen
IEEE Transactions on Pattern Analysis and Machine IntelligenceMerging and splitting eigenspace models
237 Citations2000Peter Hall, D. Marshall +1 more
New deterministic methods that, given two eigenspace models-each representing a set of n-dimensional observations-will: merge the models to yield a representation of the union of the sets and split one model from another to represent the difference between the sets are presented.
Graphical Models and Image ProcessingAn Eigenspace Update Algorithm for Image Analysis
235 Citations1997S. Chandrasekaran, B.S. Manjunath +3 more
IEEE Transactions on Pattern Analysis and Machine IntelligenceFrequency-based nonrigid motion analysis: application to four dimensional medical images
182 Citations1996Chahab Nastar, Nicholas Ayache
In this method, nonrigid motion of the deforming object contour is dynamically approximated by a physically-based deformable surface and a modal analysis which provides a spatial smoothing of the surface is used.
IEEE Transactions on Pattern Analysis and Machine IntelligenceEfficient Calculation of Primary Images from a Set of Images
180 Citations1982Hiroyasu Murakami, B. V. K. Vijaya Kumar
An iterative algorithm is proposed to calculate the eigenvectors when the rank of the correlation matrix is not large which save computation time and omputer storage requirements and gains its efficiency from the fact that only a significant set of eigenavectors are retained at any stage of iteration.
Training Models of Shape from Sets of Examples
169 Citations1992T.F. Cootes, Chris Taylor +2 more
A method for building flexible shape models is presented in which a shape is represented by a set of labelled points and a number of modes of variation are determined describing the main ways in which the example shapes tend to deform from the average.
Active object recognition
103 Citations2003D. Wilkes, John K. Tsotsos
The concept of active object recognition is introduced, and a proposal for its solution is described, which uses an efficient tree-based, probabilistic indexing scheme to find the model object that is likely to have generated the observed data.
IEEE Transactions on Information TheoryOn the generalized Karhunen-Loeve expansion (Corresp.)
97 Citations1967Y.P. Chien, King‐Sun Fu
The purpose of this correspondence is to show that the cited optimum properties can be retained by defining a generalized Karhunen-Loeve expansion which considers the possibility of two or more stochastic processes generating the random functions.
IEEE Transactions on Acoustics Speech and Signal ProcessingEfficient, numerically stabilized rank-one eigenstructure updating (signal processing)
72 Citations1990R.D. DeGroat, Richard A. Roberts
A numerical stabilization technique is developed, which eliminates the error buildup problem in a computationally efficient manner and makes the rank-one EVD update a practical numerical tool for online computation.
Active Object Recognition in Parametric Eigenspace
42 Citations1998Hermann Borotschnig, Lucas Paletta +2 more
An efficient method within an active vision framework for recognizing objects which are ambiguous from certain viewpoints is presented, which uses an appearance based object representation, namely the parametric eigenspace, and augments it by probability distributions.
Computer Vision and Image UnderstandingRecursive Estimation of Motion Parameters
32 Citations1996Subhasis Chaudhuri, Shakti Sharma +1 more
A robust algroithm that estimates the motion parameters recursively from a sequence of noisy images by using the least median of squares method in conjunction with a computationally efficient recursive scheme is presented.
IEEE Transactions on Medical ImagingReconstruction of vascular networks using three-dimensional models
17 Citations1997Peter Hall, Monique Ngan +1 more
The authors' representation and reconstruction algorithm are new and useful approaches that support a vascular catalogue containing three-dimensional (3-D) anatomical models and reconstructing vasculature from images.