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Merging and Splitting Eigenspace Models
September 2000 (vol. 22 no. 9)
pp. 1042-1049
ASCII Text
x 
 
Peter Hall, David Marshall, Ralph Martin, "Merging and Splitting Eigenspace Models," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 22, no. 9, pp. 1042-1049, September, 2000.
 
 
BibTex
x
 
@article{ 10.1109/34.877525,
author = {Peter Hall and David Marshall and Ralph Martin},
title = {Merging and Splitting Eigenspace Models},
journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence},
volume = {22},
number = {9},
issn = {0162-8828},
year = {2000},
pages = {1042-1049},
doi = {http://doi.ieeecomputersociety.org/10.1109/34.877525},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
TI - Merging and Splitting Eigenspace Models
IS - 9
SN - 0162-8828
SP1042
EP1049
EPD - 1042-1049
A1 - Peter Hall,
A1 - David Marshall,
A1 - Ralph Martin,
PY - 2000
KW - Eigenspace models
KW - principal component analysis
KW - model merging
KW - model splitting
KW - Gaussian mixture models.
VL - 22
JA - IEEE Transactions on Pattern Analysis and Machine Intelligence
ER -
 

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.

[1] J.R. Bunch, C.P. Nielsen, and D.C. Sorenson, “Rank-One Modification of the Symmetric Eigenproblem,” Numerische Mathematik, vol. 31, pp. 31-48, 1978.
[2] J.R. Bunch and C.P. Nielsen, “Updating the Singular Value Decomposition,” Numerische Mathematik, vol. 31, pp. 111-129, 1978.
[3] S. Chandrasekaran, B.S. Manjunath, Y.F. Wang, J. Winkler, and H. Zhang, “An Eigenspace Update Algorithm for Image Analysis,” Graphical Models and Image Processing, vol. 59, no. 5, pp. 321-332, Sept. 1997.
[4] R.D. DeGroat and R. Roberts, “Efficient, Numerically Stablized Rank-One Eigenstructure Updating,” IEEE Trans. Acoustics, Speech, and Signal Processing, vol. 38, no. 2, pp. 301-316, Feb. 1990.
[5] H. Murakami and B.V.K.V. Kumar, “Efficient Calculation of Primary Images from a Set of Images,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 4, no. 5, pp. 511-515, Sept. 1982.
[6] B. Moghaddam and A. Pentland, “Probabilistic Visual Learning for Object Representation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 7, pp. 696-710, July 1997.
[7] C. Nastar and N. Ayache, “Frequency-Based Nonrigid Motion Analysis: Application to Four Dimensional Medical Images,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 18, no. 11, pp. 1,067-1,079, Nov. 1996.
[8] S. Chaudhuri, S. Sharma, and S. Chatterjee, “Recursive Estimation of Motion Parameters,” Computer Vision and Image Understanding, vol. 64, no. 3, pp. 434-442, Nov. 1996.
[9] P. Hall, D. Marshall, and R. Martin, “Incrementally Computing Eigenspace Models,” Proc. British Machine Vision Conf., pp. 286-295, 1998.
[10] L. Sirovich and M. Kirby, “Low-Dimensional Procedure for the Characterization of Human Faces,” J. Optical Soc. Am., A, vol. 4, no. 3, pp. 519-524, Mar. 1987.
[11] Y.T. Chien and K.S. Fu, “On the Generalised Karhunen-Loève Expansion,” IEEE Trans. Information Theory, vol. 13, pp. 518-520, 1967.
[12] G.H. Golub and C.F. Van Loan, Matrix Computations. Johns Hopkins, 1983.
[13] T.F. Cootes, C.J. Taylor, D.H. Cooper, and J. Graham, “Training Models of Shape from Sets of Examples,” Proc. British Machine Vision Conf., pp. 9-18, 1992.
[14] A. Dempster, N. Laird, and D. Rubin, “Maximum Likelihood from Incomplete Data via the em Algorithm,” J. Royal Statistical Soc. B, vol. 39, pp. 1-38, 1977.
[15] T. Heap and D. Hogg, “Improving Specificity in PDMS Using a Heirarchical Approach,” Proc. British Machine Conf., pp. 80-89, 1997.
[16] H. Murase and S.K. Nayar, “Visual Learning and Recognition of 3-D Objects from Appearance,” Int'l J. Computer Vision, vol. 14, pp. 5-24, 1995.
[17] H. Borotschnig, L. Paltta, M. Prantl, and A. Pinz, “Active Object Recognition in Parametric Eigenspace,” Proc. British Machine Vision Conf., pp. 629-638, 1998.

Index Terms:
Eigenspace models, principal component analysis, model merging, model splitting, Gaussian mixture models.
Citation:
Peter Hall, David Marshall, Ralph Martin, "Merging and Splitting Eigenspace Models," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 22, no. 9, pp. 1042-1049, Sept. 2000, doi:10.1109/34.877525
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