Limitations of the principal-axes theory

IEEE Transactions on Medical Imaging
T Schormann, K Zilles

Abstract

The classical principal-axes transformation (PAT) has been used in numerous publications for three-dimensional (3-D) reconstructions by sequential alignment of histological sections. However, the PAT can determine at most 1/2n(n + 1) parameters (scaling-rotation) in n dimensions. Distortions (shearing) of histological sections can be described by an affine transformation with n2 parameters. An analytical model is devised for calculating rotational and scaling errors which can be determined by relating the transformation parameters of the PAT to the exact solution of a singular value decomposition (SVD) of the perturbation matrix. The results show that form and deformation of the form are intertwined and that these results can be transferred to real data. The model is important for assessing the quality that can be expected with the PAT for 3-D reconstructions if no multimodality reference is available (rigid transformation) and reveals the misalignment in terms of rotational and scaling errors resulting from the PAT as derived in a previously published paper.

References

Nov 1, 1988·Journal of Neuroscience Methods·L S Hibbard, R A Hawkins
Jun 1, 1993·Journal of Neuroscience Methods·A W Toga, P K Banerjee

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Citations

Aug 12, 1999·The Journal of Comparative Neurology·K AmuntsK Zilles
Oct 12, 2000·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·T StammbergerF Eckstein
Jun 29, 2010·Neuroinformatics·Jack L LancasterJohn Mazziotta
Mar 2, 2011·Neuroinformatics·Jack L LancasterPeter T Fox
Dec 3, 1999·The European Journal of Neuroscience·J LarssonP E Roland
Feb 1, 2011·NeuroImage·Amalia CiforAlain Pitiot
May 13, 2005·Microscopy Research and Technique·Oliver SchmittJan Modersitzki
Aug 25, 2004·NeuroImage·Grégoire MalandainWim Vanduffel
Apr 22, 2003·IEEE Transactions on Medical Imaging·Thorsten Schormann, Matthias Kraemer
Jan 13, 2006·NeuroImage·M Mallar ChakravartyD Louis Collins
Sep 8, 2001·Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences·J MazziottaB Mazoyer
Aug 28, 2001·Journal of the American Medical Informatics Association : JAMIA·J MazziottaB Mazoyer

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