Abstract
In this paper, we explore the use of over-complete spherical wavelets in shape analysis of closed 2D surfaces. Previous work has demonstrated, theoretically and practically, the advantages of over-complete over bi-orthogonal spherical wavelets. Here we present a detailed formulation of over-complete wavelets, as well as shape analysis experiments of cortical folding development using them. Our experiments verify in a quantitative fashion existing qualitative theories of neuro-anatomical development. Furthermore, the experiments reveal novel insights into neuro-anatomical development not previously documented.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Bogdanova, I., et al.: Stereographic Wavelet Frames on the Sphere. Applied and Computational Harmonic Analysis 19, 223–252 (2005)
Brechbüler, C., et al.: Parametrization of closed surfaces for 3-D shape description. Computer Vision and Image Understanding 61, 154–179 (1995)
Chi, J., et al.: Gyral development of the human brain. Ann. Neurol. 1 (1997)
Cootes, T., et al.: Active Shape Models-Their Training and Application. Computer Vision and Image Understanding 61(1), 38–59 (1995)
Daubechies, I.: Ten Lectures on Wavelets. SIAM, Philadelphia (1992)
Fischl, B., et al.: Cortical Surface-Based Analysis II: Inflation, Flattening, and a Surface-Based Coordinate System. NeuroImage 9(2), 195–207 (1999)
Fischl, B., et al.: Cortical Folding Patterns and Predicting Cytoarchictecture. Cerebral Cortex (2007)
Goodall, C.: Procrustes Method in the Statistical Analysis of Shape. Journal of the Royal Statistical Society B 53(2), 285–339 (1991)
Driscoll, J., Healy, D.: Computing Fourier Transforms & Convolutions on the 2-Sphere. Adv. in Appl. Math. 15, 202–250 (1994)
Minka, T.: Using Lower Bounds to Approximate Integrals, Technical Report (2001)
Nain, D., et al.: Multiscale 3-D shape representation and segmentation using spherical wavelets. IEEE Transactions on Medical Imaging 26, 598–618 (2007)
Schroder, P., Sweldens, W.: Spherical Wavelets: Efficiently Representing Functions on the Sphere. In: Computer Graphics Proceedings (SIGGRAPH), pp. 161–172 (1995)
Simoncelli, E., et al.: Shiftable Multi-scale Transforms. IEEE Transaction Information Theory 38(2), 587–607 (1992)
Staib, L., Duncan, J.: Model-based deformable surface finding for medical images. IEEE Transactions on Medical Imaging 15, 720–731 (1996)
Virene, E.: Reliability Growth and its Upper Limit. In: Proc. 1968 Annu. Symp. Reliability, pp. 265–270 (1968)
Yeo, B.T.T., et al.: On the Construction of Invertible Filter Banks on the 2-Sphere. IEEE Transactions on Image Processing 17(3), 283–300 (2008)
Yu, P., et al.: Cortical Surface Shape Analysis Based on Spherical Wavelets. IEEE Transactions on Medical Imaging 26(4), 582–598 (2007)
Yu, P., et al.: Cortical Folding Development Study based on Over-complete Spherical Wavelets. In: MMBIA (2007)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yeo, B.T.T., Yu, P., Grant, P.E., Fischl, B., Golland, P. (2008). Shape Analysis with Overcomplete Spherical Wavelets. In: Metaxas, D., Axel, L., Fichtinger, G., Székely, G. (eds) Medical Image Computing and Computer-Assisted Intervention – MICCAI 2008. MICCAI 2008. Lecture Notes in Computer Science, vol 5241. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85988-8_56
Download citation
DOI: https://doi.org/10.1007/978-3-540-85988-8_56
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85987-1
Online ISBN: 978-3-540-85988-8
eBook Packages: Computer ScienceComputer Science (R0)