Abstract
The exterior surface of the brain is characterized by a juxtaposition of crests and troughs that together form a folding pattern. The majority of the deformations that occur in the normal course of adult human development result in folds changing their length or width. Current statistical shape analysis methods cannot easily discriminate between these two cases. Using discrete exterior calculus and Tikhonov regularization, we develop a method to estimate a dense orientation field in the tangent space of a surface described by a triangulated mesh, in the direction of its folds. We then use this orientation field to distinguish between shape differences in the direction parallel to folds and those in the direction across them. We test the method quantitatively on synthetic data and qualitatively on a database consisting of segmented cortical surfaces of 92 healthy subjects and 97 subjects with Alzheimer’s disease. The method estimates the correct fold directions and also indicates that the healthy and diseased subjects are distinguished by shape differences that are in the direction perpendicular to the underlying hippocampi, a finding which is consistent with the neuroscientific literature. These results demonstrate the importance of direction specific computational methods for shape analysis.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Van Essen, D.: A tension-based theory of morphogenesis and compact wiring in the central nervous system. Nature 385, 313–318 (1997)
Buckner, R.: Memory and Executive Function in Aging and AD Multiple Factors that Cause Decline and Reserve Factors that Compensate. Neuron 44(1), 195–208 (2004)
Chung, M., Worsley, K., Robbins, S., Paus, T., Taylor, J., Giedd, J., Rapoport, J., Evans, A.: Deformation-based surface morphometry applied to gray matter deformation. NeuroImage 18(2), 198–213 (2003)
Fischl, B., Sereno, M., Dale, A.: Cortical surface-based analysis. II: Inflation, flattening, and a surface-based coordinate system. Neuroimage 9(2), 195–207 (1999)
Toga, A., Thompson, P.: Mapping brain asymmetry. Nature Reviews Neuroscience 4(1), 37–48 (2003)
Fillard, P., Arsigny, V., Ayache, N., Pennec, X.: A Riemannian Framework for the Processing of Tensor-Valued Images. In: Fogh Olsen, O., Florack, L.M.J., Kuijper, A. (eds.) DSSCV 2005. LNCS, vol. 3753, pp. 112–123. Springer, Heidelberg (2005)
Lepore, N., Brun, C., Chou, Y., Chiang, M., Dutton, R., Hayashi, K., Luders, E., Lopez, O., Aizenstein, H., Toga, A., et al.: Generalized Tensor-Based Morphometry of HIV/AIDS Using Multivariate Statistics on Deformation Tensors. IEEE Transactions on Medical Imaging 27(1), 129–141 (2008)
Tang, B., Sapiro, G., Caselles, V.: Diffusion of General Data on Non-Flat Manifolds via Harmonic Maps Theory: The Direction Diffusion Case. International Journal of Computer Vision 36(2), 149–161 (2000)
Perona, P.: Orientation diffusions. IEEE Image Processing 7, 457–467 (1998)
Kimmel, R., Sochen, N.: Orientation Diffusion or How to Comb a Porcupine. Visual Com. and Image Representation 13(1-2), 238–248 (2002)
Hirani, A.: Discrete exterior calculus. PhD thesis, California Institute of Technology (2003)
Grinspun, E., Gingold, Y., Reisman, J., Zorin, D.: Computing discrete shape operators on general meshes. In: Computer Graphics Forum, vol. 25, pp. 547–556. Blackwell Synergy, Malden (2006)
Lyttelton, O., Boucher, M., Robbins, S., Evans, A.: An unbiased iterative group registration template for cortical surface analysis. Neuroimage 34(4), 1535–1544 (2007)
Worsley, K., Andermann, M., Koulis, T., MacDonald, D., Evans, A.: Detecting changes in nonisotropic images. Human Brain Mapping 8(2-3), 98–101 (1999)
Fisher, M., Springborn, B., Schröder, P., Bobenko, A.: An algorithm for the construction of intrinsic delaunay triangulations with applications to digital geometry processing. Computing 81(2), 199–213 (2007)
Marcus, D., Wang, T., Parker, J., Csernansky, J., Morris, J., Buckner, R.: Open Access Series of Imaging Studies (OASIS): Cross-sectional MRI Data in Young, Middle Aged, Nondemented, and Demented Older Adults. Journal of Cognitive Neuroscience 19(9), 1498–1507 (2007)
Boucher, M., Whitesides, S., Evans, A.: Depth potential function for folding pattern representation, registration and analysis. Medical Image Analysis (2008)
Kim, J., Singh, V., Lee, J., Lerch, J., Ad-Dabbagh, Y., MacDonald, D., Lee, J., Kim, S., Evans, A.: Automated 3-D extraction and evaluation of the inner and outer cortical surfaces using a Laplacian map and partial volume effect classification. Neuroimage 27, 210–221 (2005)
Cabral, B., Leedom, L.: Imaging vector fields using line integral convolution. In: Proceedings of the 20th annual conference on Computer graphics and interactive techniques, pp. 263–270. ACM, New York (1993)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Boucher, M., Evans, A., Siddiqi, K. (2009). Oriented Morphometry of Folds on Surfaces. In: Prince, J.L., Pham, D.L., Myers, K.J. (eds) Information Processing in Medical Imaging. IPMI 2009. Lecture Notes in Computer Science, vol 5636. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02498-6_51
Download citation
DOI: https://doi.org/10.1007/978-3-642-02498-6_51
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02497-9
Online ISBN: 978-3-642-02498-6
eBook Packages: Computer ScienceComputer Science (R0)