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Chung, M.K., Singh, V., Kim,
P.T., Dalton, K.M., Davidson, R.J.
2009. Topological
characterization of signal in brain images using the min-max diagram.
12th International
Conference on
Medical Image Computing and Computer Assisted Intervention (MICCAI).
Lecture Notes in Computer
Science
(LNCS). (acceptance
rate < 32%). We present a novel computational framework for characterizing signal in brain images via nonlinear pairing of critical values of the signal. Among the astronomically large number of different pairings possible, we show that representations derived from specific pairing schemes provide concise representations of the image. This procedure yields a min-max diagram of the image data. |
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Chung, M.K., Bubenik, P.,
Kim, P.T.
2009. Persistence
diagrams of cortical surface data. Information Processing in Medica Imaging
(IPMI). Lecture Notes in
Computer Science (LNCS). (selected
for oral presentation , oral acceptance rate 17%). in press. We present a novel framework for characterizing signals in images using techniques from computational algebraic topology. This technique is general enough for dealing with noisy multivariate data including geometric noise. The main tool is persistent homology which can be encoded in persistence diagrams. These diagrams visually show how the number of connected components of the sublevel sets of the signal changes. |
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Chung, M.K., Worsley,
K.J., Nacewicz, B.M., Dalton, K.M., Davidson, R.J. 2009. Multivariate
Amygdala Shape Modeling. Department of Biostatistics and
Medical Informatics TR 206, University of Wisconsin-Madison.
submitted. Although there are many imaging studies on traditional ROI-based amygdala volumetry, there are very few studies on modeling amygdala shape variations. This paper present a first unified computational and statistical framework for modeling amygdala shape variations in a clinical population. The recently developed weighted spherical harmonic representation is used as to parameterize, to smooth out, and to normalize amygdala surfaces. |
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Chung, M.K. Hartley, R., Dalton, K.M., Davidson, R.J. 2008. Encoding cortical surface by spherical harmonics. Satistica Sinica 18:1269-1291 (Special Issue on Statistical Challenges and Advances in Brain Science). There is a lack of a unified statistical modeling framework for cerebral shape asymmetry analysis in the literature. Most previous approaches start with flipping the 3D magnetic resonance images (MRI). The anatomical correspondence across the hemispheres is then established by registering the original image to the flipped image. A difference of an anatomical index between these two images is used as a measure of cerebral asymmetry. We present a radically different asymmetry analysis that utilizes a novel weighted spherical harmonic representation of cortical surfaces. |
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Chung, M.K., Dalton, K.M.,
Davidson,
R.J. 2008. . Tensor-based
cortical surface morphometry via weighed spherical harmonic
representation. IEEE
Transactions on Medical Imaging. (invited submission based on MMBIA 2006
oral presentation). 27:1143-1151. We present a new tensor-based morphometric framework that quantifies cortical shape variations using a local area element. The local area element is computed from the Riemannian metric tensors, which are obtained from the smooth functional parametrization of a cortical mesh. For the smooth parametrization, we have developed a novel weighted spherical harmonic (SPHARM) representation, which generalizes the traditional SPHARM as a special case. |
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Chung, M.K., Dalton, K.M.,
Shen, L., L., Evans,
A.C., Davidson, R.J. 2007. Weighted
Fourier series representation and its application to quantifying the
amount of gray matter.. Special Issue of IEEE Transactions on
Medical Imaging, on Computational Neuroanatomy. 26:566-581.
(invited paper). We present a novel weighted Fourier Series (WFS) representation for cortical surfaces. The WFS representation is a data smoothing technique that provides the explicit smooth functional estimation of unknown cortical boundary as a linear combination of basis functions. The basic properties of the representation are investigated in connection with a self-adjoint partial differential equation and the traditional spherical harmonic (SPHARM) representation. To reduce steep computational requirements, a new iterative residual fitting (IRF) algorithm is developed. |
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Chung, M.K., Robbins,S.,
Dalton, K.M., Davidson,
Alexander, A.L., R.J., Evans, A.C. 2005. Cortical
thickness analysis in autism via heat kernel smoothing. NeuroImage
25:1256-1265 (selected for cover
illustration) We present a novel data smoothing and analysis framework for cortical thickness data defined on the brain cortical manifold. Gaussian kernel smoothing, which weights neighboring observations according to their 3D Euclidean distance, has been widely used in 3D brain images to increase the signal-to-noise ratio. When the observations lie on a convoluted brain surface, however, it is more natural to assign the weights based on the geodesic distance along the surface. We therefore develop a framework for geodesic distance-based kernel smoothing and statistical analysis on the cortical manifolds. |