Hanson, J.L., Ye, J., Davidson, R.J.
Pollak, S.D. 2015 Persistent
Homology in Sparse Regression and Its
Application to Brain Morphometry.
IEEE Transactions on Medical Imaging,
In this paper, by treating the the tuning parameter as an additional dimension, persistent homological structures over the parameter space is introduced and explored. The structures are then further exploited in drastically speeding up the computation using the proposed soft-thresholding technique.
|Chung, M.K., Qiu, A., Seo S.
Vorperian, H.K. 2015. Unified
heat kernel regression for diffusion, kernel
smoothing and wavelets on manifolds and its
application to mandible growth modeling in CT
images, Medical Image Analysis. 22:63-76
We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. The new kernel method is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets.
M.K. 2013. Statistical
and Computational Methods in Brain Image Analysis.
Chapman & Hall/CRC. DATA/MATLAB
The book is mainly focused on methodological issues in analyzing structural brain imaging modalities such as MRI and DTI. Concepts and methods are illustrated with real imaging applications and examples.
M.K. 2013. Computational
Neuroanatomy: The Methods, World Scientific
The main goals of this book are to provide an overview of various mathematical, statistical and computational methodologies used in computational neuroanatomy to a wide range of researchers and students, and to address important yet technically challenging topics in further detail.
H., Kang, H.K., Chung, M.K., Kim, B.-N., Lee, D.S.
brain network homology from the perspective of
Transactions on Medical Imaging. 31:2267-2277.
We propose a novel multiscale framework that models all brain networks generated over every possible threshold as the Rips filtration which is equivalent to a single linkage dendrogram.
H., Chung, M.K., Kang, H., Kim, B.-N., Lee, D.S.
shape of brain network using graph filtration and
Gromov-Haudorff metric. 14th International
Conference on Medical Image Computing and Computer
Assisted Intervention (MICCAI). Lecture Notes in
Computer Science (LNCS). 6892:302-309.
oral, oral acceptance = 4.15%).
We introduce a new framework for measuring the network difference using the Gromov-Hausdor (GH) distance, which is often used in shape analysis.
H., Lee, D.S., Kang, H., Kim, B.-N., Chung, M.K.
recovery under compressed sensing. IEEE Transactions on
Medical Imaging. Special Issue on Compressed
The sparse linear regression model with a l_1-norm penalty, also known as the least absolute shrinkage and selection operator (LASSO), was introduced for modeling sparse brain connectivity.
M.K., Worsley, K.J., Nacewicz, B.M.,
Dalton, K.M., Davidson, R.J. 2010. General
multivariate linear modeling of surface shapes
using SurfStat. NeuroImage. 53:491-505.
This paper present a first unified computational and statistical framework for modeling amygdala shape variations in a clinical population. MATLAB
S., Chung, M.K., Voperian, H.K. 2010. Heat
kernel smoothing using Laplace-Beltrami
eigenfunctions. 13th International Conference on Medical
Image Computing and Computer Assisted Intervention
(MICCAI). Lecture Notes in Computer Science (LNCS).
rate < 32%).
The Greenís function of an isotropic diffusion equation on a manifold is analytically represented using the eigenfunctions of the Laplace-Beltraimi operator. MATLAB
M.K., Adluru, N., Lee, J.E., Lazar, M., Lainhart,
J.E., Alexander, A.L., 2010. Cosine
series representation of 3D curves and its
application to white matter fiber bundles in
diffusion tensor imaging. Statistics and Its
Interface. 3:69-80. PMCID: PMC3541410
We present a novel cosine series representation for encoding fiber bundles consisting of multiple 3D curves using the cosine series expansion. We address the issue of registration, averaging and statistical inference on curves in a unified Hilbert space framework. MATLAB
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
Notes in Computer Science (LNCS). 5762:158-166.
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.
M.K., Bubenik, P., Kim, P.T. 2009. Persistence
diagrams of cortical surface data. Information Processing
in Medical Imaging (IPMI). Lecture Notes in Computer Science (LNCS).
5636:386-397. (selected for oral presentation , oral
acceptance rate 17%).
We present a novel framework for characterizing signals in images using techniques from computational algebraic topology. 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.
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). MATLAB
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. We present a radically different asymmetry analysis that utilizes a novel weighted spherical harmonic representation of cortical surfaces.
M.K., Dalton, K.M., Davidson, R.J. 2008. . Tensor-based
cortical surface morphometry via weighed spherical
harmonic representation. IEEE Transactions on
Medical Imaging 27:1143-1151 (invited submission based on MMBIA
2006 oral presentation). MATLAB
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.
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).
The weighted Fourier Series (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.
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
for cover illustration)
We present a novel data smoothing and analysis framework for cortical thickness data defined on the brain cortical manifold. 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. MATLAB