Time & Place
2018 Spring semesterT/Th 9:3010:45am
Medical Science Center 4765
Instructor
Moo K. Chung mkchung@wisc.edu
Associate Professor of Biostatistics and Medical
Informatics
Waisman Laboratory for Brain Imaging and Behavior
University of WiconsinMadison
Office: Medical
Science Center 5785, 1300 University Ave
Office Hours: T/TR
10:4512:30am. To set up separate appointments,
please email the instructor.
Course Webpage: www.stat.wisc.edu/~mchung/teaching/768

Prerequisite
 None. The course is self contained. The course is designed for graduate students, postocs and researchers who wish to learn quantitative mathematical and statistical techniques in processing and analyzing medical images. The course material is applicable to a wide variety of high dimensional nonstandard data and imaging problems beyond medical images.
Course Topics
Data & Image
Visualization:
vector & tensor visualization, shape
representation, volume & surface rendering,
visualizing relations, unstructured data, graphs
and networks
Hilbert Space in Images:
Hilbert space, functional data analysis,
functional principal component analysis, partial
differential equations, integral transforms,
diffusion, finite differences, finite element
methods, Fourier analysis
Differential & Spectral
Geometry:
Riemannian metric tensors, geodesics, tangent
spaces, LaplceBeltrami operator, Fourier analysis
on manifolds, manifolds data. symmetric
spaces, graph Laplacian, tensor geometry in images
Computational Topology:
topological spaces, simplical homology, cubical
complex, persistent homology, topological
invariants, topology corrections in images,
hierarchical clustering
Trees,
Graphs & networks:
random walks, graphical models, graph theory, hubs
& smallworldness, spectral
clustering, correlation networks, sparse networks
Regression in Images:
general linear models, matrix equations, fixed and
random effects models, longitudinal images,
logistic regression, sparse regression, compressed
sensing
Image
Resampling and Simulations:
bootstrap, jackknife, permutations, MCMC, Gibbs
Random Field Theory:
Gaussian and nonGaussian fields, covariance
functions, KarhunenLoeve expansion, multiple
comparisons
Course Evaluation
Course evaluation is based on a class project.
You can either use your own biomedical images
(after consulation with the instructor) or the
instructor will provide data. Students are
required to submit (1) research proposal, (2)
orally present the proposal, (3) submit the final
research project report and (4) do the final oral
presentation at the end of the semester. Sample
class projects in previous image analysis course
taught by the instructor can be found here.
Text Books
There is no required texbook. Lecture notes will
be provided 5 hours before each lecture in a
shared box folder. Parts of lectures will be
based on the following textbooks written by the
instructor:
Computational
Neuroanatomy: The Methods, 2012 World
Scientific Publishing
Statistical
and Computational Methods in Brain Image Analsis,
2013 CRC Press