Time & Place
2019 Spring semesterT/Th 9:3010:45am
Medical Science Center 4765
Course Webpage: www.stat.wisc.edu/~mchung/teaching/768
Instructor
Moo K. Chung, PhD
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.
Assistant Instructor
ShihGu Huaang, PhD shuang373@wisc.edu
Research Associate, Department of Biostatistics
and Medical Informatics
University of WisconsinMadison

Prerequisite
 None. The course is self
contained. The course is designed for
graduate students, postdocs and researchers
who wish to learn quantitative mathematical,
statistical and computational techniques in
processing and analyzing medical images.
However, basic understanding of linear algebra
and calculus will be useful to fully
understand lectures. 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, Advanced MATLAB programming
Hilbert Space in Images:
Hilbert spaces, Fourier analysis, functional data
analysis, functional principal component analysis,
partial differential equations, integral
transforms, diffusion, finite differences, finite
element methods
Image
Simulations:
permutation tests, Gaussian and nonGaussian
random fields, covariance functions,
KarhunenLoeve expansion, multiple comparisons
Big Image Data:
Largescale image
computation, scalable computation, online
algorithms
Differential & Spectral
Geometry:
Riemannian metric tensors, geodesics, tangent
spaces, LaplceBeltrami operator, Fourier analysis
on manifolds, manifolds data, graph Laplacian,
tensor geometry in medical images
Computational Topology:
topological spaces, simplical homology, cubical
complex, persistent homology, topological
invariants, surface mesh topology, topology
corrections in images, hierarchical clustering
Trees,
Graphs & Networks:
random walks, graphical models, graph theory, hubs
& smallworldness, spectral
clustering, correlation networks, sparse network,
hierarchical networks
Regression in
Images and manifolds:
general linear models, matrix equations, fixed and
random effects models, longitudinal images,
logistic regression, sparse regression, compressed
sensing
Course Materials
There is no required textbook. Lecture slides and
additional notes will be provided 5 hours before
each lecture in http://www.stat.wisc.edu/~mchung/teaching/768/lectures.
Parts of lectures will be based on the following
three text books written by the instructor:
Statistical and Computational Methods in Brain Image Analsis, 2013 CRC Press
Brain Network Analysis, 2019 Cambridge University Press
Course Evaluation
Course evaluation is based on class attendance,
discussion participants and a class project. You
can either use your own biomedical images (after
consulation with the instructor) or the instructor
will provide publishable 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.