Statistical Methods for Medical Image Analysis

BMI/STAT- 768 (2019 spring semester)

Instructor    Moo K. Chung

Time & Place

2019 Spring semester
T/Th 9:30-10:45am
Medical Science Center 4765
Course Webpage:


Moo K. Chung, PhD
Associate Professor of Biostatistics and Medical Informatics
Waisman Laboratory for Brain Imaging and Behavior
University of Wiconsin-Madison

Office: Medical Science Center 5785, 1300 University Ave
Office Hours: T/TR 10:45-12:30am. To set up separate appointments, please email the instructor.

Assistant Instructor
Shih-Gu Huaang, PhD
Research Associate, Department of Biostatistics and Medical Informatics
University of Wisconsin-Madison

  1. Prerequisite

  2. 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 non-Gaussian random fields, covariance functions, Karhunen-Loeve expansion, multiple comparisons

Big Image Data:
Large-scale image computation, scalable computation, online algorithms

Differential & Spectral Geometry:
Riemannian metric tensors, geodesics, tangent spaces, Laplce-Beltrami 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 & small-worldness, 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  Parts of lectures will be based on the following three text books written by the instructor:

Computational Neuroanatomy: The Methods, 2012 World Scientific Publishing
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.

Skeleton representation of lung blood vessel tree obtained from CT. Students will learn advanced  data and image representation and visualization techniques as well as quantification methods used in medical image processing and analysis. Read book chapter Chung et al. 2018 for more detail on the vessel tree modeling.