Statistical Methods for Medical Image Analysis

BMI/STAT- 768 (2018 spring semester)

Instructor    Moo K. Chung

Time & Place

2018 Spring semester
T/Th 9:30-10:45am
Medical Science Center 4765


Moo K. Chung
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.
Course Webpage:

  1. Prerequisite

  2. 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, Laplce-Beltrami 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 & small-worldness, 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 non-Gaussian fields, covariance functions, Karhunen-Loeve 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

Skeleton representation of lung blodd vessel tree obtained from CT. Students will learn avanced  data and image representation and visualizaiton techniques as well as quantification methods used in medical image processing and analysis.