Geometric and Topological Methods in Biomedical Image Analysis

Part of Computational Geometry Week (CG Week 2021)

Virtual, June 7-11, 2021


Bei Wang
Assistant Professor
School of Computing
Scientific Computing and Imaging Institute
University of Utah
beiwang AT

Chao Chen
Assistant Professor
Department of Biomedical Informatics
Stony Brook University
chao.chen.1 AT


The Workshop

In biomedical image analysis, many problems require reconstruction, comparison, summarizing, and visualization of biomedical systems with complex geometry and topology. Computational geometry and topology can play crucial and natural roles in this domain, by delivering solutions with theoretical guarantees or rationales. This workshop is intended to provide a forum to promote the interaction between experts in the fields of biomedical image analysis, computational geometry, and topological data analysis. To this end, the workshop will consist of a keynote talk and multiple invited talks. We expect such interaction will help identifying new research opportunities in biomedical research for the computational geometry and topology communities.

Confirmed Keynote Speaker

Baba C. Vemuri (University of Florida)

Bio: Baba Vemuri received his PhD in Electrical and Computer Engineering from the University of Texas at Austin in 1987. He then joined the Department of Computer and Information Sciences at the University of Florida, Gainesville, where he currently holds the Wilson and Marie Collins Professorship in Engineering. His research interests include Geometric Deep Learning, Geometric Statistics, Medical Image Computing, Computer Vision, Machine Learning and Information Geometry. He has published over 200 refereed journal and conference articles in the aforementioned areas and received several best paper awards. He has served as a program chair and area chair of several IEEE sponsored conferences. He was an associate editor for several area journals and is currently an associate editor for the Journal of Medical Image Analysis and the International Journal of Computer Vision (IJCV). Professor Vemuri is a recipient of the IEEE Computer Society’s Technical Achievement Award and is a fellow of the IEEE and ACM.

Confirmed Invited Speakers

Shantanu Joshi (University of California Los Angeles)
Mathieu Carrière (Inria Sophia Antipolis)
Zhengwu Zhang (UNC Chapel Hill)
Prateek Prasanna (Stony Brook University)
Anna Song (Imperial College London)


The workshop will span two half days. For the 1st half day session on Wednesday, June 9, we plan to hold one plenary talk (1 hour, 45 minutes followed by 15 minutes discussions and questions) and 1 invited talk (30 minutes, 20 minutes followed by 10 minutes discussions and questions). For the 2nd half day session on Friday, June 11, we plan to hold 4 invited talks (30 minutes, 20 minutes followed by 10 minutes discussions and questions).

Intended Audience

The workshop primarily targets the computational geometry and computational topology community represented at SoCG. It is also suitable for general SoCG attendees interested in learning the applications of geometry and topology in medical imaging. Our aim is to help both theoretical and applied communities exchange and learn from each other.

Schedule (all time in EST)

Tentative Schedule

Wednesday, June 9, 2021
Time Speaker Title
1:40 - 2:40 PM EST Baba C. Vemuri (Keynote) ManifoldNet: A Deep Neural Network for Manifold-Valued Data with Applications
2:40 - 3:10 PM EST Shantanu Joshi Geometric Data Alignment of Biomedical Signals and Shapes
Friday, June 11, 2021
Time Speaker Title
2:40- 3:10 PM EST Mathieu Carrière Topological Analysis of Immunofluorescence Images
3:10 - 3:40 PM EST Anna Song Signed Distance Persistent Homology of Tubular Shapes
3:40 - 4:10 PM EST Zhengwu Zhang Surface-Based Connectivity Integration
4:10 - 4:40 PM EST Prateek Prasanna Radiomics and Pathomics in Precision Medicine – Why Domain Still Matters


ManifoldNet: A Deep Neural Network for Manifold-Valued Data with Applications

Baba C. Vemuri

Developing deep neural networks (DNNs) for manifold-valued data sets has gained significant interest of late in the deep learning research community. Manifold-valued data abound in the Medical Imaging and Computer Vision domains, e.g., diffusion tensor images (DTI), shapes (landmarks), covariance matrices, and others. In this talk, a novel theoretical framework for DNNs tailored for manifold-valued data inputs dubbed, ManifoldNet, will be presented.

Analogous to vector spaces where convolutions are equivalent to computing weighted means, manifold-valued data convolutions will be defined using the weighted Frechet Mean (wFM). To this end, a provably convergent recursive algorithm for computation of the wFM of the given data is presented, where the weights are to be learned. Further, the proposed wFM operator is provably equivariant to the natural group actions admitted by the data manifold and achieves a contraction mapping. A novel network architecture to realize the ManifoldNet will be detailed during the talk. Experiments showcasing the performance of the ManifoldNet on regression and classification problems in Neuroimaging will be presented. Finally, if time permits, a generalization of the ManifoldNet to accommodate higher order manifold-valued convolutions will be briefly discussed.

Geometric Data Alignment of Biomedical Signals and Shapes

Shantanu Joshi

This talk presents approaches for geometric alignment of signals, functional measures and diffusion measures from neuroimaging data. We present methods for temporal alignment of both amplitude and phase of the functional magnetic resonance imaging (fMRI) time course and spectral densities. Experimental results show significant increases in pairwise node to node correlations and coherences following alignment. Additionally, we show results for task based fMRI signals, where we see improved power of detection of clusters and activations for single subject data. We also present a geometric approach for minimizing the variability in the shape of along-tract diffusion profiles by performing diffeomorphic alignment across the tracts as well as across populations. Finally, we present an approach for accelerating the alignment process using deep learning.

Topological Analysis of Immunofluorescence Images

Mathieu Carrière

Persistent homology is a common tool of topological data analysis, which aims at computing and encoding the geometry and topology of given datasets. In this talk, I will present a novel application of persistent homology to characterize the spatial arrangement of immune and tumor cells in the context of breast cancer. More specifically, quantitative and robust characterizations are built by computing (multi-parameter) persistent homology out of a staining technique (called quantitative multiplex immunofluorescence) which allows to obtain spatial coordinates and stain intensities on individual cells. The resulting persistence modules are then converted into descriptors (persistence diagrams for scalar filtrations, multi-parameter persistence images for multi-parameter filtrations) and evaluated as characteristic biomarkers of cancer subtype and overall survival. This provides new insights and possibilities on the general problem of building (topology-based) biomarkers for immune responses.

Signed Distance Persistent Homology of Tubular Shapes

Anna Song

Tubular shapes arise in many important biological structures and systems, and in biomedical images. Their rich branching morphologies, shaped by interactions and remodeled by diseases, contain a wealth of information on the properties of the biological environment and insight on disease progression. I will present some preliminary results studying these structures using persistent homology with sublevel set filtration given by a signed distance function. The map is defined with respect to the surface of the shape, with negative values inside the region enclosed by the surface, and positive values outside. This simple idea is tested on synthetic tubular shapes generated by the "curvatubes" model (, as well as on real proprietary data in the form of confocal images of bone marrow vasculature. The ultimate long-term goal is to quantify how acute myeloid leukemia (AML) remodels and degrades the bone marrow vessels during its progression, and improve our understanding of the cellular interactions in the bone marrow.

This work is in joint collaboration with my supervisors, Anthea Monod and Dominique Bonnet, as well as Antoniana Batsivari and Jeremy Pike.

Surface-Based Connectivity Integration

Zhengwu Zhang

The integration of structural (SC) and functional connectivity (FC) remains a necessary and challenging frontier for neuroscience research due to signal and image processing limitations. Diffusion (dMRI) and resting-state functional MRI (rs-fMRI) provide the signals in white (WM) and gray matter (GM) for SC and FC. The integration of structural and functional connectivity thus far has been limited to atlas-based parcellation studies. We present a novel atlas-free processing pipeline and some analysis methods to explore the integration of structural and functional connectivity at high spatial resolution. This processing pipeline overcomes a few important limitations: 1. it utilizes the geometry of the brain to impose prior knowledge, allowing all white matter fibers to end on the WM-GM surfaces; 2. it smoothes the sparse SC into a dense one for a better comparison with FC. The pipeline also outputs a new biomarker that can be used to study various clinical questions - the integrity/correlation between FC and SC at each vertex on the WM-GM surface. We will demonstrate this pipeline using a few healthy subjects.

Radiomics and Pathomics in Precision Medicine – Why Domain Still Matters

Prateek Prasanna

The success of diagnostic and prognostic tools often depends on accurate and timely interpretation of imaging presentations. As growing evidence suggests that heterogeneity is prevalent across multiple length scales, such as radiology and histology, new computational approaches that model the hierarchical heterogeneity in a clinically intuitive and interpretable way are a need of the hour. This presentation will discuss our work on developing computational imaging biomarkers for precision medicine. We will discuss several biology and domain-inspired imaging features for early diagnosis and treatment response assessment in lung and brain cancers, and more recently in COVID-19 prognosis. These features, spanning morphology, texture, topology, and geometry of phenotypic attributes deliver an imaging proof and appreciation of the systemic nature of disease. In order to provide greater interpretability of these imaging phenotypes and to enable the creation of more precise and tailored prognostic models, we will discuss the underlying histologic characteristics obtained via morphometric and graph-based approaches.