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How to Measure Cortical Folding from MR Images: a Step-by-Step Tutorial to Compute Local Gyrification Index

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Published on: January 2, 2012

Persistence diagrams of cortical surface data.

Moo K Chung¹, Peter Bubenik, Peter T Kim

¹Department of Biostatistics and Medical Informatics, University of Wisconsin, Madison, WI 53706, USA. mkchung@wisc.edu

Information Processing in Medical Imaging : Proceedings of the ... Conference

|August 22, 2009

Summary

We introduce a new computational algebraic topology framework for image signal analysis. This method, using persistent homology, reveals differences in brain structure between control and autistic groups.

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Area of Science:

Computational topology
Image analysis
Data science

Background:

Traditional image analysis often relies on statistical methods like mean signal quantification.
Existing techniques may not fully capture complex signal variations or handle geometric noise effectively.
Computational algebraic topology offers novel approaches for signal characterization.

Purpose of the Study:

To present a novel framework for characterizing image signals using computational algebraic topology.
To demonstrate the utility of persistent homology for analyzing noisy multivariate data.
To compare the proposed method with traditional statistical parametric mapping.

Main Methods:

Utilizing persistent homology, a tool from computational algebraic topology.
Encoding topological features into persistence diagrams to visualize signal changes.
Analyzing local critical values of functions, differing from mean-based statistical approaches.
Applying the framework to simulated 1D signals and 2D cortical thickness data.

Main Results:

The framework effectively characterizes signals in both simulated and real-world imaging data.
Persistence diagrams provide visual insights into signal structure and changes.
Application to cortical thickness data revealed significant differences between control and autistic groups.
Extra homological structures were observed in the control group compared to the autistic group.

Conclusions:

Computational algebraic topology provides a powerful, novel framework for image signal quantification.
Persistent homology offers a robust method for data reduction and analysis, especially with noisy data.
The method highlights potential biomarkers for neurological conditions like autism by detecting structural differences.