Extraction of Dominant Extremal Structures in Volumetric Data Using Separatrix Persistence
Article first published online: 18 OCT 2012
© 2012 The Authors Computer Graphics Forum © 2012 The Eurographics Association and Blackwell Publishing Ltd.
Computer Graphics Forum
Volume 31, Issue 8, pages 2554–2566, December 2012
How to Cite
Günther, D., Seidel, H.-P. and Weinkauf, T. (2012), Extraction of Dominant Extremal Structures in Volumetric Data Using Separatrix Persistence. Computer Graphics Forum, 31: 2554–2566. doi: 10.1111/j.1467-8659.2012.03222.x
- Issue published online: 26 OCT 2012
- Article first published online: 18 OCT 2012
- Feature extraction;
- discrete Morse theory;
- Morse-Smale complex
- I.4.7 [Image Processing and Computer Vision];
- Feature Measurement—Feature representation
Extremal lines and surfaces are features of a 3D scalar field where the scalar function becomes minimal or maximal with respect to a local neighborhood . These features are important in many applications, e.g. computer tomography, fluid dynamics, cell biology . We present a novel topological method to extract these features using discrete Morse theory. In particular, we extend the notion of ‘separatrix persistence’ from 2D to 3D, which gives us a robust estimation of the feature strength for extremal lines and surfaces. Not only does it allow us to determine the most important (parts of) extremal lines and surfaces, it also serves as a robust filtering measure of noise-induced structures. Our purely combinatorial method does not require derivatives or any other numerical computations .