Mapper is a topological construction similar to a Reeb graph, and is used to summarize the shape of a dataset as a (generalized) graph. Formally, mapper can be constructed for any connected space and algorithms have been developed to compute mapper for point clouds and 2D images. In this paper, we extend mapper to 3D volumetric images. We use our algorithm to compute mapper for scans of barley generated using computed tomography. We demonstrate the flexibility of the construction by highlighting different aspects of the morphology through different choices of starting parameters. Applying mapper to this type of data provides an integrated means of visualization, segmentation and clustering, and can thus be used to study the topology of any 3D object.
|Title of host publication||Mathematical Morphology and Its Applications to Signal and Image Processing - 14th International Symposium, ISMM 2019, Proceedings|
|Editors||Bernhard Burgeth, Andreas Kleefeld, Benoît Naegel, Nicolas Passat, Benjamin Perret|
|Number of pages||12|
|Publication status||Published - 2019|
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
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- Computed tomography
- Image processing
- Topological data analysis
- Topological mapper