Master's thesis, Institute for Visualization and Data Analysis (Computer Graphics Group), Karlsruhe Institute of Technology (KIT), 2025.
In volume rendering, transfer functions translate raw scalar values into visual attributes like color and opacity, determining which structures emerge and how they're interpreted. Designing them is often difficult - for large, complex volumes it requires manual tweaking, repeated trials, and deep domain expertise.
This thesis introduces a topology-guided method to streamline and partly automate transfer-function design using persistent homology, a tool from topological data analysis. Persistent homology tracks how features such as separate regions or cavities appear and disappear as intensity thresholds vary. By generating persistence diagrams, the approach pinpoints the most significant, lasting features and uses them to place transfer functions in a way that's both data-driven and transparent.
A prototype visualization system implements this idea and was tested on several datasets, showing improved visual clarity, less manual adjustment, and better highlighting of key structures compared to standard 2D transfer function histograms.
- Language / rendering: C++, Vulkan
- GUI: Dear ImGui
- Core method: Persistent homology computed on filtered cubical complexes (lower-star filtration), using the standard boundary matrix reduction algorithm, extended with a merge tree for tracking feature origin back to voxel regions
- Interaction: 2D transfer function editor (scalar × gradient magnitude), persistence diagram / barcode panel with scalar and gradient modes, and Boolean set operations (union, intersection, difference) on selected topological features
- Persistence can also be computed from either the raw scalar field or the gradient magnitude, which highlight different kinds of structures:
- Rendering modes: Iso-surface mode for precise geometric boundaries, and volume-highlight mode for viewing selected features in the context of the full volume
Evaluated on three volumetric datasets from the Open SciVis Datasets collection: a silicium grid simulation, a tooth CT scan, and a head MRI (CISS) highlighting cerebrospinal fluid cavities.