Reeb Graphs

VTK’s main source tree now includes topological scalar field analysis features through the vtkReebGraph class suite.

A Reeb graph is a concise representation of the connectivity evolution of the level sets of a scalar function. It is particularly useful in visualization (optimal seed set computation, fast flexible isosurface extraction, automated transfer function design, feature-driven visualization, etc.) and computer graphics (shape deformation, shape matching, shape compression, etc.).

vtkReebGraph implements one of the latest and most robust Reeb graph computation algorithms from “Robust on-line computation of Reeb graphs: simplicity and speed”, V. Pascucci, G. Scorzelli, P.-T. Bremer and A. Mascarenhas, ACM Transactions on Graphics, Proc. of SIGGRAPH 2007). The VTK integration has been achieved J. Tierny and others.

vtkReebGraph provides methods for computing multi-resolution topological hierarchies through topological simplification. Topological simplification can be either driven by persistence homology concepts (default behavior) or by application specific metrics (see vtkReebGraphSimplificationMetric). In the latter case, designing customized simplification metric evaluation algorithms enables the user to control the definition of what should be considered as noise or signal in the topological filtering process.

Reeb graphs can be computed from 2D data (vtkPolyData, with triangles only) or 3D data (vtkUnstructuredGrid, with tetrahedra only), sequentially (see the “Build” calls) or in streaming (see the “StreamTriangle” and “StreamTetrahedron” calls).

vtkReebGraph inherits from vtkMutableDirectedGraph. Each vertex of a vtkReebGraph object represents a critical point of the scalar field where the connectivity of the related level set changes (creation, deletion, split or merge of connected components). A vtkIdTypeArray (called “Vertex Ids”) is associated with the VertexData of a vtkReebGraph object, in order to retrieve if necessary the exact Ids of the corresponding vertices in the input mesh.

The edges of a vtkReebGraph object represent the regions of the input mesh separated by the critical contours of the field, and where the connectivity of the input field does not change. A vtkVariantArray is associated with the EdgeData of a vtkReebGraph object and each entry of this array is a vtkAbstractArray containing the Ids of the vertices of those regions, sorted by function value (useful for flexible isosurface extraction or level set signature computation, for instance).

See Graphics/Testing/Cxx/TestReebGraph.cxx for examples of traversals and typical usages (customized simplification, skeletonization, contour spectra, etc.) of a vtkReebGraph object.

Example Reeb graph images are shown below.

This entry was posted in Technique and tagged , , . Bookmark the permalink.