Histograms & Isosurfaces

Histograms and Isosurface Statistics

In studying topological acceleration of isosurface extraction, I started to get curious about the algorithmic cost of isosurface extraction, and this led one of my PhD students in the direction of analysing the relationship between isosurface statistics, histograms, and integration. Initially, this just involved empirical plots, which made it clear that there was a deep relationship (IEEE Visualization 2006 Best Research Paper Award):

In turn, this exposed a relationship with the Federer Co-Area Formula:

Eventually, we managed to nail down the theory, tying the relationship together with some fundamental mathematics:

Other Research Topics:

Contour Tree Computation
Scalar Topological Visualisation
Isosurface Acceleration
Isosurface Quality
Direct Volume Rendering
Topological Comparisons
Multivariate Topology
Fiber Surfaces
Aerial Urban LiDAR
Aerial Urban LiDAR
Exascale Data Analysis