Moments in Graphics
A blog by Christoph Peters

Image-based Visualization of Large Volumetric Data Using Moments

Tobias Rapp, Christoph Peters, Carsten Dachsbacher.
2022–04 in IEEE Transactions on Visualization and Computer Graphics (Proc. PacificVis) 28, 6.
Official version


We present a novel image-based representation to interactively visualize large and arbitrarily structured volumetric data. This image-based representation is created from a fixed view and models the scalar densities along each viewing ray. Then, any transfer function can be applied and changed interactively to visualize the data. In detail, we transform the density in each pixel to the Fourier basis and store Fourier coefficients of a bounded signal, i.e. bounded trigonometric moments. To keep this image-based representation compact, we adaptively determine the number of moments in each pixel and present a novel coding and quantization strategy. Additionally, we perform spatial and temporal interpolation of our image representation and discuss the visualization of introduced uncertainties. Moreover, we use our representation to add single scattering illumination. Lastly, we achieve accurate results even with changes in the view configuration. We evaluate our approach on two large volume datasets and a time-dependent SPH dataset.

Keywords: image-based visualization, volume rendering, unstructured volumes, moments, MESE, Fourier reconstruction


richtmeyer_meshkov_instability_bounded_mese reconstruction_graphs



This work has been accepted to PacificVis 2022 and selected as one of the papers to be published directly in IEEE Transactions on Visualization and Computer Graphics. The presentation is on April 11th. The author's version has been published on 31st of March 2022.