Verifying volume rendering using discretization error analysis

Tiago Etiene, Daniel Jönsson, Timo Ropinski, Carlos Scheidegger, João L D Comba, Luis Gustavo Nonato, Robert M. Kirby, Anders Ynnerman, Cláudio T. Silva

Research output: Contribution to journalArticlepeer-review


We propose an approach for verification of volume rendering correctness based on an analysis of the volume rendering integral, the basis of most DVR algorithms. With respect to the most common discretization of this continuous model (Riemann summation), we make assumptions about the impact of parameter changes on the rendered results and derive convergence curves describing the expected behavior. Specifically, we progressively refine the number of samples along the ray, the grid size, and the pixel size, and evaluate how the errors observed during refinement compare against the expected approximation errors. We derive the theoretical foundations of our verification approach, explain how to realize it in practice, and discuss its limitations. We also report the errors identified by our approach when applied to two publicly available volume rendering packages.

Original languageEnglish (US)
Article number6532282
Pages (from-to)140-154
Number of pages15
JournalIEEE Transactions on Visualization and Computer Graphics
Issue number1
StatePublished - Jan 2014


  • Discretization errors
  • testing
  • verifiable visualization
  • verification
  • volume rendering

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Computer Graphics and Computer-Aided Design


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