Frequency domain volume rendering by the wavelet X-ray transform

Michel A. Westenberg, Jos B.T.M. Roerdink

Research output: Contribution to journalArticleAcademicpeer-review

32 Citations (Scopus)
388 Downloads (Pure)


We describe a wavelet-based X-ray rendering method in the frequency domain with a smaller time complexity than wavelet splatting. Standard Fourier volume rendering is summarized and interpolation and accuracy issues are briefly discussed. We review the implementation of the fast wavelet transform in the frequency domain. The wavelet X-ray transform is derived, and the corresponding Fourier-wavelet volume rendering algorithm (FWVR) is introduced. FWVR uses Haar or B-spline wavelets and linear or cubic spline interpolation. Various combinations are tested and compared with wavelet splatting (WS). We use medical MR and CT scan data, as well as a 3-D analytical phantom to assess the accuracy, time complexity, and memory cost of both FWVR and WS. The differences between both methods are enumerated.
Original languageEnglish
Pages (from-to)1249-1261
Number of pages13
JournalIeee transactions on image processing
Issue number7
Publication statusPublished - Jul-2000


  • wavelet X-ray transform
  • wavelet splatting
  • Fourier-wavelet volume rendering
  • Fourier volume rendering

Cite this