Frequency domain volume rendering by the wavelet X-ray transform

Author

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

Author_Institution

Dept. of Math. & Comput. Sci., Groningen Univ., Netherlands

Volume

9

Issue

7

fYear

2000

fDate

7/1/2000 12:00:00 AM

Firstpage

1249

Lastpage

1261

Abstract

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

Keywords

Fourier analysis; Haar transforms; biomedical MRI; computational complexity; computerised tomography; frequency-domain analysis; interpolation; medical image processing; rendering (computer graphics); splines (mathematics); wavelet transforms; 3-D analytical phantom; B-spline wavelet; CT scan imaging; FWVR; Fourier-wavelet volume rendering algorithm; Haar wavelet; MR imaging; accuracy; cubic spline interpolation; fast wavelet transform; frequency domain volume rendering; interpolation; linear spline interpolation; memory cost; standard Fourier volume rendering; time complexity; wavelet X-ray transform; Computed tomography; Costs; Fourier transforms; Frequency domain analysis; Imaging phantoms; Interpolation; Spline; Testing; Wavelet domain; Wavelet transforms;

fLanguage

English

Journal_Title

Image Processing, IEEE Transactions on

Publisher

ieee

ISSN

1057-7149

Type

jour

DOI

10.1109/83.847837

Filename

847837