Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Display of Surfaces from Volume Data
IEEE Computer Graphics and Applications
A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Footprint evaluation for volume rendering
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
A family of polynomial spline wavelet transforms
Signal Processing
An introduction to wavelets
Frequency domain volume rendering
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
View interpolation for image synthesis
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
ACM Transactions on Graphics (TOG)
Fast volume rendering using a shear-warp factorization of the viewing transformation
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Wavelets and subband coding
Introduction to volume rendering
Introduction to volume rendering
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
The mathematics of computerized tomography
The mathematics of computerized tomography
The wavelet X-ray transform
Frequency domain volume rendering by the wavelet X-ray transform
IEEE Transactions on Image Processing
Comparison of morphological pyramids for multiresolution MIP volume rendering
VISSYM '02 Proceedings of the symposium on Data Visualisation 2002
Accelerating Fourier volume rendering by polar coordinate data representation
Computer Methods and Programs in Biomedicine
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This paper describes an extension to Fourier-wavelet volume rendering (FWVR), which is a Fourier domain implementation of the wavelet X-ray transform. This transform combines integration along the line of sight with a simultaneous 2-D wavelet transform in the view plane perpendicular to this line. During user interaction, only low resolution images are computed based on wavelet approximation coefficients. When user interaction ceases, the images are refined incrementally with the wavelet detail coefficients. The extension proposed in this paper is similar to a technique called view interpolation, which originates from the field of computer graphics. View interpolation is used to speed up rendering of complex scenes by precomputing images from a number of selected viewpoints. For intermediate viewpoints, rendering is performed by interpolating the precomputed images. In this paper, we show that for FWVR the speed of rendering low resolution images is increased by interpolation of precomputed sets of wavelet approximation coefficients in the Fourier domain. The differences with traditional view interpolation are that (i) interpolation is performed on the wavelet approximation coefficients in the Fourier domain and not on images, and (ii) interpolation is performed during user interaction only. When interaction ceases, ordinary FWVR progressively renders an image at high quality. Medical CT data are used to assess the accuracy and performance of the method. We use regular angular sampling of spherical coordinates which determine the viewing direction. The results show that angle increments as large as 10 degrees result in only a small degradation of image quality.