Fourier volume rendering

In computer graphics we have traditionally rendered images of data sets specified spatially, Here, we present a volume rendering technique that operates on a frequency domain representation of the data set and that efficiently generates line integral projections of the spatial data it represents, The motivation for this approach is that the Fourier Projection-Slice Theorem allows us to compute 2-D projections of 3-D data seta using only a 2-D slice of the data in the frequency domain. In general, these “X-ray-like” images can be rendered at a significantly lower computational cost than images generated by current volume rendering techniques, Additionally, assurances of image accuracy can he made.

[1]  E. O. Brigham,et al.  The Fast Fourier Transform , 1967, IEEE Transactions on Systems, Man, and Cybernetics.

[2]  R. Bracewell,et al.  Fast two-dimensional Hartley transform , 1986, Proceedings of the IEEE.

[3]  M. Levoy,et al.  Fast volume rendering using a shear-warp factorization of the viewing transformation , 1994, SIGGRAPH.

[4]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[5]  Pat Hanrahan,et al.  Volume Rendering , 2020, Definitions.

[6]  P. Hanrahan.  Three-pass affine transforms for volume rendering , 1990, VVS.

[7]  Craig Upson,et al.  V-buffer: visible volume rendering , 1988, SIGGRAPH.

[8]  Arie E. Kaufman,et al.  Non-Existence of the Wavelet Slice-Projection Theorem , 1994 .

[9]  R. M. Mersereau,et al.  Digital reconstruction of multidimensional signals from their projections , 1974 .

[10]  Arie Kaufman,et al.  Volume Visualization (Tutorial) , 1991 .

[11]  D. Kocur.  Semisystolic implementation of second-order Volterra digital filters based on recurrence algorithm of Volterra filtering , 1989 .

[12]  Brian K. Rutt,et al.  Fast reprojection of volume data , 1990, [1990] Proceedings of the First Conference on Visualization in Biomedical Computing.

[13]  Ronald N. Bracewell,et al.  The Fourier Transform and Its Applications , 1966 .

[14]  Stephen A. Dyer,et al.  Digital signal processing , 2018, 8th International Multitopic Conference, 2004. Proceedings of INMIC 2004..

[15]  John E. Howland,et al.  Computer graphics , 1990, IEEE Potentials.

[16]  P. E. Anuta,et al.  Spatial Registration of Multispectral and Multitemporal Digital Imagery Using Fast Fourier Transform Techniques , 1970 .

[17]  Cornelis H. Slump,et al.  A multi-ASIC real-time implementation of the two dimensional affine transform with a bilinear interpolation scheme , 1995, J. VLSI Signal Process..

[18]  Marc Levoy,et al.  Display of surfaces from volume data , 1988, IEEE Computer Graphics and Applications.

[19]  J. A. Parker,et al.  Comparison of Interpolating Methods for Image Resampling , 1983, IEEE Transactions on Medical Imaging.

[20]  M. R. Civanlar,et al.  Optimal pulse shape design using projections onto convex sets , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[21]  Jorge Herbert de Lira,et al.  Two-Dimensional Signal and Image Processing , 1989 .

[22]  C. H. Paik,et al.  Fast Hartley transforms for image processing. , 1988, IEEE transactions on medical imaging.

[23]  E. Maeland.  On the comparison of interpolation methods. , 1988, IEEE transactions on medical imaging.

[24]  SabellaPaolo.  A rendering algorithm for visualizing 3D scalar fields , 1988 .

[25]  P. Hanrahan.  Three-pass affine transforms for volume rendering , 1990, VVS.

[26]  Lee Westover,et al.  Footprint evaluation for volume rendering , 1990, SIGGRAPH.

[27]  A. Papoulis.  A new algorithm in spectral analysis and band-limited extrapolation. , 1975 .

[28]  M. Ekstrom,et al.  Multidimensional signal processing , 1982 .

[29]  M. Cahtwiught,et al.  Fourier Methods for Mathematicians Scientists and Engineers , 1990 .

[30]  M. F.,et al.  Bibliography , 1985, Experimental Gerontology.

[31]  Lee Westover,et al.  Interactive volume rendering , 1989, VVS '89.

[32]  Turner Whitted,et al.  An improved illumination model for shaded display , 1979, CACM.

[33]  William E. Lorensen,et al.  Marching cubes: A high resolution 3D surface construction algorithm , 1987, SIGGRAPH.

[34]  Paolo Sabella,et al.  A rendering algorithm for visualizing 3D scalar fields , 1988, SIGGRAPH.

[35]  Ronald N. Bracewell.  Assessing the Hartley transform , 1990, IEEE Trans. Acoust. Speech Signal Process..

[36]  Marc Levoy,et al.  Frequency domain volume rendering , 1993, SIGGRAPH.

[37]  Mark Cartwright.  Fourier Methods for Mathematicians, Scientists and Engineers , 1990 .

[38]  A.K. Krishnamurthy,et al.  Multidimensional digital signal processing , 1985, Proceedings of the IEEE.

[39]  Dekun Yang,et al.  New fast algorithm to compute two-dimensional discrete Hartley transform , 1989 .