## CABIOS COMMUNICATION

### BibTeX

@MISC{_cabioscommunication,

author = {},

title = {CABIOS COMMUNICATION},

year = {}

}

### OpenURL

### Abstract

Image and volume data rotation with 1- and 3pass algorithms Three different implementations of the 3-pass algorithm of image and volume data rotation are illustrated and discussed. The three protocols use interpolation in real domain, with a peculiar implementation of the Shannon reconstruction, or phase shifts in Fourier domain. Accuracy and speed of the three methods are compared with corresponding values obtained with a 1-pass method. The results indicate that for low or moderate accuracy, 1-pass is more convenient than 3-pass rotation for both accuracy and speed. Very accurate rotations can be obtained in reasonable time if all steps of 3-pass rotation are performed in the Fourier domain. The computer processing of large arrays of experimental data involves two conflicting aspects: computing time and accuracy. Rotation and projections of large images or of volume data are typical tasks in which the two aspects are to be carefully balanced. For this reason, multi-step algorithms (Catmull and Smith, 1980; Paeth, 1986) to perform rotations in a seemingly fast and accurate way have been welcomed with enthusiasm (Wolberg, 1990), and raise continuing interest (see, for example, Unser et al., 1995). In this report, we present our experience with methods for the rotation of images and volume data, with 1- and 3-pass algorithms. It is worth recalling some tasks which require two- (2D) and three-dimensional (3D) functions to be accurately rotated stepwise to obtain sets of projections; typical examples are the computation of sinograms for the angular reconstitution method (van Heel, 1987) or for checking reconstruction algorithms (Bellon and Lanzavecchia, 1995). Projections of preliminary 3D reconstructions are used to improve tomographic results (Gilbert, 1972; Harauz and Ottensmeyer, 1984) or to obtain a sampled 3D Radon transform (Radermacher, 1994). Another field requiring rotations of volume data is multimodal imaging, a frontier in clinical diagnosis. Multimodal information is obtained by merging the results of X-ray, MR and emission tomography (Meyer et al., 1995; van den Elsen Diparlimento di Chimica Slrutturale e Slereochtmica Inorganica,

### Citations

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(Show Context)
Citation Context ...e to be carefully balanced. For this reason, multi-step algorithms (Catmull and Smith, 1980; Paeth, 1986) to perform rotations in a seemingly fast and accurate way have been welcomed with enthusiasm (=-=Wolberg, 1990-=-), and raise continuing interest (see, for example, Unser et al., 1995). In this report, we present our experience with methods for the rotation of images and volume data, with 1- and 3-pass algorithm... |

279 | Cubic convolution interpolation for digital image processing
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(Show Context)
Citation Context ... s per projection. The results of the present study show that 3-pass rotation is not convenient if low or moderate accuracy is sought. This conclusion can be extended to the use of cubic convolution (=-=Keys, 1981-=-) and of splines encompassing small numbers of samples (Danielsson and Hammerin, 1992). High accuracy can be obtained with 3-pass methods using either wide interpolation windows or shifts carried out ... |

51 |
3-D transformations of images in scanline order
- Catmull, Smith
- 1980
(Show Context)
Citation Context ...omputing time and accuracy. Rotation and projections of large images or of volume data are typical tasks in which the two aspects are to be carefully balanced. For this reason, multi-step algorithms (=-=Catmull and Smith, 1980-=-; Paeth, 1986) to perform rotations in a seemingly fast and accurate way have been welcomed with enthusiasm (Wolberg, 1990), and raise continuing interest (see, for example, Unser et al., 1995). In th... |

48 |
Iterative methods for the three-dimensional reconstruction of an object from projections
- Gilbert
- 1972
(Show Context)
Citation Context ...econstitution method (van Heel, 1987) or for checking reconstruction algorithms (Bellon and Lanzavecchia, 1995). Projections of preliminary 3D reconstructions are used to improve tomographic results (=-=Gilbert, 1972-=-; Harauz and Ottensmeyer, 1984) or to obtain a sampled 3D Radon transform (Radermacher, 1994). Another field requiring rotations of volume data is multimodal imaging, a frontier in clinical diagnosis.... |

47 | Angular reconstitution – a posteriori assignment of projection directions for 3-D reconstruction - heel - 1987 |

44 |
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(Show Context)
Citation Context ...s (Catmull and Smith, 1980; Paeth, 1986) to perform rotations in a seemingly fast and accurate way have been welcomed with enthusiasm (Wolberg, 1990), and raise continuing interest (see, for example, =-=Unser et al., 1995-=-). In this report, we present our experience with methods for the rotation of images and volume data, with 1- and 3-pass algorithms. It is worth recalling some tasks which require two- (2D) and three-... |

25 | Viergever, “Automatic registration of CT and MR brain images using correlation of geometrical features - Elsen, Maintz, et al. - 1995 |

22 |
Three-dimensional reconstruction from random projections: Orientational alignment via Radon transforms
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(Show Context)
Citation Context ...and Lanzavecchia, 1995). Projections of preliminary 3D reconstructions are used to improve tomographic results (Gilbert, 1972; Harauz and Ottensmeyer, 1984) or to obtain a sampled 3D Radon transform (=-=Radermacher, 1994-=-). Another field requiring rotations of volume data is multimodal imaging, a frontier in clinical diagnosis. Multimodal information is obtained by merging the results of X-ray, MR and emission tomogra... |

12 |
High-accuracy rotation of images
- Danielsson, Hammerin
- 1992
(Show Context)
Citation Context ...ss rotation is not convenient if low or moderate accuracy is sought. This conclusion can be extended to the use of cubic convolution (Keys, 1981) and of splines encompassing small numbers of samples (=-=Danielsson and Hammerin, 1992-=-). High accuracy can be obtained with 3-pass methods using either wide interpolation windows or shifts carried out in Fourier domain. From this point of view, the Paeth algorithm may become convenient... |

11 |
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(Show Context)
Citation Context ...g and, in all three steps, interpolation in real domain. In the second version, still with lateral padding, the effect of Sv is obtained by a phase delay in Fourier domain or 'Fourier interpolation' (=-=Fraser, 1989-=-). A third version, suitable for images enclosed in a circle with r = 0.9 x rmax, uses Fourier interpolation in all steps. Interpolations in real domain are carried out with the 'moving window Shannon... |

8 |
Three-dimensional structure determination by electron microscopy, p. 127–186
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(Show Context)
Citation Context ...nterpolations yield the highest accuracy. We use this type of process to rotate volume data around two or three axes. For instance, to obtain projections with conical tilt geometry (see, for example, =-=Hoppe and Hegerl, 1980-=-), the data need to be rotated around two axes; on the same computer used for all tests reported here, 128 conical Image and volume data rotation projections of an array of 64 3 voxels are obtained in... |

7 |
A Fast Algorithm for General Raster Rotation, Graphics Gems
- Paeth
- 1990
(Show Context)
Citation Context ...y. Rotation and projections of large images or of volume data are typical tasks in which the two aspects are to be carefully balanced. For this reason, multi-step algorithms (Catmull and Smith, 1980; =-=Paeth, 1986-=-) to perform rotations in a seemingly fast and accurate way have been welcomed with enthusiasm (Wolberg, 1990), and raise continuing interest (see, for example, Unser et al., 1995). In this report, we... |

5 | Avoidance of additional aliasing in multipass image rotations - Fraser, RA - 1994 |

5 |
Direct Three-Dimensional Reconstruction of Macromolecular Complexes from Electron Micrographs," Ultramicroscopy 12,309
- Harauz, Ottensmeyer
- 1984
(Show Context)
Citation Context ...ethod (van Heel, 1987) or for checking reconstruction algorithms (Bellon and Lanzavecchia, 1995). Projections of preliminary 3D reconstructions are used to improve tomographic results (Gilbert, 1972; =-=Harauz and Ottensmeyer, 1984-=-) or to obtain a sampled 3D Radon transform (Radermacher, 1994). Another field requiring rotations of volume data is multimodal imaging, a frontier in clinical diagnosis. Multimodal information is obt... |

4 |
A bevy of novel interpolating kernels for the Shannon reconstruction of highbandpass images
- Lanzavecchia, Bellon
- 1995
(Show Context)
Citation Context ...ormed in the Fourier domain; this rotation does not require a second buffer, (d) All three steps are done in the Fourier domain. (Lanzavecchia and Bellon, 1994) and using novel interpolating kernels (=-=Lanzavecchia and Bellon, 1995-=-) which make it possible to tailor the interpolation for the desired band-pass (in the low-pass sense). The value reconstructed in a point re [0, JV], *JJ(r), is obtained as the discrete convolution o... |

3 |
Two-dimensional resampling of line scan imagery by one-dimensional processing,” Photogrammetric Eng
- Friedman
- 1981
(Show Context)
Citation Context ...e convenient since it cuts away two small slices in the first shift. To avoid this, the image should be confined within a circular area with r = 0-9 x ''max or could be padded with two lateral bands (=-=Friedman, 1981-=-). Images are most often sampled in rasters 2" x 2" pixels wide, suitable for filtering and correlation analysis; lateral bands about 2"~* pixels wide are convenient. We have implemented Paeth's metho... |

2 | A fast algorithm for transposing large multidimensional image data sets, Ultramicroscopy 38 - Heel - 1991 |

1 |
A direct Fourier method (DFM) fox X-ray tomographic reconstructions and the accurate simulation of sinograms
- Bellon, Lanzavecchia
- 1995
(Show Context)
Citation Context ...ely rotated stepwise to obtain sets of projections; typical examples are the computation of sinograms for the angular reconstitution method (van Heel, 1987) or for checking reconstruction algorithms (=-=Bellon and Lanzavecchia, 1995-=-). Projections of preliminary 3D reconstructions are used to improve tomographic results (Gilbert, 1972; Harauz and Ottensmeyer, 1984) or to obtain a sampled 3D Radon transform (Radermacher, 1994). An... |

1 |
A moving window Shannon reconstruction for image interpolation
- Lanzavecchia, Bellon
- 1994
(Show Context)
Citation Context ...rforming the second pass, (c) Same as in (b) with the second pass performed in the Fourier domain; this rotation does not require a second buffer, (d) All three steps are done in the Fourier domain. (=-=Lanzavecchia and Bellon, 1994-=-) and using novel interpolating kernels (Lanzavecchia and Bellon, 1995) which make it possible to tailor the interpolation for the desired band-pass (in the low-pass sense). The value reconstructed in... |

1 | FT3D: Three dimensional Fourier analysis on small Unix workstation for E.M. and tomographic studies - S, Tosoni - 1993 |

1 | Simultaneous usage of homologous points, lines, and planes for optimal, 3-D linear registration of multimodality imaging data - R, A, et al. - 1995 |

1 | A rotation method for raster image using skew transformation - Tosoni, TanakaA, et al. - 1986 |