A. Tanaka, M. Kameyama, S. Kazama, and O. Watanabe, "A rotation method for raster image using skew transformation," in IEEE Conference on Computer Vision and Pattern Recognition, pp. 272--277, 1986.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a massively parallel volume rendering algorithm on the Connection Machine. They use a shearing technique to transform and resample the volume such that the view rays are in effect parallel to one of the coordinate axes. The particular shearing technique used is based on pure shears [Paeth, 1986; Tanaka et al. 1986] as opposed to shear scale transforms [Hanrahan, 1990; Smith, 1987] The 4 decomposition of a single axis rotation into pure shear transformations is given by 0 B cos 0 sin sin cos 1 C A = 0 B 1 0 tan a 2 0 1 1 C A 0 B 1 0 sin 1 1 C A 0 B 1 ....

Tanaka, A., Kameyama, M., Kazama, S., and Watanabe, O. A Rotation Method for Raster Image Using Skew Transformations. In Proceedings IEEE Conference on Computer Vision and Pattern Recognition, pages 272--277, June 1986. 23

....for any associative (not necessarily commutative) operator , 5] Compositing ( is associative. Numerical integration is also associative. In the next section we further discuss the mapping and our generalizations from [15] 2. 1 Processor Assignment by Permutation Warp Paeth [8] Tanaka et al. [11], and Schroeder et al. 9] have used pure shear matrix decomposition of rotation to create efficient resampling algorithms. The technique is a refinement of multipass filtering where the transform is restricted to rotation. By not actually resampling data, and using the shears only to calculate ....

....being calculated are unique, but processors may receive more than one message because of virtualization. The density of messages across the network is the same if the slice and dice virtualization is used and communication remains efficient. 4 Time Quality Trade offs Multipass shears, 8] 9][11][12] and direct warping, Section 2 [15] are not equivalent. Because each resampling discards the prior data, a shear filtering approach has more resolution error and interpolation error than a comparable direct filter. After a shear, all that is stored is the new samples. We used two test ....

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Tanaka, A., M. Kaneyama, S. Kazama, and O. Watanabe. A Rotation Method For Raster Image Using Skew Transformation. In Proceedings IEEE Conference on Computer Vision and Pattern Recognition (June 1986), 272-277.

....the resampling, but also may cause a situation (called bottleneck) where a beam (a volume row) is first shrunk and then magnified so that the original beam can not be recovered. A three shear decomposition of a 2D image rotation was introduced independently by Paeth [8] and Tanaka et al. [13], expressed as: R 2D (ff) cos ff Gamma sin ff sin ff cos ff = 1 0 Gamma tan ff 2 1 1 sin ff 0 1 1 0 Gamma tan ff 2 1 (1) A 1D shear operation does not suffer from any bottleneck problems and its resampling is also much simpler. A straightforward extension of this method to 3D ....

A. Tanaka, M. Kameyama, S. Kazama, and O. Watanabe. A rotation method for raster image using skew transformation. Proc IEEE Conf on Computer Vision and Pattern Recognition, pages 272--277, June 1986.

....6.12 4.77 4.45 4.53 30 6.87 5.63 5.61 5.73 40 7.21 5.80 5.69 6.49 50 7.56 6.80 6.56 6.74 60 7.77 5.94 6.34 6.92 70 7.17 6.56 6.72 6.93 80 6.37 5.98 6.35 6.94 Table 1: Timings for various angles of image rotation for a 1024 Theta 768 pixel image pattern of data transfer. The algorithm in [4] was used, which partitions the rotation into three shears. The first two stages of the algorithm may be performed on the same processor but, for the transition from vertical to horizontal shear, it is necessary for each processor to make a one tomany data transfer. In fact, the number of messages ....

A. Tanaka, M. Kameyama, S. Kazama, and O. Watanabe. A Rotation Method for Raster Image Using Skew Transformation. In IEEE Conference on Computer Vision and Pattern Recognition, pages 272-- 277, 1986.

....the processor, is by a scanline algorithm. A scanline algorithm is one in which each step of the algorithm is confined to operations on scan or raster lines of an image. Scanline algorithms have been developed for DRAFT 3 affine transforms or warps [7] and in particular for image rotations [8, 9]. These algorithms are suitable for hardware implementation [10, 11] since they break the geometric transform into a number of simple repeatable operations which might be represented by components such as shift registers. Look Up Tables (LUTs) can be employed to avoid trigonometric calculations. ....

....including use of a Hermite interpolator. Finally, Section V provides a summary and draws some conclusions. II. Resampling a Scanline Algorithm Though it may be inconvenient for a hardware implementation by having more than two skews, the thrice skew image rotation algorithm introduced in [9] avoids rescaling 1 and provides an isomorphic function for all angles in the first quadrant. 2 The algorithm decomposes the rotation into a horizontal skew, followed by a vertical skew, followed by another horizontal skew: 1 Rescaling would run the danger of aliasing through undersampling. ....

A. Tanaka, M. Kameyama, S. Kazama, and O. Watanabe, "A rotation method for raster image using skew transformation," in IEEE Conference on Computer Vision and Pattern Recognition, pp. 272--277, 1986.

....p OS SS I J I B I B J 31 To calculate the discrete samples of requires reconstruction of at points , which do not in general lie at s samples. Quality versus cost trade offs have resulted in many approximations of reconstruction [BARR81] BENN84] CATM80] FRASE85] PAET86] SCHR91] SMIT87] [TANA86] [WEIM80] WEIN90] Image warping is done in a one pass transforms, direct warps, and multiple pass transforms, multipass warps. Direct warps and multipass warps may be performed by serial or parallel algorithms. Image warping has many applications in computer graphics and image processing. ....

.... and Overlapped Forwards J x y , I p I forward backward direct multipass multipass direct lookup table on the fly lookup table on the fly I) direction II) lookup tables III) filter type IV) restrictions direct Affine: Forward MCCMF (EREWF) Separable: SMIT87] Rotation: Rotation: [TANA86] Orthogonal: WEST90] direct multipass General poly fit: YOKO86] General: WOLB89] Texture Map: FEIB80] General: GOSH89] General: WEIN90] direct direct direct General: Backwards MCCMB (CREWB) WEIM80] PAET86] SCHR91] CATM80] DREB88] HANR90] linear scanline adjacent convolve nth order ....

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A. Tanaka, M. Kaneyama, S. Kazama, and O. Watanabe, "A Rotation Method For Raster Image Using Skew Transformation," Proceedings IEEE Conference on Computer Vision and Pattern Recognition (June 1986) pp. 272-277.

....function at each point, the program looks up the nearest precalculated value. A plot of the quantized cubic interpolation kernel is given in Figure 6.1. The figure shows the entire kernel for the 4 pixel region of support. 6.3. 1 Multiple pass Rotations Rotation by the three pass method of shears [104, 105] was also studied to determine its utility in parallel and sequential tomographic reconstruction. In the continuous domain, the three pass method realizes rotations exactly by shifting each row independently, followed by a shift of each column, and completed by another shift of each row. Equation ....

A. Tanaka, M. Kameyama, S. Kazama, and O. Watanabe, "A rotation method for raster image using skew transformation," in Proc IEEE Conf Comput Vision and Pattern Recognit, pp. 272--277, 1986.

....p p T p T p ( p T 1 p ( I J I x y , J x y , B I B J 2 To calculate requires a reconstruction of at point , because does not, in general, lie at one of s samples. Quality versus cost trade offs have resulted in many approximations of reconstruction [1] 3] 8] 14] 16] [17] [20] 21] A resampling step, or pass is a filtering operation. Image warping is performed by a single resampling, direct warps, and multiple resamplings, multipass warps. Direct warps and multipass warps may be implemented as serial or parallel algorithms. Image warping has many applications in ....

....allows dramatic improvements in algorithms such as coordinate calculations by differencing, efficient partitioning, and job assignment. Fig. 2 Warping Classification, with new algorithms: Backwards MCCMB and Forwards MCCMF Restricting 2D transforms to rotation allowed researchers [14] 16][17] to optimize by decomposing into multiple passes of two or three matrices. A nonscaling sequence of shears developed by [14] 17] is, EQ 1) A shear is a transform that operates on only one coordinate. Shears may scale (stretch or shrink axes) or not scale (distances are preserved) Nonscaling ....

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A. Tanaka, M. Kaneyama, S. Kazama, and O. Watanabe, "A Rotation Method For Raster Image Using Skew Transformation," in Proceedings IEEE Conference on Computer Vision and Pattern Recognition, June 1986, pp. 272-277.

....the present three shear decomposition approach generalizes to any linear transformations of unit determinant in any number of dimensions. 1 Introduction In two dimensions, a rotation can be expressed as a composition of three shears along two given orthogonal axes (see Paeth[5] and Tanaka et al.[8]) as illustrated below. R R R R S 1 Gamma S 2 Gamma S 3 Gamma Figure 1: Two dimensional rotation achieved by a succession of three shears. In three dimensions, rotations and shears form a much more complex picture; generalizations from two dimensions are not automatic. Since a ....

A. Tanaka, M. Kameyama, S. Kazama, and O. Watanabe, A rotation method for raster image using skew transformations, Proc. IEEE Conf. on Computer Vision and Pattern Recognition, pp 272--277, IEEE, 1986.

....for any associative (not necessarily commutative) operator , 16] 25] Compositing ( is associative. Numerical integration is also associative. FIGURE 4 Transforms and Communications in Permutation Warping for a Single Voxel 2. 1 Processor Assignment by Permutation Warp Paeth [24] Tanaka et al. [31], Schr der et al. 27] and we [35] have used pure shear matrix decomposition of rotation to create efficient resampling algorithms. A pure shear is a non scaling transform of a single coordinate. The technique is a refinement of multipass filtering where the transform is restricted to rotation. ....

....T ( 1 = T 12 . EQ 1) The other four equations are found by setting (EQ 2) The solution using s as given is , and . A special case is rotation, where , EQ 3) and by insertion and reduction by the half angle formula, and . This derivation shows how to calculate the result given in [24] [31]. The same approach is used for three dimensional equiareal transforms solving a system of ten equations with nine unknowns in (EQ 4) and (EQ 5) EQ 4) EQ 5) The system appears to be over constrained, but can in fact be solved. The symbolic solution from Mathematica (TM) 39] is, ....

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Tanaka, A., Kaneyama, M., Kazama, S., and Watanabe, O. A Rotation Method For Raster Image Using Skew Transformation. Proc. IEEE Conference on Computer Vision and Pattern Recognition. IEEE Computer Society, 1986, pp. 272-277.

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A. Tanaka, M. Kameyama, S. Kazama, and O. Watanabe, "A rotation method for raster image using skew transformation," in IEEE Conference on Computer Vision and Pattern Recognition, pp. 272--277, 1986.

No context found.

A. Tanaka, M. Kameyama, S. Kazama, O. Watanabe: "A Rotation Method for Raster Image Using Skew Transformation", Proceedings of the IEEE, 1986, pp. 272-277

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