### Table 6. The diffusion tensor.

1973

### Table 3: Maximum value of the discrete solution for different diffusion tensors and in- terpolation techniques.

"... In PAGE 19: ...xes. The solution profiles are shown on Fig. 12. Maximum values of the discrete so- lutions are collected in Table3 . The inverse distance weighting interpolation method reduces overshoots and makes the scheme more robust.... ..."

### Table 1 Diffusion equations used in image processing. The general form of the equations is

1999

"... In PAGE 2: ... JPEG has a characteristic blocking-artefact (Figures 1,2,3 and 6). PDEs of Table1 were tested as perceptually adaptive filters for compression artefact reduction in [8]. The adequate perceptually adaptive filter fell out to be the PMC-AD, since it suppresses noise while performing shape enhancement.... ..."

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### Table 1: Classi cation of diffusion tensor anisotropy.

"... In PAGE 1: ... The relative differences be- tween the eigenvalues are related to the anisotropy of the diffusion. Three basic types of anisotropy are usually considered in the liter- ature (see Table1 ). A thorough discussion of diffusion tensors and other derived quantities can be found in [8, 16].... ..."

### Table 1 Performance of diffusion tensor registration according to intensity information

"... In PAGE 8: ... The results of this evaluation are displayed in Fig. 3 and summarized in Table1 . When performing registration of artificially deformed data sets, TC showed significantly increased performance in EDIV, MSE, and OVL (P H11021 0.... ..."

### Table 1: Mapping of data parameters to visualization parameters for diffusion tensor example.

"... In PAGE 5: ... We built the visualization in four layers that are illustrated in Figs 9 and 10. Table1 summarizes the mapping of data values to image contents. The layers are discussed individually in the following paragraphs.... ..."

### Table 1. The Perpendicular and Parallel Tensor Components for Translation and Rotation of Ellipsoids.

"... In PAGE 5: ... DttH14067 H11005 1 a GH20851 pH20852H208492 H11002 p2H20850 H11002 1 1 H11002 p2 (13a) DttH11036 H11005 1 2a GH20851 pH20852H208492 H11002 3p2H20850 H11001 1 1 H11002 p2 (13b) DrrH14067 H11005 1 a3p2 3H208491 H11002 p2GH20851 pH20852H20850 2H208491 H11002 p2H20850 (13c) DrrH11036 H11005 1 a3 3H20849GH20851 pH20852H208492 H11002 p2H20850 H11002 1H20850 2H208491 H11002 p4H20850 (13d) GH20851 pH20852 H11005 logH208751 H11001 H208811 H11002 p2 p H20876H20882H208811 H11002 p2, for prolate ellipsoids, p H11021 1 (13e) GH20851 pH20852 H11005 ArcTanH20851H20881p2 H11002 1H20852/H20881p2 H11002 1, for oblate ellipsoids, p H11022 1. (13f) Table1 presents the computation of the parallel and perpen- dicular components of the translational and rotational diffusion tensors for both prolate and oblate spheroids as a function of axial ratio. The quantities in Table 1 are the result of extrapolations to infinite N on the basis of triangulations performed with Math- ematica.... In PAGE 5: ... (13f) Table 1 presents the computation of the parallel and perpen- dicular components of the translational and rotational diffusion tensors for both prolate and oblate spheroids as a function of axial ratio. The quantities in Table1 are the result of extrapolations to infinite N on the basis of triangulations performed with Math- ematica. Figure 3, shows sample triangulations for an oblate and a prolate spheroid, while Figure 4 shows a typical extrapolation for one of the tensor properties, along with statistical information for the least squares fit.... In PAGE 5: ...ery fine tip of the needle. The error is barely over 0.1%, even in this worst case. The data in Table1 and Figure 4 show that, with sufficient precision, the discretization error can indeed be eliminated. The numerical results are essentially exact (with one exception) with errors in the fifth decimal place (0.... In PAGE 7: ... The Area Correction: Motivation It is fairly obvious that the tessellation of the surface yields an area smaller than the true surface area of the ellipsoid, leading to less friction: this is the shape and area error. The data of Table1 show that this error can also be essentially eliminated with the area correction, even with a finite discretization. The area correction is a nonuniform scaling of the super G matrix elements, and is based on the area dependence of the exact integration of the Oseen tensor over a triangle.... In PAGE 8: ...as a tetrahedron. The important realization is that the area correc- tion, implemented as described below, avoids this problem com- pletely and yields extremely accurate transport properties (includ- ing the intrinsic viscosity, and for polygonal shapes), as shown for the ellipsoids in Table1 , above. Other Errors The solution of the system of eq.... ..."