### TABLE 3. STEINER RATIOS OF VARIOUS POLYHEDRA WITH AN EXTRA CENTRAL POINT.

1995

Cited by 5

### Table 1. Behaviour of Taylor apos;s expansion of the cost function Order of expansion Triangulation 1 Triangulation 2 Triangulation 3 Triangulation 4

"... In PAGE 15: ...n Fig. 3 and Fig. 4. We give in Table1 the results of the computing of j(I + V ) obtained when using the Taylor apos;s expansion of j at the point I, which have to be compared with the ones obtained when computing directly j(I + V ) on the modi ed domain. Note that the nodal table is made of the components of the map I in an appropriate basis.... ..."

### Table 1 Comparison of MV with other triangulations.

"... In PAGE 12: ...ig. 4. The Delaunay triangulation, DEL, a locally optimal triangulation, FDD, and the globally optimal triangulation, MV, for two small point sets. Table1 compares triangulations and their quality. More speci cally, it compares each triangulation X 2fPL, DEL, FPD, FPN, FDD, FDN g with MV , the optimum triangulation.... ..."

### Table 4. Behaviour of Taylor apos;s series of the cost function with a bad triangulation Order of expansion Triangulation 2.3 Triangulation 2.4 Triangulation 2.5

"... In PAGE 19: ...249 We give in Table4 the results of the computing of j(I + V ) obtained when using Taylor apos;s expansion of j at the point I for these di erent perturbations, which have to be compared on the one hand with the direct computation of j(I + V ) on those perturbations with bad triangulation (triangulations 2.3, 2.... ..."

### Table 1: Batched 1-Steiner (B1S) statistics: the performance gures denote percent improvement over MST cost. Also given are statistics regarding the number of Steiner points produced, the number of rounds, and the number of Steiner points produced in each round.

1994

"... In PAGE 20: ... As is the convention in the Steiner approximation literature [27], we evaluate the performance of our method by comparing the cost of our solutions to the MST cost over the same inputs. Performance results are summarized in Table1 and are illustrated in Figures 14(a) through 14(c). B1S yields Steiner trees with cost averaging almost 11% less than the MST cost.... ..."

Cited by 35

### Table 2: Batched 1-Steiner statistics: the performance gures denote percent improvement over MST cost. Also given are statistics regarding the number of Steiner points produced, the number of rounds, the the number of Steiner points induced per round.

### Table 4-3: Finite element. Greedy triangulation. 83 control points and 27 check points.

1996

"... In PAGE 30: ... RMSE for 83 control points and 27 check points for polynomials or orders one to ten. Table4 -1 shows the RMSE for the control points. Higher order polynomials result in a lower RMSE, but not necessarily a better distortion model.... In PAGE 30: ... Higher order polynomials result in a lower RMSE, but not necessarily a better distortion model. This is not merely conjecture as shown by Table4 -2. The excursions which characterize polynomials are minimal with low order polynomials, but increase in magnitude as the polynomial order increases.... In PAGE 31: ...0 0.299 1.554 1.582 Table4 -1: Polynomial registration. 83 control points Polynomial RMSE -- Check Points Degree x y total 1 22.... In PAGE 31: ...0 10.323 68.148 68.925 Table4 -2: Polynomial registration. 27 check points.... In PAGE 32: ....3.2.1 Greedy Triangulation Table4 -3 shows the results from using the Greedy triangulation and three different grid resolutions. The most obvious result is surprising.... In PAGE 32: ... Another interesting observation is with respect to the gridding effect. It is quite evident if the grid is not dense enough as shown in Table4 -4. The transformed image will appear even less smooth than a standard piecewise linear model over triangles.... In PAGE 32: ... Table4... In PAGE 33: ....236 0.992 1.019 Table4 -5: Finite element.... In PAGE 33: ....681 1.787 5.010 Table4 -6: Finite element Delaunay triangulation. 83 control points and 27 check points.... In PAGE 33: ... An unexpected outcome from the gridding process is its potential usefulness for distortion diagnostics. The gridding effect, see Table4 -7, is highly local and given a large RMSE, indicative of the need to collect additional control points for linear piecewise warping. Table 4-8 lists the RMSEs using all of the ground control points.... In PAGE 33: ... The gridding effect, see Table 4-7, is highly local and given a large RMSE, indicative of the need to collect additional control points for linear piecewise warping. Table4 -8 lists the RMSEs using all of the ground control points. Finite Element RMSE -- Grid Points Grid x ytotal 30x30 1.... In PAGE 33: ....165 0.721 0.740 Table4... In PAGE 34: ....135 0.628 0.643 Table4 -8: Finite Element.... In PAGE 34: ...222 2.773 Table4 -9: Multiquadric method.... In PAGE 35: ...089 2.806 Table4 -10: MQ (no polynomial precision), MQ (linear precision) and TPS (linear precision by default). 83 control points and 27 check points.... ..."

Cited by 1

### Table 4-6: Finite element Delaunay triangulation. 83 control points and 27 check points.

1996

"... In PAGE 30: ... RMSE for 83 control points and 27 check points for polynomials or orders one to ten. Table4 -1 shows the RMSE for the control points. Higher order polynomials result in a lower RMSE, but not necessarily a better distortion model.... In PAGE 30: ... Higher order polynomials result in a lower RMSE, but not necessarily a better distortion model. This is not merely conjecture as shown by Table4 -2. The excursions which characterize polynomials are minimal with low order polynomials, but increase in magnitude as the polynomial order increases.... In PAGE 31: ...0 0.299 1.554 1.582 Table4 -1: Polynomial registration. 83 control points Polynomial RMSE -- Check Points Degree x y total 1 22.... In PAGE 31: ...0 10.323 68.148 68.925 Table4 -2: Polynomial registration. 27 check points.... In PAGE 32: ....3.2.1 Greedy Triangulation Table4 -3 shows the results from using the Greedy triangulation and three different grid resolutions. The most obvious result is surprising.... In PAGE 32: ... Another interesting observation is with respect to the gridding effect. It is quite evident if the grid is not dense enough as shown in Table4 -4. The transformed image will appear even less smooth than a standard piecewise linear model over triangles.... In PAGE 32: ...788 5.434 Table4 -3: Finite element.... In PAGE 32: ...139 1.177 Table4... In PAGE 33: ....236 0.992 1.019 Table4 -5: Finite element.... In PAGE 33: ... An unexpected outcome from the gridding process is its potential usefulness for distortion diagnostics. The gridding effect, see Table4 -7, is highly local and given a large RMSE, indicative of the need to collect additional control points for linear piecewise warping. Table 4-8 lists the RMSEs using all of the ground control points.... In PAGE 33: ... The gridding effect, see Table 4-7, is highly local and given a large RMSE, indicative of the need to collect additional control points for linear piecewise warping. Table4 -8 lists the RMSEs using all of the ground control points. Finite Element RMSE -- Grid Points Grid x ytotal 30x30 1.... In PAGE 33: ....165 0.721 0.740 Table4... In PAGE 34: ....135 0.628 0.643 Table4 -8: Finite Element.... In PAGE 34: ...222 2.773 Table4 -9: Multiquadric method.... In PAGE 35: ...089 2.806 Table4 -10: MQ (no polynomial precision), MQ (linear precision) and TPS (linear precision by default). 83 control points and 27 check points.... ..."

Cited by 1

### TABLE 2. STEINER RATIOS OF VARIOUS POLYHEDRA. We tried placing an extra central point inside these polyhedra:

1995

Cited by 5