### Table 1. Performance of approximate geodesic algorithm

"... In PAGE 6: ...4GHz workstation with 4GB RAM. For a sherd mesh with 17K triangles, our algorithm takes 16 seconds on the Pentium IV and 14 seconds on the Xeon as seen in Table1 . The number of extra vertices and edges, and its impact on performance is also reported.... ..."

### Table 1: Comparison of the methods for calculating bounding spheres on random points using -search and centroid-farthest-point method.

1997

"... In PAGE 6: ... EXPERIMENTAL RESULTS In this section, we give our empirical test results. First, we compare the spheres obtained from our approxi- mation algorithm and the sphere resulting from using the centroid of the data as the center and distance of this center to the farthest point as the radius ( Table1 , Figure 7). Then, we look at the similarity searches performance of the SS+-tree on uniform point data comparing the e ect of using di erent bounding envelopes for the nodes.... In PAGE 6: ... Lastly, we compare the performance of the SS+-tree on the eigenface data.22 The comparison between the -search and the centroid-farthest point method to calculate the bounding spheres of 10 and 100 random points (for 100 trials each) ( Table1 and Figure 7 respectively) suggest that the advantage of using a smaller bounding sphere will be more evident for high-dimensional space. Although the ratio between the radius of the spheres produced by the search and centroid-farthest-point method (r-ratio) is not large, the ratio between volumes (V -ratio) can be quite signi cant in a high dimensional space.... ..."

Cited by 14

### Table 1: Balancing geodesics. This table shows the balancing of the spectral contribu- tions from the twisted geodesics in Tetra and Didi. Here l is length, and wl the total spectral contribution (weight) of geodesics of length l, measured in units of the spectral contribution of a primitive half-twisting geodesic of length l. The point of this table is to demonstrate that wl is the same for Tetra and Didi. For geodesics of a speci c kind, n tells the number of geodesics; t the twist (either 1 4 or 1 2 ); k the imprimitivity exponent; and w the aggregate spectral weight for geodesics of this kind. An individual geodesic with imprimitivity exponent k has weight 1=k if it is half-twisting, and 2=k if it is quarter-twisting. Weights do not depend on the handedness of the twist, so we do not distinguish between 1=4{twisting and 3=4{twisting geodesics.

in T

2004

"... In PAGE 9: ... Weights do not depend on the handedness of the twist, so we do not distinguish between 1=4{twisting and 3=4{twisting geodesics. The relevant computations are indicated in Table1 . Here we will explain in- formally what lies behind the computations in the table.... ..."

### Table 2: Geodesic distances between two sets of cluster cen- ters and modified Hausdorff distances of matching points.

in shape

"... In PAGE 5: ... It is easy to see that when the number of clusters increases, the matching improves as the modified Hausdorff distance decreases. In the third column in Table2 , we list the geodesic dis- tances between the two sets of cluster centers after pair- wise warping and clustering all the pair of corpus callo- sum point sets. Using the cluster centers as landmarks, a diffeomorphic mapping of the space is induced.... ..."

### Table 2. Closest and farthest points for the transformed domain.

### Table 1. Closest and Farthest Points for the Transformed Domain.

### Table 1: Approximations ^ for a sampling of and d values.

2005

"... In PAGE 10: ...3 of the Appendix provides such an assessment by comparing performances over di erent slices of the d- plane and over a range of r values. Below we simply compare the accuracies at a scattering of points on this plane via Table1 which shows the actual numerical values of that the three approximations (4.... In PAGE 34: ... However, such an assessment is di cult to illustrate through 2- dimensional plots. To supplement Table1 , which showed how the three approximations behave on a sampling of points from the ( ; d) plane, in this section we present experimental results on some slices of this plane, where we either keep d xed and vary , or we keep xed and vary d. For all our evaluations, the r values were computed using (A.... ..."

Cited by 19

### Table 6: Experimental and approximate theoretical values for the location of the 50% Hamiltonian point for Degreebound graphs of various sizes.

1998

"... In PAGE 20: ... A larger variance in hardness was observed with the Hamiltonian graphs. Table6 shows the distribution with respect to the number of search nodes required. Unlike Gn;m and Degreebound graphs, these graphs could not be solved in only n search nodes.... ..."

Cited by 16

### Table 3. Retinal code of the homotopic dilation (left, the other directions are deduced by rotation), and of the geodesic SKIZ (right).

2002

"... In PAGE 4: ... This procedure, that needs 3 bits of memory too, will be used in the next section. The classical approximation of the SKIZ by the dual homotopic kernel is computed thanks to the relaxation of the homotopic dilation operator, shown on Table3 (left), that uses 3 bits of memory. The geodesic SKIZ is simply obtained by computing a logical and with the image of reference, so it uses 4... ..."

Cited by 1