"... In PAGE 3: ... a55 a138a109a143a139a140a91a145 is the resulting average code-length for the two coding methods. From the results of Table2 it is clear that the canonical Huffman coding of lattice codevectors is, as it was expected, the best method in terms of average code-length. 4.... ..."

"... In PAGE 16: ...III-850 PC using Matlab 6.0. In our first example, we consider a mixture of two Laplacian signals. The results of the different algorithms are shown in Table2... ..."

"... In PAGE 4: ... Solid lines in Figure 3, 6 and 9 depict the first 100 of 1000 tests. Data in Table1 were derived using graphs of size BEBCBC A2 BEBCBC vertices with 1000 experiments. The numbers of levels needed to reduce the graph at the base level (level 0) to a graph consisting of a single vertex (top of the pyramid) are given in Figure 3 (a),(b).... In PAGE 4: ... Poor reduction factors are likely, as can be seen in Figure 3, especially when the images are large. This is due to the evolution of larger and larger variations between the vertex degrees in the contracted graphs ( Table1 ). The absolute maximum in-degree was 148.... In PAGE 8: ... For the case of the graph with size BEBCBC A2 BEBCBC vertices, MIDES needed 13 levels in comparison to 15 levels in the worst case of MIES. The number of iterations needed to complete the maximum independent set was comparable with the one of MIS ( Table1 ). The MIDES algorithm shows a better reduction... ..."

"... In PAGE 12: ...5 and Tables 1, 2, and 3. The statistics of vertex degree 3 is given in Table1 . These parameters are of importance because they are directly related to the memory costs of the representation of graph [Jol02, Jol01].... In PAGE 13: ... Poor reduction factors are likely, as can be seen in Figure 9, especially when the images are large. This is due to the evolution of larger and larger variations between the vertex degrees in the contracted graphs ( Table1 , a0 a14a9a27a30a29a2a1 a16 a10 a4a3 a5 a3 a6a5a8a7 and Figure 8). The abso- lute maximum indegree was 148.... In PAGE 14: ...Table1 ). To summarize the reduction factor were always under the theoretical upper bound of a2 a3 a5 .... In PAGE 14: ... We see that the reduction factor is higher than a2a4a3a6a5 (dashed line) even in the worst case. Also the maximum indegree of the vertices is much smaller (a0 a14a26a27a30a29a13a1 a16 a10 a4 a2 a3 a2 a8a7 ) than for MIS (a0 a14a26a27a30a29a13a1 a16 a10 a3 a5 a3 a6a5a8a7 , Table1 ). For MIES and MIDES we have not encountered nodes with large neighborhood as for MIS.... In PAGE 14: ... For the case of the graph with size a2 a5 a5 a2 a2 a5 a5 vertices, MIDES needed 13 levels in comparison to 15 levels in the worst case of MIES. The number of iterations needed to complete the maximum independent set was comparable with the one of MIS ( Table1 ). The MIDES algorithm shows a better reduction factor than MIES, as can be seen in Figure 11 and Table 3 (a0 a14 a7a6 a16 a11a10 a2a4a3a9a5 a2 ).... In PAGE 14: ...4 Experiments with D3P The Figure 12 gives the reduction factors (a6 ) for vertices, (a31 ) for edges and (a8 ) for faces. The experiments show that poor reduction factors are likely, because of the large degree of vertices (a0 a14a26a27a30a29a13a1 a16 a10 a69a18 a2 a2 a3 a9a7 a2 , Table1 ). Also the height of the pyramid is related to the complexity of the vertices, which is why the D3P gives the highest pyramids (a0 a14a28a56 a31a49a25a26a10a32a56 a36 a16 a37a10 a11a13a11 a3 a2 a1a0 ).... In PAGE 19: ...Discussion of Results In Table1 a more extensive comparison is made using 1000 graphs of size a2 a5 a5 a2 a2 a5 a5 . We extract three parameters, the maximum (max), the mean (mean) and the standard deviation (std) of the vertex degree for any graph in the contraction process.... In PAGE 19: ... This means that D3P better fit to the distribution of values associated with the vertices [Jol02, Jol01]. The last line in Table1 shows the vertex complexity on base level a57 a12 . Table 2 gives statistics about height of the image pyramid and about number of iteration (a1 a25a26a36a38a31 a1 a29a13a36a40a25 a8 a0 a48a6 ) to complete the maximal independent set.... ..."

"... In PAGE 12: ... These parameters are of importance because they are directly related to the memory costs of the representation of graph [Jol02, Jol01]. In Table2 the mean and standard deviation for height of the pyramid, and for the number of iteration for corrections are given. The mean and standard deviation of the decimation ratio for vertices and edges is given in Table 3.... In PAGE 19: ... The last line in Table 1 shows the vertex complexity on base level a57 a12 . Table2 gives statistics about height of the image pyramid and about number of iteration (a1 a25a26a36a38a31 a1 a29a13a36a40a25 a8 a0 a48a6 ) to complete the maximal independent set. Table 3 gives the statistics about the decimation ratios of vertices and edges.... ..."

"... In PAGE 16: ... The noise-free image needed in equation (26) was obtained by averaging 4 noisy images of the object. Table1 shows the experimentally computed and theoretically estimated standard deviations of di erent focus measures. We see that the two values are close thus verifying Equation (26).... In PAGE 16: ... The standard deviation of these 10 positions was the experimental ARMS error. The resulting values are shown in the last two columns of Table1 . We see that they are very close.... ..."