### Table 2. Performance comparison between graph cuts and topol- ogy cuts with the same initialization and parameter values. Image Size Graph Cuts Topology Cuts

in Topology Cuts: A Novel Min-Cut/Max-Flow Algorithm for Topology Preserving Segmentation in N-D Images

"... In PAGE 8: ... Our al- gorithm gives a result (Figure 8 (c)) that faithfully conforms to the initialization, which is more meaningful than that of the standard graph cuts algorithm (Figure 8 (b)). Table2 shows the comparison between the graph cuts implementation [5] and our topology cuts algorithm3. 8.... ..."

### Table 1. Comparison of graph cut and progressive cut in speed

"... In PAGE 6: ... Another notable strength of the new algorithm is that it provides a faster visual feedback. Since the eroded graph is generally much smaller than the graph on the whole image, the computational cost in the optimization process is greatly reduced, as demonstrated by Table1 in Sec.... In PAGE 7: ...n Sec2.3.5, we have mentioned that the our algorithm will save much time than the existing graph cut methods [1,2], due to the eroded graph. To demonstrate this strength, we compare the time cost of our algorithm with that of existing graph cut method in Table1 , using Indian girl , man , pity dog , sleepy dog , bride , and little girl as the test images. The running time is tested on a PC of P4-3.... ..."

### Table 1: Comparative properties of the graph-cut functional minimization algorithms.

### Table 2: Graph cut timings for the flower garden sequence (all in minutes:seconds ). Note that in each case, the graph cut algorithm is iterated four times for convergence.

2001

"... In PAGE 24: ... Note that in each case, the graph cut algorithm is iterated four times for convergence. A table comparing the timings for hierarchical graph cuts with different extents of overloading is shown in Table2 . L-to-1 refers to a coarse level representing L original levels.... ..."

Cited by 64

### Table 1: Test graphs and cut sizes for partitioning in 2 and 64 parts. Number in brackets indicate run times in seconds.

1997

"... In PAGE 8: ... Please note that for partitioning in 64 parts, the methods of Chaco, Metis and PARTY are performed by recursive bisection. Table1 shows some characteristics of the graphs and the partitioning results. For graph lh, the total number of edges and the total number of edge weights are shown.... ..."

Cited by 20

### Table 2.1: Comparative properties of the graph-cut functional minimization

2004

### Table 3: Cutting plane for low density graphs

2002

Cited by 5

### Table 4: Cutting plane for medium density graphs

2002

Cited by 5

### Table 5: Cutting plane for high density graphs

2002

Cited by 5

### Table 6: Graph partitions of random graphs generated by cutting the hypercube and grid em-

"... In PAGE 16: ... We #0Cnd that the bisection widths for hypercube embeddings are about the same for all hyperplanes whereas for grid embeddings, the two partitions dividing the grid in half vertically and horizontally give the best partitions. Table6 shows how the Mob hypercube and grid embedding algorithms perform as graph- partitioning algorithms. The data for random graphs on the performance of the Mob graph- partitioning algorithm and the KL graph-partitioning algorithm is taken from our study of local search graph-partitioning heuristics in #5B19,21#5D.... In PAGE 17: ...Table6 by the percentage of all edges that cross the cut between A and B.We found that 16-to-1 grid and hypercube embeddings with our Mob-based heuristics produced bisection widths comparable to those for the Mob heuristic for graph-partitioning.... In PAGE 17: ... The performance of the Mob embedding algorithms interpreted as graph-partitioning algorithms is remarkable, considering that Mob is optimizing the #5Cwrong quot; cost function. While the data in Table6 cannot show conclusively how good the Mob embedding algorithms are, the existence of a better graph-embedding algorithm would also imply the existence of a better graph-partitioning algorithm. 3.... ..."