# Fast Equipartition of Complex 2D Shapes with Minimal Boundaries +
## 6 Experimental Evaluation
### Comparisons on LEMS and MPEG7 Datasets  
In the following, we present comparisons of the proposed and baseline methods on the normalized total intrinsic boundary length (\(NL\)) and in terms of computational efficiency.  
Table 2 shows the average \(NL\) for nine different values of \(N\in\{2,\ldots,10\}\) of _SEP-PSO FBC_, _SEP-FBC_, _SEP-RG_, and _SEP-ILS_ methods computed on MPEG7 and LEMS datasets. We find that _SEP-PSO FBC_ clearly outperforms the other methods in any dataset under \(NL\) and \(Pr(m/NL)\) metrics. It should be noted that _UPF-FBC_ is clearly the most computationally efficient method since it is about six, thirty, and sixty times faster than _SEP-RG_, _SEP-PSO FBC_, and _SEP-ILS_, respectively. _SEP-FBC_ also outperforms _SEP-RG_ and _SEP-ILS_ under the intrinsic boundary length. _SEP-RG_ outperforms _SEP-ILS_ under the intrinsic boundary length and computational cost. According to Table 2, in 89.2% and 87.9% of shapes for LEMS and MPEG7 datasets, respectively, the proposed methods clearly outperform, in terms of the intrinsic boundary length, the current methods from the literature (_SEP-RG_ and _SEP-ILS_). On average, the \(NL\) of the _SEP-PSO FBC_ is 7% and 7.4% lower compared to the corresponding \(NL\) of the top-performing method _SEP-RG_ from the literature on LEMS and MPEG7 datasets, respectively.  
Figure 12 shows the \(NL\) metric of the _SEP-PSO FBC_, _SEP-FBC_, _SEP-RG_, and _SEP-ILS_ methods computed on LEMS and MPEG7 datasets for different values of \(N\). We find that for any dataset and value of \(N\), _SEP-PSO FBC_ clearly outperforms the other methods. More specifically, _SEP-PSO FBC_ produces a lower \(NL\) than _SEP-PSO_ ranging from \([2.7\%,9\%]\) on the LEMS and MPEG7 datasets. _SEP-PSO FBC_ produces a lower \(NL\) than _SEP-RG_ ranging from \([3.5\%,12.5\%]\) on the LEMS and MPEG7 datasets. _SEP-ILS_ outperforms _SEP-RG_ and _SEP-ILS_ under any dataset and value of \(N\). Therefore, the results of the figure agree with the corresponding results of Table 2, showing that the top-performing method is the _SEP-PSO FBC_.  
Figure 13 shows the average \(AET\) (in secs) of the _SEP-PSO FBC_, _SEP-FBC_, _SEP-RG_, and _SEP-ILS_ methods computed on all images of LEMS and MPEG7 dataset for different  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & & **LEMS Dataset** & & & **MPEG7 Dataset** \\ \hline
**Methods** & **NL** & **Pr (m/NL)** & **AET** & **NL** & **Pr (m/NL)** & **AET** \\ \hline
**SEP-PSO FBC** & **0.384** & **76.89\%** & **11.26** & **0.350** & **74.48\%** & 6.049 \\ \hline
**SEP-FBC** & 0.405 & 12.33\% & **0.28** & 0.368 & 13.42\% & **0.184** \\ \hline
**SEP-RG** & 0.413 & 8.11\% & 1.46 & 0.378 & 8.46\% & 1.145 \\ \hline
**SEP-ILS** & 0.584 & 1.12\% & 21.49 & 0.572 & 0.96\% & 9.727 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The average \(NL\), _Pr_ (m/NL) and _AET_ (in secs) of the _SEP-PSO FBC_, _SEP-FBC_, _SEP-RG_, and _SEP-ILS_ methods computed on all shapes of LEMS and MPEG7 dataset.  
Figure 11: The relative frequency histogram of (**a**) circularity and (**b**) solidity for the LEMS and the MPEG-7 datasets.  
values of \(N\). For a better visualization of the results, we set the scale of the y-axis to be logarithmic. The results of the figure agree with the corresponding _AET_ of Table 2, showing that under any value of \(N\), the most computationally efficient method is the _SEP-FBC_.