# Fast Equipartition of Complex 2D Shapes with Minimal Boundaries +
## 6 Experimental Evaluation
### Evaluation of the Proposed Methods  
In the following, we present comparisons between the proposed methods _SEP-PSO FBC_ and _SEP-FBC_ on the normalized total intrinsic boundary length (\(NL\)). According to our methodology, it holds that _SEP-PSO FBC_ outperforms _SEP-FBC_ since it combines _SEP-FBC_ and PSO framework to find better initial centroids. Next, we examine how the difference in performance of the proposed methods is affected by the complexity of the shapes. To do so, we create three equal-sized groups of shapes for each dataset with low, medium, and high values of circularity. The set with low circularity values consists of 33.3% of shapes with lower circularity values, and so on. Similarly, we create three equal-sized groups of shapes for each dataset with low, medium, and high solidity values. Figure 14 depicts the average _NL_ metric for nine different values of \(N\in\{2,\ldots,10\}\) of the methods _SEP-PSO FBC_ and _SEP-FBC_ computed on (a-c) LEMS and (d-f) MPEG7 datasets for (a) and (d) low; (b) and (e) medium; (c) and (f) high circularity shapes. Figure 15 depicts the average _NL_ metric for nine different values of \(N\in\{2,\ldots,10\}\) of the methods _SEP-PSO FBC_ and _SEP-FBC_ computed on (a-c) LEMS and (d-f) MPEG7 datasets for (a) and (d) low; (b) and (e) medium; (c) and (f) high solidity shapes. In both datasets, _SEP-PSO FBC_ demonstrates a higher outperformance than _SEP-FBC_ in shapes with low circularity or solidity than in those with high circularity or solidity. Therefore, in general, the more complex the shape, the higher the outperformance of _SEP-PSO FBC_ since under complex shapes there may exist more candidate positions for the initial centroids that should be examined to find the best equipartition. Figure 12: The average _NL_ metric for nine different values of \(N\in\{2,\ldots,10\}\) of the methods _SEP-PSO FBC_, _SEP-FBC_, _SEP-FBC_, _SEP-RG_, and _SEP-ILS_ methods computed on (a) LEMS and (b) MPEG7 datasets. Figure 13: The average execution time (AET) in seconds of the methods _SEP-PSO FBC_, _SEP-FBC_, _SEP-RG_, and _SEP-ILS_ methods computed on all images of LEMS and MPEG7 dataset. In Figure 16, we present the results of _SEP-PSO FBC_ and _SEP-FBC_ for the two shapes of the LEMS (first two columns) and MPEG7 (last two columns) datasets with \(N\in\{2,\ldots,9\}\), where the outperformance of _SEP-PSO FBC_ is maximized to show the upper limit of this outperformance. Under any value of \(N\), it holds that _SEP-PSO FBC_ provides better solutions in terms of _NL_ metric than the corresponding solutions of _SEP-FBC_. In most cases, the proposed solutions of _SEP-PSO FBC_ significantly differs from the corresponding solutions of _SEP-FBC_ showing the importance of the selection of initial centroids, especially when a complex shape is given. Figure 14: The average _NL_ metric for nine different values of \(N\in\{2,\ldots,10\}\) of the methods _SEP-PSO FBC_ and _SEP-FBC_ computed on (**a–c**) LEMS and (**d–f**) MPEG7 datasets for (**a,d**) low, (**b,e**) medium, and (**c,f**) high circularity shapes. Figure 15: The average _NL_ metric for nine different values of \(N\in\{2,\ldots,10\}\) of the methods _SEP-PSO FBC_ and _SEP-PSO FBC_ computed on (**a–c**) LEMS and (**d–f**) MPEG7 datasets for (**a,d**) low, (**b,e**) medium, and (**c,f**) high solidity shapes. In Figure 17, we perform a sensitivity analysis of the _NL_ metric for the parameter \(\lambda\) and different values of \(N\) under the _SEP-FBC_ method and the MPEG7 dataset. We study how the _NL_ metric of _SEP-FBC_ method is affected by different values of the parameter \(\lambda\in\{N+1,2N+1,3N+1,4N+1,5N+1\}\), defined in Section 3. As expected, the higher value of \(\lambda\), the lower _NL_ metric, which is true for any value of \(N\). In this experiment, it  
Figure 16: Results of _SEP-PSO FBC_ and _SEP-FBC_ for the two shapes of LEMS (first two columns) and MPEG7 (last two columns) datasets, where the outperformance of _SEP-PSO FBC_ is maximized.