# Active Contours in the Complex Domain for Salient Object Detection
## 4 Experiment Analysis and Results
### Discussion  
The effectiveness and stability of the proposed algorithm are verified based on both synthetic and natural images in this section. The major contribution of our ACCD_SOD model is the complex domain. Our model introduces a novel algorithm while using the complex domain that simultaneously gives salience cues and finds the exact boundary. The proposed ACCD_SOD model obtains salience detection results using the global complex force function. Our primary aim is proposing a model that controls the initialization irregularity in active contour and is also capable of eliminating the expensive re-initialization. Pixelwise salience detection provides such a solution for initialization and  
Figure 11: Precision-recall (PR) curves comparing the proposed approach with existing ones. Our algorithm outperforms the others, except TIP. Figure 12: ROC curves comparing the performance of our proposed algorithm with that of five state-of-the-art models. the subsequent foreground identification. The model resolves not only the problem of initialization by complex domain, but, precisely makes the most excellent use of low pass filter in complex domain to eliminate the problem of re-initialization. It is clear from the results that our algorithm detects the boundary accurately without repeated iterations or an extra initialization step. Figures 1, 4 and 7 prove that the algorithm directly initialize on the object boundary. Among the methods that are involved in comparison, the DRLSE model is over reliant to the initialization and creating numerical error. The LI model requires the convolution before the repetition and, therefore, the functioning time of the computing is decreased, but the initial contour is ineffective in robustness. The RBS model used the local interior and exterior statistics to initialize every pixel, which increases the computational complexity. The LFE model applies local information to handle intensity-inhomogeneity for creating acceptable segmentation decisions but sensitive to noise. SDREL fail on images with complex background, as investigated by a researcher [44; 45; 46; 47]. Proved from our results, the complex domain provides a smooth curve and, meanwhile, its implementation reduces the computational cost when comparing to the other model. Our proposed model shows high robustness compared to the SDREL, RBS, CV, LI, DRLSE, and LFE models and accommodates inhomogeneous images. It avoids reinitialization and thus also reduces the computational cost. The complex force function has a relatively extensive capture range and accommodates small concavities. We examine that, in both situations with strong objects or week objects, our complex domain approach achieves encouraging results. The proposed approach can be implemented and suited to different modality of images. However, the proposed approach detects and recognizes approximate boundaries in the presence of weak objects. Therefore, the evaluation capacity is reduced in the presence of poor and low quality or heavy blur. The heavy noise also reduced the estimation ability due to the impact on the edge of the object. Our proposed model is not considerable for images, like texture. The parameter setting process plays an important role in the ultimate result of ACMs and it can produce a great performance improvement if the proper parameters are given to an active contour model. If the value of parameter \(\alpha\) is large, the propagation of dynamic interface cause results and it cannot be controlled. In the case of small \(\alpha\), then contour lost its propagation speed. It is difficult to choose a proper value of \(\alpha\). In both cases, if value is too large or in the case of too small value of \(\alpha\), the performance and result will be effected and undesirable. Therefore, we set proper and fixed value of the parameter alpha (\(\alpha\)) = 0.4 for all synthetic and natural images. The value of the computation parameter should be accurately used.