# An Image Segmentation Method Based on Improved Regularized Level Set Model
## 4 Experimental Results
### Comparative Evaluation  
In addition to the visual evaluation, the DICE coefficient (_Dice_) [80] and the Jaccard similarity index (_JSI_) [81] are often used as two important criteria for evaluating the segmentation accuracy of a target region. Following the experimental techniques designed in [34; 75], the tested images were selected randomly from the BSDS500 database. Note that BSDS500 contains hundreds of natural images and their ground-truth segmentation maps generated by multiple individuals [82]. To enhance the coherency of our work with the above algorithms and compare it well with the CV model [48], the LBF model [49], and the LIF model [50], this next batch of experiments is conducted to further test our proposed IRLS-IS model on fifteen representative real-world color images, which are chosen from the Berkeley segmentation data set 500 (BSDS500).  
_Dice_ characterizes spatial overlaps between the segmented regions and the ground truth, and the formula of _Dice_[77] is expressed as  
\[Dice(G,S)=\frac{2N(A\cap B)}{N(A)+N(B)}, \tag{17}\]  
where \(\cap\) represents an intersection operator, N(\(\cdot\)) describes the number of pixels in the enclosed set, A represents the results of the IRLS-IS model to segment images, and B describes the ground truths. It is noted that the value of Dice is between 0 and 1. If the Dice is closer to 1, the segmentation results are more accurate [59]. Then, the Dice results of the four compared models are depicted in Table 1, where the best values are in bold font.  
The _JSI_ is the second statistical measure used for the quantitative evaluation in this paper, and the formula for the _JSI_[83] is  
\[JSI(s_{1},s_{2})=\frac{|s_{1}\cap s_{2}|}{|s_{1}\cup s_{2}|}, \tag{18}\]  
where s\({}_{1}\) describes the segmented volume and s\({}_{2}\) denotes the ground truth. The value of JSI is from 0 to 1. It is obvious that when the value of JSI is closer to 1, the more similar s\({}_{1}\) is to s\({}_{2}\).  
Then, the precision of segmenting the Berkeley color images is measured by the _JSI_ value, as shown in Table 1, where the bold font indicates the best result. As we can see from Table 1, the IRLS-IS method achieves the best values for the _Dice_ and _JSI_ on the thirteen-image data. On image ID: 102061, the _Dice_ and _JSI_ values of IRLS-IS are 0.01% and 0.02% less than those of CV, respectively, so they are almost the same. On image ID: 147091, the values of IRLS-IS are 0.2% and 0.3% less than those of CV, respectively, and then they only have subtle differences. Thus, the proposed IRLS-IS algorithm obtains the optimal values of _Dice_ and _JSI_ on the selected fifteen image data. In summary, these results demonstrate that our IRLS-IS method is indeed efficient and outperforms the three currently available approaches.  
Figure 8: Comparisons of the three models in segmenting an image with a cerebral infarction: (**a**) The original image; (**b**) The segmentation results of the DRLSE model; (**c**) The segmentation results of the LSACM model; (**d**) The segmentation results of the IRLS-IS model.  
The abovementioned experimental results and analyses fully demonstrate the validity and stability of our IRLS-IS method. The new distance regularization term proposed in this paper not only avoids the problem of reinitialization but also initializes the level set function to a constant. It effectively solves the problem of selecting the initial size of the level set. In addition, the new distance regularization term is more robust than that proposed by [PERSON] and allows the partial differential equations to evolve with a large time step. Therefore, our IRLS-IS model successfully segments several noisy images and inhomogeneous images, efficiently handles some complex medical images, and reduces the iterations and the running time of the central processing unit (CPU) of computer.