# A Mixed Method with Effective Color Reduction
## 4 Results and Discussion
### Results of Other Methods
To complete the comparison, the execution time of the methods must be taken into consideration. The information shown in Figure 4 allows for this comparison. Figure 4a shows the values for the noniterative methods and also includes the results of BS+ITATCQ3 at iteration 5, in order to better interpret the values of this figure. On the other hand, Figure 4b shows the results of the iterative methods. In this second case, the results of BS+ITATCQ3 are those corresponding to iteration 25. To complete the information, Figure 4 also shows the average execution time of BS+ATCQ, BS and ITATCQ, discussed in the previous subsections. It can be clearly seen that the methods represented in Figure 4a are faster than the method described in this article, although they always generate worse images than the proposed method, except WATCQ. As far as WATCQ is concerned, it only generates better quality images than BS+ITATCQ3 at iteration 5 for 15 cases out of 96, and this value reduces to 7 cases when comparing the results of BS+ITATCQ3 at iteration 25. Regarding the methods represented in Figure 4b, ABC+ATCQ, ATCQ+FA, KM and BSKM clearly consume more time than BS+ITATCQ3. On the other hand, SFLA is slower than BS+ITATCQ3, but the difference is smaller. The two desirable features of a color quantization method are its speed and the good quality of the images it generates. To try to compare both features at the same time, a scoring method was defined. First, the average MSE and execution time of each method were computed, considering all the images of the test set and all the palettes. Then, these average values were sorted from worst to best. After this, score 1 was assigned to the method with the worst value and increasingly integer scores were assigned to the sorted methods. As a result, the methods were assigned a score between 1 and 15 when considering the average MSE, while this range was reduced to 1-14 when considering the average execution time, since the execution time is the same for MC and WU methods. Once these two scores were defined, the average of both values was computed. Figure 8 shows the scores assigned for both criteria and the average value. The methods are represented and sorted by increasing average value. It can be clearly observed that BSKM and ABC+ATCQ obtain the best scores when MSE is considered, but they obtain the worst scores when the execution time is considered. On the contrary, MC obtains the best score for the execution time but the worst for MSE. When the average of both scores is considered, WATCQ obtains the best result and the proposed method obtains the second best result. To sum up the results previously presented, the WU, OC, NQ, VB and MC methods are faster than BS+ITATCQ3, but they also generate worse images than BS+ITATCQ3. The WATCQ method is also faster than BS+ITATCQ3, but it generates worse images in most cases. On the contrary, the iterative  
Figure 8: Scores assigned to the quantization methods, based on the average mean squared error (MSE) and execution time, along with the mean of both scores. methods are slower that BS+ITATCQ3, but some of them can obtain better images than it. Among these methods, ABC+ATCQ and BSKM are the ones that obtain better quality images compared to the proposed method, but they are also the slowest. For example, 25 iterations of BS+ITATCQ3 consume 15 s on average to generate an image with 256 colors. For this same case, BSKM and ABC+ATCQ consume 74 and 162 s, respectively. Therefore, although both methods can obtain better images in many cases, a lot of time is required to obtain a small reduction in the error of the quantized image. However, more iterations of BS+ITATCQ3 could be executed, generating a better quality image and in less time than both methods.