**3. Experiments**

The proposed method has been tested on natural images including flowers, fruits, pedestrians and landscape, as well as synthetic images such as patterns with pure colors (see Figure 10). The experiments were carried out on both simulation view and human tests. Figure 11 shows the images of protanopia color vision deficiency with different sensitive from 0.3 to 0.9 after our re-coloring technique. For the color vision deficiency view simulation, we compared the results of the proposed approach with the methods presented by Kuhn et al. [37], Rasche et al. [17] and Huang et al. [12]. Figure 12 shows the results of the deuteranopia color vision deficiency simulation and re-coloring using different algorithms. While all methods are able to separate the flower from the leaves, our result is more distinguishable and much closer to original color.

(**g**) Pedestrian 2

*Sensors* **2019**, *19*, 2250

**Figure 11.** Enhancement sensitive of protanopia color vision deficiency, (**a**) with sensitivity 0.3, (**b**) with sensitivity 0.5, (**c**) with sensitivity 0.7, (**d**) with sensitivity 0.9.

(**e**) (**f**) (**g**) (**h**)

**Figure 12.** The comparison of deuteranopia simulation of the flower image in Figure 9a. (**a**) Machado's CVD simulation. (**b**) Our re-coloring technique after Machado's CVD simulation. (**c**) Brettel's CVD simulation. (**d**) Kuhn's re-coloring technique after Brettel's CVD simulation. (**e**) Rasche's CVD simulation. (**f**) Rasche's re-coloring after CVD simulation. (**g**) Huang's CVD simulation. (**h**) Huang's re-coloring after CVD simulation.

## *3.1. Root Mean Square*

We use the root mean square (RMS) value to measure the difference between two images. That is, to evaluate how far between the CVD view simulation and the image processed after our re-coloring algorithm. We calculate the RMS value with k-neighborhood defined by

$$RMS\_i = \frac{1}{N} \sqrt{\frac{1}{2} \sum\_{j=-k}^{k} \left[ (a\_{i+j}^r - a\_{i+j}^t)^2 + (b\_{i+j}^r - b\_{i+j}^t)^2 \right]}$$

where *a<sup>r</sup> <sup>i</sup>*+*<sup>j</sup>* and *<sup>b</sup><sup>r</sup> <sup>i</sup>*+*<sup>j</sup>* are *<sup>a</sup>*∗*b*<sup>∗</sup> in *<sup>L</sup>*∗*a*∗*b*<sup>∗</sup> of the reference image, *<sup>a</sup><sup>t</sup> <sup>i</sup>*+*<sup>j</sup>* and *<sup>b</sup><sup>t</sup> <sup>i</sup>*+*<sup>j</sup>* are *a*∗*b*<sup>∗</sup> in *L*∗*a*∗*b*<sup>∗</sup> of the target image, and *N* is the number of elements in k-neighbor.

An example of tritanopia CVD simulation and the re-coloring results is shown in Figure 13. Compared to the results obtained from Kuhn's and Huang's methods, our approach provides better

contrast between the colors. Figure 14 shows the comparison of the RMS values on several test images using the proposed technique and Kuhn's method. The higher RMS value is displayed in dark blue, and the lowest value is shown in white. The figures indicate that, although the distributions of our and Kuhn's results are similar, the RMS values of ours are higher than Kuhn's, which implies a better separation in colors. Additional results of various types of test images are shown in Figure 15. The results of CVD simulation, re-coloring using the proposed technique and CVD simulation on the re-colored images are shown in the first, second and third column, respectively.

**Figure 13.** The comparison of tritanopia simulation of the pencil image. (**a**) The original image. (**b**) The CVD simulation using Machado's method. (**c**) Machado's CVD simulation on the image processed by the proposed re-coloring technique. (**d**) The CVD simulation using Brettel's method. (**e**) Brettel's CVD simulation on the image processed by the Kuhn's re-coloring technique. (**f**,**g**) CVD simulation and re-coloring using Huang's approach.

**Figure 14.** The comparison of RMS values between our method and Kuhn's method. (**a**) The RMS value between Figures 6a and 12a. (**b**) The RMS value between Figure 12b and 12a. (**c**) The RMS value between Figures 6a and 12c. (**d**) The RMS value between Figure 12d and 12c. (**e**) The RMS value between Figure 13a and 13b. (**f**) The RMS value between Figure 13c and 13b. (**g**) The RMS value between Figure 13a and 13d. (**h**) The RMS value between Figure 13e and 13d.

(**d**) CVD simulation. (**e**) Our re-coloring. (**f**) CVD simulation.

**Figure 15.** The results of CVD simulation, re-coloring using the proposed technique and CVD simulation on the re-colored images for some test images in Figure 10 (the first two columns) and 15 (the third column).
