**3. Results**

The results of the test can be seen in Table 18. V (A ⇒ B) and T (A ⇒ B) indicate the degree of feeling of the difference in depth between colors A and B perceived through visual and tactile sense, respectively. After having all the results, the visual and tactile feeling of the difference in depth between colors were subtracted as a way to measure the difference of depth feeling between the visual and the thermal cues. As an example for understanding the table, the columns related to (3 ⇒ 2) will be explained.


**Table 18.** Results of the final test.

V(3 ⇒ 2) is the visual different of depth created when looking at color 2 after color 3. Because of the chromostereoptic effect, most people find the red to be nearer than the blue and, as a result, the effect is that of looking at a color that is nearer than the first one. This effect is related to the positive scale from [0, +5], with a higher number if the depth difference between both colors is felt higher. Similarly, T(3 ⇒ 2) is the depth sensation created by touching the color that is at 26 ◦C after the one that is at 14 ◦C, also graded in the same manner (considering that, as has been proved before, most people feel warmer temperatures as that of something being nearer to us). As a result, we can compare V(3 ⇒ 2) to T(3 ⇒ 2) to assess how similarly or differently the thermal cue allows the user to be aware of the depth difference between two objects or colors compared to the depth difference acquired by the visual sense.

As can be seen in the results, most of the times the difference between the visual and thermal tactile depth feeling was less than one whole scale degree. However, there seem to be some extreme differences in some cases, usually given by the fact that the chromostereoptic effect is not totally universal and a few people seem to perceive the depth levels differently. Such is the case with the participant number seven, who felt that, visually, color 1 was actually farther away than color 2 by a considerable distance.

However, even with this little differences, the average difference between visual and thermal tactile depth cues was less than two whole scale degrees for the comparison between color 1 and color 2, and only −0.1 degree of difference between color 3 and color 2. These are promising results that show that the temperature mapping is a proper translation for depth. Nevertheless, some statistical data analysis can also be performed for narrowing down the confidence interval of the mean difference between visual and temperature cue-based depths. However, since the sample data is not too large, any outlier should be properly spotted and deleted from the sample. For that, first, the median and quartiles of both columns are calculated as in equations 1 and 2. For ease of reading, the column representing V(1 ⇒2)–T(1 ⇒ 2) will be called A, and the column representing the value V(3 ⇒ 2)–T(3 ⇒ 2) will be called B.

$$Q\_{A1} = \frac{-1 - 1}{2} = -0.5 \, Q\_{A2} = \frac{0 + 1}{2} = 0.5 \, Q\_{A3} = \frac{5 + 3}{2} = 4 \tag{1}$$

$$Q\_{B1} = \frac{0+0}{2} = 0\\ \ Q\_{B2} = \frac{0+0}{2} = 0\\ \ Q\_{B3} = \frac{1+1}{2} = 1 \tag{2}$$

The interquartile range is then calculated:

$$IQR\_A = Q\_{A3} - Q\_{A1} = 4.5 \, IQR\_B = Q\_{B3} - Q\_{B1} = 1 \tag{3}$$

Any value that is below the first quartile or above the third one by an amount of 1.5*IQR* would be considered an outlier. However, in this case there is no outlier so all data needs to be used for the statistical analysis. For calculating the confidence interval of both column A and column B values, the t-distribution is used since not the mean nor the standard deviation of the population are known. Also, other distributions, such as the normal distribution, give better results only when the number of samples exceeds 30.

First, the mean and the standard deviation of columns A and B can be calculated as in (4), where μ is the mean, σ is the standard deviation, *N* is the number of values, and *xi* is each individual value.

$$
\mu = \sqrt{\frac{\sum (\mathbf{x}\_i)}{N}} \,\sigma = \sqrt{\frac{\sum \left(\mathbf{x}\_i - \mu\right)^2}{N}} \tag{4}
$$

The results after applying those formulas are: μ*A* = 1.63, μ*B* = −0.13, σ*A* = 3.07, σ*B* = 1.64. The confidence interval for the population mean following a t-distribution can be calculated as in (5), where *tn*−1. is the cumulative probability of the t-distribution given a degree of freedom and confidence level, and *n* is the degrees of freedom calculated as *N* − 1.

$$
\mu \pm t\_{n-1} \frac{\sigma}{\sqrt{n}} \tag{5}
$$

As can be seen in Figure 22, in this case, for a confidence level of 95%, the value of *tn*−<sup>1</sup> is 2.365. As a result, the population average of column A and column B falls, with a 95% of confidence, within the range that can be seen in (6). It can be observed that in the case of column B, the difference between the visual and temperature-based depth assessment would not be larger than a scale degree and a half (of the 5-point scale degree that has been defined above). In the case of column A, there is more uncertainty due to the small sample size, but the result is still promising and encouraging for considering temperature-depth mapping and its based temperature interaction for artwork exploration as an interesting option for future assistive devices for the VIP.

$$
\mu\_A = [-0.9366, \ 4.1966]
\
\mu\_B = [-1.5011, \ 1.2411] \tag{6}
$$


**Figure 22.** T-distribution table indicating the cumulative probabilities depending on the confidence level. (https://www.tdistributiontable.com).

In conclusion, the accuracy of the proposed algorithm was verified through the experimental process and the temperature cues were found to be a promising way for conveying the chromostereoptic depth of the artwork. The next step was to install the prototype at an exhibition hall in Chungju Sungmo school for the visually impaired in Korea (Figure 23) to assess the responses of the visually impaired users. The reaction of the users was observed and visitors were briefly interviewed for finding out their impressions about the prototype.

**Figure 23.** Temperature-depth system prototype being exhibited together with other art assistive devices for the visually impaired at the Chungju Sungmo School for visually impaired people, in Korea. The temperature prototypes, of which there are two, are placed in the right side.

### *Comments from the visually impaired users at exhibition hall*

Visually impaired and sighted visitors were briefly interviewed after using the temperature-depth art prototype exhibited in the Chungju Sungmo School for the blind of Korea. They were asked to comment about their feelings and thoughts regarding the temperature interface and its use for representing depth. In general the responses were positive, with some people stating that it was really interesting to explore the artwork in di fferent ways for which they had not been able to do before. Also, some sighted school teachers pointed about the fact that this kind of new interactions keeps some of the visually impaired people interested in learning since most of the books and tools they use to learn are only braille books or audio recordings. Most of the VIP agreed that temperature was an intuitive way of describing depth because of the correlation between warm and near, and cold and far that we stated above. Also, some of them added, especially the children, that the temperature gave a gamification-like feeling to the prototype, making the artwork exploration more enjoyable and engaging. This statement about the gamification making art exploration engaging and interesting seems to be directly correlated to the teachers' comments about VIP getting a lot of benefit from new and unusual ways of interaction for keeping up interest by trying out new ways of learning. There were also some complaints, particularly about the fact that in the boundaries of the objects, the temperature from adjacent objects would mix a little bit and the distinction between temperatures was not very clear at those points. Also, some of them suggested that the same system could also be used for adding temperature to some hot or cold objects, such as the sun or water, instead of for representing depth, which could be done instead by adding a third dimension to the tactile model.
