The existing correlation between warm and near, and cold and far, was utilized for conveying depth and distance by means of temperature cues. The main idea is simple: the nearer an object is to the user, the warmer the temperature cue. Similarly, the farther an object from the user, the cooler the temperature cue for that object. This idea can be applied in many ways, but we decided to follow a simple mapping method which is explained next, in four steps:
The temperature range is selected. This can be selected freely (as long as it falls within the comfortable temperature range stated above). In general, the visual perceived distance between the extreme depth levels will be assessed and the extreme temperatures selected accordingly (higher temperature difference for higher distances). However, if the simpler algorithm is to be used, then the extremes depth levels will always be linked to the extreme temperatures of 14 and 38 °C, regardless of their perceived relative distance.
The total number of perceived depth levels are counted. For example, in the case of an image with two objects, one in front of the other, there are two depth levels: front and back.
The temperature is equally divided in as many temperatures as needed for assigning a temperature to each depth level. The highest temperature and the lowest one are usually assigned to the nearest and the farthest depth level respectively but the use of other initial temperatures might also be possible if is it is considered more appropriate by the designer.
Optionally, if the difference between the temperatures of two consecutive depth levels is less than 3 °C, some of the consecutive depth levels are clustered together. In other words, some objects from different depth levels are put into a similar intermediate depth level. This helps the user recognizing the different depth levels better by decreasing the total different temperatures to be felt and recognized.
Following these four steps creates a simple mapping that does not consider the absolute distance between depth levels (except for the nearest and farthest depth levels, whose relatively absolute distance is considered for choosing the initial temperature range), but only the number of depth levels and the order in which they approach the user. More complex mappings could be designed, such as a mapping which took into consideration the absolute depth levels of all the features. However, this simple mapping is enough for conveying the different depth levels through temperature cues to give an idea to the VIP of where the different features of the artwork are placed according to depth.
Next, this temperature-depth mapping will be applied and examples of its use will be given in two different types of applications: for representing depth of the different objects of a bi-dimensional artwork and for representing color-based depth of a bi-dimensional image (an effect called chromostereopsis).
2.2.1. Application 1: Artwork Depth
The temperature-depth mapping can be used to convey through temperature the different depth levels of the objects of an artwork. In that way, the visually impaired user can sense more deeply the depth presented in a painting.
In this case, different temperatures for the objects that are at different levels of depth are assigned by following the method presented above.
Before applying the method, first, some techniques used by artists for creating the illusion of depth in visual arts will be contemplated and the method applied to those simple cases. After that, some examples of the temperature-depth mapping method presented above will be applied to two real famous artworks.
Illusion of depth in 2D visual arts
In 2D visual arts, there are many ways of creating the illusion of depth, such as:
Overlapping and layering
Size and placement and perspective
Texture and detail
Color, hue, and value
The most relevant ones are layering and overlapping, shading, and size, placement and perspective. However, color, hue, and value can also contribute to create strong feelings of depth, an effect called chromostereopsis [2
]. This effect will be explored separately in the following section. First, shading and size, placement and perspective techniques will be explained (since layering and overlapping is a really intuitive and common technique, no explanation will be given).
Volumetric objects always create shade when being hit by a source of light. As a result, in 2D visual arts, the use of light and shade is one of the methods for creating the illusion of depth. Figure 6
shows an example of an effect called “the crater illusion” [2
] in which the central square seems to be in front of the background (right image) or behind the background (left image) depending on the position of highlighted or shadowed edges. The results of applying the depth-temperature algorithm in this case can be seen in Table 7
, for the left side of the figure, and in Table 8
for the right side of the figure.
Size, placement, and perspective
Vertical placement: we perceive objects that are placed lower in the image as closer to us, and objects that are placed higher as being further away. A really clear example of this will be seen later when we apply the temperature-depth mapping algorithm to the artwork “Starry Night” by Vincent Van Gogh.
Diagonal perspective: we perceive diagonal lines as receding into the distance. As shown in Figure 7
and Table 9
, the red-colored square seems to recede due to the diagonal perspective.
In this painting, by Matisse (Figure 8
), there are seven different elements, which can be seen in Table 8
. The dancers have been numbered to aid identification. By looking at the drawing, sighted people can generally agree on five different levels of depth, these levels of depth have been linked to the different depth layers from 1 to 5, with 1 being the nearest layer and 5 being the farthest depth layer from the viewers’ location as a reference. Nearer depth layered elements need to have higher temperatures so temperatures are assigned to the extreme layers (38 °C for the Dancer 5 °C and 14 °C for Sky) and then that temperature range is divided by five (since we have five depth layers). The reason for choosing 38 °C and 14 °C was because Sky and Dancer 5 are visually really far away from each other, so the temperature for those extreme depth layers were chosen in a way that the temperature difference was maximum: the lowest and highest temperatures from the defined [14 °C, 38 °C] temperature range in which we are working. The resulting temperatures are linked to their respective layers and they can all be seen in Table 10
In the case of “Starry Night
” (Figure 9
) by Van Gogh, there are many depth layers, as can be seen in Table 11
. As before, these depth layers are selected in a visual way, by contemplating the artwork and choosing the main depth levels defined by the features. In our case, nine depth layers were defined. However, since such a high number of layers would force the user to feel and differentiate many different temperatures, we decided to simplify the number of depth layers. For that, elements were visually and conceptually grouped to check whether some of the elements from different depth levels could be grouped under a common depth level. As a result, the starts and the moon, and the mountain and the forest (both pairs of elements having both conceptual common traits and being visually near to each other) were grouped together in two common depth levels. This can be seen in Table 11
where Forest and Mountains share depth layer number 3, and Stars and Moon share the layer number 4. In this way, the number of temperatures is less and the user can identify the different temperatures and depth layers in an easier way. Therefore, even though technically the forest and the mountains are not in the same depth level, we can simplify it to aid identification. In general, this technique should be performed when the temperature difference between layers becomes less than 3 °C.
2.2.2. Application 2: Chromostereopsis
Another possible application of the temperature-depth algorithm is for conveying the effect of chromostereopsis through temperature. Chromostereopsis [2
] is the effect produced by colors on a flat two-dimensional surface by which each color seems to be located in different depth planes, in spite of the two-dimensionality of the image [19
]. It is important not to mistake this effect with the association made by artists between red colors and blue colors as advancing and receding colors, since that idea might be based on the brightness produced by atmospheric haze, which is associated with distance, rather than with the effect of chromostereopsis [20
]. Chromostereopsis is produced by an effect called chromatic aberration, which is the result from the differential refraction of light depending on its wavelength, causing some light rays to converge before others in the eye and/or to be located on non-corresponding locations of the two eyes during binocular viewing.
Next, an exploratory analysis of the main features that make a color seem farther or nearer will be given, followed by a simple algorithm for conveying chromostereoptic depth by means of temperature. However, first, a brief explanation about colors needs to be given.
The spectrum of color is a continuous one for which there has been several representation models [21
]. One of the earliest models is called the Munsell color model, which organized the color perception into a color cylindrical space with three dimensions: hue, chroma (or saturation), and value (or lightness), as can be seen in Figure 10
Hue refers to the color itself. Luminance means the brightness of a color. The higher the luminance, the closer it is to white, and the lower the luminance, the closer it is to black. Saturation is the vividness (clearness) of a color. As an example, 27 colors of varied hue, luminance, and saturation can be seen in Figure 11
The chromostereoptic effect is complex and its effects can vary due to many different reasons. Nevertheless, for simple images and in a dark background, red objects tend to appear closer to the observer than blue objects, as can be seen in Figure 12
. There, the red and blue stripes will seem to be in separated depth levels for most observers, with the red being apparently nearer to the observer.
This can be extrapolated to warm and cool colors, since, in general (and always when in a black background) warm colors come forward and cool colors retreat [16
]. However, in [20
] researches have also proved that, when the background is white, the effect is reversed, and the warm color seems to be further away than the cool one, as can be seen in Figure 13
, which sets the same blue and red colored image to both a black and white background.
An algorithm for conveying the chromostereoptic effect in simple images through temperature cues will be presented. However, first it is necessary to find out why some of these colors seem to recede or advance when in company with other colors. Even though warm colors tend to be felt nearer and cool colors tend to be felt further away, that is not always the effect produced. It seems that the most important features for this chromostereoptic effect in simple images are luminance and saturation.
], it was observed that one of the reasons why some colors seemed nearer than others was luminance difference, with bright objects appearing closer than dim ones. This would support the claim that “warm colors tend to advance and cool colors recede” since warm colors tend to be brighter than cool colors. In the following Figure 14
, and Table 12
and Table 13
, the same color can be seen next to each other with different luminance levels. In both cases, the high luminance version of the color seems to be nearer than the dark color.
], patches of colored paper against a black background were shown to a total of 17 subjects. In general, they seemed to agree that a desaturation of a color made its depth effect be diminished. This can be seen in Figure 15
, where two colors appear at different levels of saturation. In both cases the muted color (the one that is less clear) seems to be farther away. As before, the range of temperature between both colors can be selected freely after assessing the visual depth contrast (similar to applying the first step of the mapping method stated above) as long as the saturated color is the warmest. We chose again the extreme temperatures, as can be seen in Table 14
and Table 15
Chromostereoptic Temperature-Depth Algorithm
Considering all these features, an algorithm for representing simple chromostereoptic effects with temperature was designed. The algorithm consists of several steps:
First, the background needs to be chosen (sometimes there is no background or the background color can be simplified and not used, especially when it is a color that is not black nor white). If there is a clear background and it is black or white, it will influence the direction in which the chromostereoptic effect is produced so it is important to take it into consideration.
For each color that is not the background, the saturation and luminance level needs to be calculated, summed up, and halved. So, for each color, a value representing its level of saturation and luminance is acquired.
The defined temperature range (which is again selected freely through visual relative distance assessment, like was explained in the first version of the temperature-depth mapping method above) is divided by the total number of colors.
Each one of the temperatures is then assigned to each color in order, according to their luminance-saturation level value. If there is no background or there is a background and it is black, higher luminance-saturation values correspond to higher temperatures; if the background is white, lower luminance-saturation values correspond to lower temperatures.
The algorithm is presented in a more formal and concise way here:
For each color (except background) => find saturation and luminance level
For each color (except background) => (saturation + luminance)/2
Order colors by its luminance-saturation value from highest to lowest into a vector V
If white background: reverse V.
Select temperature range and divide it by number of colors.
For each color in V, assign the temperatures in order from highest to lowest.
As an example, the temperatures of the different colors of two artworks will be shown next.
In Figure 16
and Figure 17
, two artworks of the artist called Mark Rothko can be seen. The temperatures were chosen by following the chromostereopsis-temperature algorithm presented above. For calculating the saturation and luminance level of each color, an app called “Visual Color Picker 2.6”, created by NOVOSIB software co., was used. The saturation (S), lumination (L), and the hexadecimal color code are shown in both Table 16
and Table 17
, where the final depth temperatures of each color is also given. The temperature range selected was the 14 °C and 38 °C. As commented before, this is the temperature range to select when the simplest temperature-depth mapping is desired, one in which the extreme depth levels are always mapped to the extreme temperatures, which users can feel without pain. Similarly, the number of depth layers in each image are three, since those are the number of clearly differentiated colors which contribute to the chromostereoptic effect.