Encyclopedia of Color Science and Technology

2016 Edition
| Editors: Ming Ronnier Luo


Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-8071-7_270

Transparency/translucency: a. the degree of visibility of an object through a medium; b. the property of a material or substance by which objects may be seen through that material or substance. Transparency occurs when objects are clearly perceived through the medium, while translucency occurs when they appear hazy. Very often the term transparency is used instead of translucency.

The episcotister model is suitable to describe transparency percept as it involves different areas separated by clear margins, while variations of this model are required to deal with translucency, due to blurred edges which add some degree of opacity to the impression of transparency.

First of all figural and topological conditions, not handled here, must be met: they essentially consist of figural unity of the transparent layer, continuity of the boundary line, and adequate stratification. Another strong factor which strengthens the figural organization is the movement, either of the background or of the transparent medium; this in turn makes transparency more evident. Transparency can also disambiguate objects (plaids) moving in different directions which otherwise would appear as a structure moving in another direction. Devices which induce strong depth perception, like natural or simulated stereopsis, also increase the evidence of the transparency effect.

Transparency involves the distinct perception of the rear and front colors along the same direction of sight well differentiated also where they are superimposed. This part of the definition is very restrictive as there are cases in which one sees objects behind and through another object, but the colors perceived in the overlapping area amazingly differ from those in plain view. In these cases no color constancy is achieved, and no model seems presently applicable.

History of the Model

Models are known physical phenomena, with characteristics analogous to those to be described, whose explanatory structure is heuristically applied to not yet known phenomena (for instance, the atomic planetary model by Rutherford, the hydraulic analogy of electricity, and so on). A different definition of models includes just the mathematical formulation of relevant relationships which describe the phenomenon.

The episcotister model derives from experiences with rotating wheels, used to produce different colors by mixing two or more sources of radiation. Most times the disk is divided in two or more differently painted parts, and at a fusion speed temporal resolution of human eye cannot distinguish the different parts, but confuses them and sees only one color. This method of mixing radiation was made famous by Maxwell from whom it took the name. Sometimes instead of a solid disk, only two symmetrical sectors are spun so to mix rays from the background with those from the solid sectors. Although the laws governing these kinds of mixtures are well known, the actual perception does not always conform the prediction of seeing one resulting color, as sometimes two colors are instead seen in the overlapping area. This outcome happens when some figural conditions are fulfilled, and the figure of a transparent disk is visible in front of a background completely or partially covered and stratified in depth. This experience led to theoretical and experimental analysis of the psychological impression of transparency.

Field of Applications

Knowledge about transparency has been mainly applied to food and drink analysis, skin and cosmetics, medicine, dentistry, architecture, textile manufacturer, art, graphics, design, fashion, painting, printing, and others.


Metelli’s Episcotister Model of Perceptual Transparency

Metelli’s model [1] consists of a wheel, rotating at fusion speed in front of a background, divided in two parts: an empty sector (totally transmitting area) and a solid sector (reflecting area). It is a kind of special filter, like a riddled surface, which transmits and reflects light at the same time.

Through the open part of the episcotister (or through the holes of the riddled surface), light coming from the back object can reach the observer’s eye without being spectrally modified. The size of the open sector (or of the holes in the riddled surface) determines how much light is transmitted to the observer: from a maximum when the whole disk is completely open to zero when the whole disk is solid. Therefore, the episcotister and the riddled surface behave like a neutral filter by decreasing the intensity of the light passing through them by a certain amount without changing its spectral distribution.

In turn the solid part of the episcotister (or the solid part of the riddled surface) can reflect light to the observer and this is mixed with the light from the back. As both the open and the filled sectors of the episcotister (or the holes and the solid part of the riddled surface) together cannot be larger or smaller than the whole disk (or surface), their proportion can vary from 0 to 1: if α is the proportion of the open sector to the whole disk, (1–α) is the proportion of the solid sector (or of the solid riddled surface). As one increases, the other decreases accordingly: for this reason the mixture of the two lights, that coming from the background and that coming from the surface of the episcotister (or riddled surface), is a special kind of mixture called partitive. If a is the vector describing the light coming from the background not modified by a filter, and t is the vector describing the light coming from the solid surface of the filled episcotister, the presence in the rotating disk of an open sector of size α determines the partitive mixture described by the following equation:
$$ \boldsymbol{q} = {\alpha}^{\ast}\boldsymbol{b}+{\left(1\hbox{--} \alpha \right)}^{*}\boldsymbol{t} $$
where q is the vector describing the mixture of the two lights (a and t) arriving at the observer’s eye.

This equation perceptually means that the back color b is visible in the color q proportionally to α, and the color corresponding to t is visible in q proportionally to (1–α). The reduced visibility of the two colors due to the transparency factor α means that they are not perceived as completely in plain sight, but one appears transparent and the other seen by transparency. Both the lights coming from the back opaque objects and the front transparent object arrive at the observer reduced in intensity but unchanged in their spectral composition. Therefore α means how much color of the background is visible in the overlapping area: this dimension corresponds to the degree of perceived transparency of the fore object and according to Metelli is a logarithmic function of it, while α is a neutral (achromatic) multiplicative factor. The additive factor t, which can be interpreted as either the reflectance characteristic of the object or the light (luminance) reflected by it, corresponds to the color of the filter and can assume all values form 0 to 1 (black and white, respectively).

If the episcotister rotates over a uniform background, it appears like an opaque disk, and the same happens when physically transparent sheets are superimposed over a uniform surface. This effect shows that physical transparency is not sufficient condition to perceive transparency. Another particular case of transparency is obtained when a transparent sheet completely covers a background figure without sharing their margins with it: this effect has been little studied [2]. The case of riddled surface can be extended, by analogy, to textured surfaces, in which the density of the texture plays the role of color.

Equation 1 can be interpreted in two different ways, by analogy with a chemical reaction: by reading it from right to left, it means that the partitive mixture of the two colors b and t gives rise to the resulting and univocally defined color q; but if one reads it from left to right, the equation can describe a color scission, that is, the color q can partitively split into the two components b and t. This scission, described by many researchers, would be in the model the opposite process of fusion and occurs in the perception of two colors in the same area, one in front and the other in the back. According to a different wording, this scission would be a case of double representation in gestalt terms. In this latter case, however, an indefinite number of b and t pairs can be obtained because α is not determined. Therefore, at least two equations are necessary to derive a specific pair of α and t, and a second background color seen through the transparent object must be present. For instance, in Fig. 1, the episcotister should not only rotate over the green background figure but also over the white background a, and in this case another partitive mixture would be described by the following equation:
Transparency, Fig. 1

Top row: three different episcotisters over three identical backgrounds. b = vector defining the color of the background; t = vector defining the color of the solid sector of the episcotister; q = vector defining the color of the overlapping area; α = a measure of the open sector of the episcotister, which can vary from 0 to 1. Middle row: three riddled circular surfaces. The ratio holes/total surface (α) can vary from 0 to 1. Bottom row: the perceptual effects

$$ \boldsymbol{p} = {\alpha}^{\ast}\boldsymbol{a}+{\left(1\hbox{--} \alpha \right)}^{*}\boldsymbol{t} $$
where p is the vector describing the mixture of the two lights (a and t) arriving at the observer’s eye.
The determination of α and t, characteristics not present in the stimulation, can be univocally found, starting from the colors of the display in the bottom row of Fig. 1 according to the following equations:
$$ \alpha = \left(\boldsymbol{p}\hbox{--} \boldsymbol{q}\right)/\ \left(\boldsymbol{a}\hbox{--} \boldsymbol{b}\right) $$
$$ \boldsymbol{t} = \left(\left(\boldsymbol{a}\ \boldsymbol{q}\right) - \left(\boldsymbol{b}\ \boldsymbol{p}\right)\right)/\left(\boldsymbol{a}+\boldsymbol{q}-\boldsymbol{p}-\boldsymbol{b}\right) $$
Once the a (the lightest area which is perceived in the background) and b background colors and the t color of the transparent virtual object have been chosen and the degree α of transparency is decided, the regions of the mosaic of Fig. 2 are filled with the colors determined according to Eqs. 1 and 2.
Transparency, Fig. 2

Transparent gray disks of different t color (at left) and different degrees (α) of transparency (at right) over a white and black chessboard

The colors of the transparent disks and their degree of transparency can be computed according to Eqs. 3 and 4 from the colors of Fig. 2. The formal independence of α and t is a feature of the model. The square wave margins between colors in the overlapping areas are characteristics of the transparency effect, while blurred margins denote translucency [2, 3]. The alpha blending procedure in computer graphics is based on this model [4].

The model of the episcotister applied to transparency phenomena entrains also some constraints and consequences. The most important is that α [4] cannot be higher than 1 (an open sector larger than 360° is inconceivable) and lower than 0 (and likewise is inconceivable an open sector smaller than 0°). This involves that, by assuming a as the vector of the lightest color in the background and b of the other background color (both perceived as such), the difference pq must be smaller than the difference ab: the contrast (here measured as a color difference) between the colors covered by the transparent object is always lower than the contrast between the two background colors in plain view. In other words the transparent object reduces the color contrast in the overlapping area. Secondly, as α must be positive (a negative open sector is a nonsense), the color difference between p and q must go in the same direction of the color difference between a and b. If these conditions are not met, usually transparency cannot be perceived and the model cannot be applied, i.e., nothing can be stated about the possible transparency effect on this basis.

Transparency and Color Constancy

Transparency, like illumination, involves color constancy: first, the colors of the background perceived through the transparent medium should appear the same as those in plain view, and secondly, the color of the transparent medium should also appear the same in all its parts. The analogy with illumination is justified by the often quoted example of a transparent medium as a spectrally selective filter. Models based on simple filters have been shown not to work because the colors of the overlapping regions can be quite unexpected and sometimes color constancy does not occur at all: for instance, through a red filter a red surface appears white and a green surface appears black. Therefore, filter models usually include either the need of previous experience or some constancy constraints. A model based on the illumination analogy [5] considers the cone excitations as the basis for describing the necessary color conditions of an impression of transparency. This can occur when cone-excitation ratios between the colors in plain view (a, b, …) remain the same between the colors (p, q, …), i.e., under the transparent medium. Although color constancy is a strong requirement for perceiving transparency, it can be very weak or even null and nevertheless a generic impression of transparency is still possible (Fig. 3). This makes the study or perceptual transparency quite difficult [6].
Transparency, Fig. 3

An example of impression of transparency without color constancy (from Metzger). When the disks are rotating, the impression is much stronger

Transparency, Fig. 4

Attilio Taverna. Left: Sentieri interrotti 1992. Right: Blue geometric storm 1992. Transparency effects are obtained by painting each overlapping area with the partitive mixture of the back and front colors. Also perceptual space organization is affected by transparency

Transparency and Contrast

The model specifies a, b, t, p, q by the achromatic reflectance characteristics of the surfaces (objects, materials, media) and describes the reduced contrast in the superimposition area by a reflectance difference, while further developments of the model specify colors by lightness Munsell values [7], by luminance [8], or by log luminance [9]. On the other side, there is no unique shared measure of contrast, and sometimes one can use the Michelson contrast [3] which seems to supply a better fitting model, suitable to explain why usually light filters seem more opaque and dark filters more transparent, although this model too is not general [10]. In any case the filter reduces the contrast of the colors seen behind it because as they get closer, the more dense (or less transparent) is the filter [4]. Apparent contrast is further reduced by blurred edges [2].

Color contrast is relevant in determining the relative stratification of the surfaces, i.e., what is seen in front and what behind, as higher contrast results in larger distance in depth. Contrast does not depend only on color difference but also on the shape of the margins: Craik-O’Brien-Cornsweet edges (blurred versus sharpened) can invert the contrast appearance and as a consequence the relative depth of the surfaces, making transparent what was opaque and the reverse [11]. This effect can be obtained also by simple line drawings, where their contrast with the background determines the different object stratifications and the consequent transparent appearance.

A Qualitative Account of the Model in the Achromatic Domain

The possibility of perceiving transparency can be described as a function of the ordinal position of colors in the regions divided by X junctions [12, 13]. If all colors present in a transparent display are achromatic, and therefore characterized by one dimension, two ordinal conditions of transparency are prescribed by the model: |a–b| > |p–q| and p > q if a > b (or p < q if a < b). A better prediction of transparency is achieved with the single ordinal condition: p ɛ (a,q) (or q ɛ (q,b)) [14].

Another improvement of the model states that, instead of Eq. 3, the apparent density ψ (inverse of transparency) of the filter [15] depends on three color differences:
$$ \uppsi ={\mathrm{w}}_1\left|\mathrm{a}-\mathrm{p}\right|+{\mathrm{w}}_2\left|\mathrm{b}-\mathrm{q}\right|+\left(1-{\mathrm{w}}_1-{\mathrm{w}}_2\right)\left(\mathrm{k}-\left|\mathrm{p}-\mathrm{q}\right|\right) $$
where the weight coefficients w1 and w2 express a compromise between the three differences.

Transparency and Pictorial Art

Since centuries the transparency effect is used both to represent translucent or transparent objects and to enrich the color variety of a painting.

Many methods have been adopted to render transparent objects, all having in common the purpose of showing two colors, one in front and one in the back, the latter visible through the former. One method is just to put in the overlapping areas the color which would be obtained by partitive mixture of the back and the front colors (Fig. 4), following, not necessarily consciously, the episcotister model.
Transparency, Fig. 5

Ravenna: Baptistery of Aryans, fifth century (detail). Picture by Incola (Wiki) [http://it.wikipedia.org/wiki/File:Soffitto_Battistero_Ariani_Ravenna.jpg#filehistory] Water and body colors seen from some distance partitively fuse because under spatial discrimination threshold, an impression of transparency arises in the observer

Another method reaches the same results by using small mosaic tesserae to be looked at a certain distance so to produce spatial color mixtures (Fig. 5).
Transparency, Fig. 6

Hans Memling, fifteenth century. Portrait of a young lady (Sibylla Sambetha). Musea Brugge, Sint-Janshospitaal. Copy purchased from Lukas Art in Flanders, o.n. 1376 (2012)

Another method is the veiling procedure obtained through semitransparent paints, as shown in Fig. 6: the back and the transparent colors are both visible where they overlap. Lastly, a final method consists in accentuating the borders between the opaque and the transparent medium, by simulating Cornsweet edges and introducing a depth displacement between opaque and transparent surfaces.

Improvements of the Model

As the colors in plain view and those covered by the transparent medium, represented in suitable color system, according to the model converge in a point corresponding to the color t, the model has been called convergence model [4]. The convergence point can lie outside the color solid and still perception of transparency can be possible [6], although not always [16]. In this partitive model, α defines the position of the color p between the color a and the color t. According to current opinion, the colorimetric distance between the two colors a and t should not be large; otherwise, transparency perception would not occur. The reason is that [17] the color p should not be just a colorimetric intermediate between a and t, but should appear similar both to a and t, and this would be a strong condition to see both colors in the overlapping area: opponent a and t would not allow transparency. A development of the model has been proposed [17] in which the Natural Color System [18], based on the pure perceptive similarity of all color to the six Hering prototypical unique colors W K Y R B G, should be used to describe the relevant color relationships in transparency perception (Fig. 7). The notation of colors in this system clearly shows similarity relationships and therefore the possibility of seeing two colors in a not-unique (i.e., perceptually mixed) color; spatial induction can sometimes add the necessary missing shades (especially if p is a neutral color).
Transparency, Fig. 7

In the upper part the external areas represent, in isolation, the background in plain view and the internal areas the overlapping surfaces, whose colors have been determined in the NCS. The bottom part shows the complete mosaic resulting when the separated areas are joined



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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of PsychologyUniversity of PaduaPaduaItaly