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  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.
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 . 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.
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 .
The model of the episcotister applied to transparency phenomena entrains also some constraints and consequences. The most important is that α  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 p–q must be smaller than the difference a–b: 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 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 , by luminance , or by log luminance . On the other side, there is no unique shared measure of contrast, and sometimes one can use the Michelson contrast  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 . 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 . Apparent contrast is further reduced by blurred edges .
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 . 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)) .
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.
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
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