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SKIING WITH LAMBERT  --  SNOW, ILLUMINATION AND MACHINE VISION  (continued)


4. Lost Structure -- How Snow Turns Invisible (continued)


4.2 Snow and its Different Illuminants
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Key words:
surface structure | Lambert | angle | luminance | overcast sky | sun |



Now we look at a structured snow surface. It consists of LAMBERTian surface elements that are slanted at various ANGLEs: fig. 4_d.

fig. 4_d: snow surface elements (simplified); 3 kByte

fig. 4_d: snow surface elements (simplified)

Though snow is quite a good approximation of a LAMBERTian reflector, still real snow surfaces in the SUNshine do not look homogeneously white (i.e., without any structure). Why that? Did LAMBERT fail?
No, he didn't. Shadows are the solution. Consider fig. 4_e.

fig. 4_e: sunlit snow surface; 11 kByte

fig. 4_e: SUNlit snow surface

Where the snow structure produces an obscuration of SUNlight, only blue skylight is left over for illuminating the shadows. And so the shadows, contrasting to all the SUNlit areas, make snow SURFACE STRUCTURE visible.
The structure shines up in the good contrast between SUNlit areas (light and yellowish) and shadow areas (darker and blueish).

Compare this to the result of an illumination from OVERCAST SKY (fig. 4_f):

fig. 4_f: snow surface under overcast sky; 7 kByte

fig. 4_f: snow surface under OVERCAST SKY

This equal illumination from all spatial directions is prevailing only above the timber line and when sky is overcast.
All structure elements of the snow surface are illuminated equally and  --  according to (eqn. 5) in para. 4.1  --  will exhibit the same LUMINANCE ("brightness") to the eye.
No differences between the surface elements shine up; everything looks equally white.
Skiing under this kind of illumination feels funny:
you don't see the ups and downs of the track; you don't see your speed; you even might get dizzy when stopping.
And from these effects we can also see that snow is quite a good approximation of a LAMBERTian radiator:
the ANGLE between the snow surface and the eye does not have any influence on our seeing it bright or dim.

By the way: in laboratory, this kind of illumination is produced by "integrating spheres", sometimes called "Ulbricht spheres". An application example is shown in para. 5.2, scanning printed matters.

Now imagine a skiing track that has trees (or the dark slope of a neighbouring mountain) on one side.
Here, illumination from the OVERCAST SKY reaches the snow surface no longer from a half sphere, but from little more than a quarter sphere.
Differently slanted surface elements attain different LUMINANCEs, becoming visually discernible  --  and making the skier's visual task easier.




Continued: 5. Application / 5.1 Story from Factory Floor

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Last modified Nov.22nd, 2009