In HD we often refer to the range of available colors as a color gamut. Such a color gamut is typically plotted on a two-dimensional diagram, called a CIE chart, as shown in at the top of this blog. Each color is characterized by its x/y coordinates.
Good enough for government work, perhaps. But for HDR, with its higher luminance levels and wider color, the gamut becomes three-dimensional.
For HDR the color gamut therefore becomes a characteristic we now call the color volume. It isn’t easy to show color volume on a two-dimensional medium like the printed page or a computer screen, but one method is shown below. As the luminance becomes higher, the picture eventually turns to white. As it becomes darker, it fades to black. The traditional color gamut shown on the CIE chart is simply a slice through this color volume at a selected luminance level, such as 50%.
Three different color volumes—we still refer to them as color gamuts though their third dimension is important—are currently the most significant. The first is BT.709 (sometimes referred to as Rec.709), the color gamut used for pre-UHD/HDR formats, including standard HD.
The largest is known as BT.2020; it encompasses (roughly) the range of colors visible to the human eye (though ET might find it insufficient!).
Between these two is the color gamut used in digital cinema, known as DCI-P3.
About 576 megapixels for the entire field of view.
Consider a view in front of you that is 90 degrees by 90 degrees, like looking through an open window at a scene. The number of pixels would be:
90 degrees * 60 arc-minutes/degree * 1/0.3 * 90 * 60 * 1/0.3 = 324,000,000 pixels (324 megapixels).
At any one moment, you actually do not perceive that many pixels, but your eye moves around the scene to see all the detail you want. But the human eye really sees a larger field of view, close to 180 degrees. Let’s be conservative and use 120 degrees for the field of view. Then we would see:
A measure of how large the object appears to an observer looking from that point. Thus. A measure for objects in the sky. Useful to retuen the size of the sun and moon… and in perspective, how much of their contribution to lighting. Solid angle can be represented in ‘angular diameter’ as well.
A solid angle is expressed in a dimensionless unit called a steradian (symbol: sr). By default in terms of the total celestial sphere and before atmospheric’s scattering, the Sun and the Moon subtend fractional areas of 0.000546% (Sun) and 0.000531% (Moon).
On earth the sun is likely closer to 0.00011 solid angle after athmospheric scattering. The sun as perceived from earth has a diameter of 0.53 degrees. This is about 0.000064 solid angle.
The mean angular diameter of the full moon is 2q = 0.52° (it varies with time around that average, by about 0.009°). This translates into a solid angle of 0.0000647 sr, which means that the whole night sky covers a solid angle roughly one hundred thousand times greater than the full moon.
The apparent size of an object as seen by an observer; expressed in units of degrees (of arc), arc minutes, or arc seconds. The moon, as viewed from the Earth, has an angular diameter of one-half a degree.
The angle covered by the diameter of the full moon is about 31 arcmin or 1/2°, so astronomers would say the Moon’s angular diameter is 31 arcmin, or the Moon subtends an angle of 31 arcmin.
If you have no previous experience with Unity, start with these six video tutorials which give a quick overview of the Unity interface and some important features http://unity3d.com/support/documentation/video/
import math,sys
def Exposure2Intensity(exposure):
exp = float(exposure)
result = math.pow(2,exp)
print(result)
Exposure2Intensity(0)
def Intensity2Exposure(intensity):
inarg = float(intensity)
if inarg == 0:
print("Exposure of zero intensity is undefined.")
return
if inarg < 1e-323:
inarg = max(inarg, 1e-323)
print("Exposure of negative intensities is undefined. Clamping to a very small value instead (1e-323)")
result = math.log(inarg, 2)
print(result)
Intensity2Exposure(0.1)
Why Exposure?
Exposure is a stop value that multiplies the intensity by 2 to the power of the stop. Increasing exposure by 1 results in double the amount of light.
Artists think in “stops.” Doubling or halving brightness is easy math and common in grading and look-dev. Exposure counts doublings in whole stops:
+1 stop = ×2 brightness
−1 stop = ×0.5 brightness
This gives perceptually even controls across both bright and dark values.
Why Intensity?
Intensity is linear. It’s what render engines and compositors expect when:
Summing values
Averaging pixels
Multiplying or filtering pixel data
Use intensity when you need the actual math on pixel/light data.
Formulas (from your Python)
Intensity from exposure: intensity = 2**exposure
Exposure from intensity: exposure = log₂(intensity)
Guardrails:
Intensity must be > 0 to compute exposure.
If intensity = 0 → exposure is undefined.
Clamp tiny values (e.g. 1e−323) before using log₂.
Use Exposure (stops) when…
You want artist-friendly sliders (−5…+5 stops)
Adjusting look-dev or grading in even stops
Matching plates with quick ±1 stop tweaks
Tweening brightness changes smoothly across ranges
Use Intensity (linear) when…
Storing raw pixel/light values
Multiplying textures or lights by a gain
Performing sums, averages, and filters
Feeding values to render engines expecting linear data
Examples
+2 stops → 2**2 = 4.0 (×4)
+1 stop → 2**1 = 2.0 (×2)
0 stop → 2**0 = 1.0 (×1)
−1 stop → 2**(−1) = 0.5 (×0.5)
−2 stops → 2**(−2) = 0.25 (×0.25)
Intensity 0.1 → exposure = log₂(0.1) ≈ −3.32
Rule of thumb
Think in stops (exposure) for controls and matching. Compute in linear (intensity) for rendering and math.
Note. The Median Cut algorithm is typically used for color quantization, which involves reducing the number of colors in an image while preserving its visual quality. It doesn’t directly provide a way to identify the brightest areas in an image. However, if you’re interested in identifying the brightest areas, you might want to look into other methods like thresholding, histogram analysis, or edge detection, through openCV for example.
An exposure stop is a unit measurement of Exposure as such it provides a universal linear scale to measure the increase and decrease in light, exposed to the image sensor, due to changes in shutter speed, iso and f-stop.
+-1 stop is a doubling or halving of the amount of light let in when taking a photo
1 EV (exposure value) is just another way to say one stop of exposure change.
Same applies to shutter speed, iso and aperture.
Doubling or halving your shutter speed produces an increase or decrease of 1 stop of exposure.
Doubling or halving your iso speed produces an increase or decrease of 1 stop of exposure.
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![[gamma correction test]](http://www.madore.org/~david/misc/color/gammatest.png "sRGB gamma correction test")
