“Fix your gaze on the black dot on the left side of this image. But wait! Finish reading this paragraph first. As you gaze at the left dot, try to answer this question: In what direction is the object on the right moving? Is it drifting diagonally, or is it moving up and down?”
A number of problems in computer vision and related fields would be mitigated if camera spectral sensitivities were known. As consumer cameras are not designed for high-precision visual tasks, manufacturers do not disclose spectral sensitivities. Their estimation requires a costly optical setup, which triggered researchers to come up with numerous indirect methods that aim to lower cost and complexity by using color targets. However, the use of color targets gives rise to new complications that make the estimation more difficult, and consequently, there currently exists no simple, low-cost, robust go-to method for spectral sensitivity estimation that non-specialized research labs can adopt. Furthermore, even if not limited by hardware or cost, researchers frequently work with imagery from multiple cameras that they do not have in their possession.
To provide a practical solution to this problem, we propose a framework for spectral sensitivity estimation that not only does not require any hardware (including a color target), but also does not require physical access to the camera itself. Similar to other work, we formulate an optimization problem that minimizes a two-term objective function: a camera-specific term from a system of equations, and a universal term that bounds the solution space.
Different than other work, we utilize publicly available high-quality calibration data to construct both terms. We use the colorimetric mapping matrices provided by the Adobe DNG Converter to formulate the camera-specific system of equations, and constrain the solutions using an autoencoder trained on a database of ground-truth curves. On average, we achieve reconstruction errors as low as those that can arise due to manufacturing imperfections between two copies of the same camera. We provide predicted sensitivities for more than 1,000 cameras that the Adobe DNG Converter currently supports, and discuss which tasks can become trivial when camera responses are available.
The power output of a light source is measured using the unit of watts W. This is a direct measure to calculate how much power the light is going to drain from your socket and it is not relatable to the light brightness itself.
The amount of energy emitted from it per second. That energy comes out in a form of photons which we can crudely represent with rays of light coming out of the source. The higher the power the more rays emitted from the source in a unit of time.
Not all energy emitted is visible to the human eye, so we often rely on photometric measurements, which takes in account the sensitivity of human eye to different wavelenghts
Most software around us today are decent at accurately displaying colors. Processing of colors is another story unfortunately, and is often done badly.
To understand what the problem is, let’s start with an example of three ways of blending green and magenta:
Perceptual blend – A smooth transition using a model designed to mimic human perception of color. The blending is done so that the perceived brightness and color varies smoothly and evenly.
Linear blend – A model for blending color based on how light behaves physically. This type of blending can occur in many ways naturally, for example when colors are blended together by focus blur in a camera or when viewing a pattern of two colors at a distance.
sRGB blend – This is how colors would normally be blended in computer software, using sRGB to represent the colors.
Let’s look at some more examples of blending of colors, to see how these problems surface more practically. The examples use strong colors since then the differences are more pronounced. This is using the same three ways of blending colors as the first example.
Instead of making it as easy as possible to work with color, most software make it unnecessarily hard, by doing image processing with representations not designed for it. Approximating the physical behavior of light with linear RGB models is one easy thing to do, but more work is needed to create image representations tailored for image processing and human perception.
Spectralon is a teflon-based pressed powderthat comes closest to being a pure Lambertian diffuse material that reflects 100% of all light. If we take an HDR photograph of the Spectralon alongside the material to be measured, we can derive thediffuse albedo of that material.
The process to capture diffuse reflectance is very similar to the one outlined by Hable.
1. We put a linear polarizing filter in front of the camera lens and a second linear polarizing filterin front of a modeling light or a flash such that the two filters are oriented perpendicular to eachother, i.e. cross polarized.
2. We place Spectralon close to and parallel with the material we are capturing and take brack-eted shots of the setup7. Typically, we’ll take nine photographs, from -4EV to +4EV in 1EVincrements.
3. We convert the bracketed shots to a linear HDR image. We found that many HDR packagesdo not produce an HDR image in which the pixel values are linear. PTGui is an example of apackage which does generate a linear HDR image. At this point, because of the cross polarization,the image is one of surface diffuse response.
4. We open the file in Photoshop and normalize the image by color picking the Spectralon, filling anew layer with that color and setting that layer to “Divide”. This sets the Spectralon to 1 in theimage. All other color values are relative to this so we can consider them as diffuse albedo.
It lets you load any .cube LUT right in your browser, see the RGB curves, and use a split view on the Granger Test Image to compare the original vs. LUT-applied version in real time — perfect for spotting hue shifts, saturation changes, and contrast tweaks.
A LUT (Lookup Table) is essentially the modifier between two images, the original image and the displayed image, based on a mathematical formula. Basically conversion matrices of different complexities. There are different types of LUTS – viewing, transform, calibration, 1D and 3D.
Of all the pigments that have been banned over the centuries, the color most missed by painters is likely Lead White.
This hue could capture and reflect a gleam of light like no other, though its production was anything but glamorous. The 17th-century Dutch method for manufacturing the pigment involved layering cow and horse manure over lead and vinegar. After three months in a sealed room, these materials would combine to create flakes of pure white. While scientists in the late 19th century identified lead as poisonous, it wasn’t until 1978 that the United States banned the production of lead white paint.
To measure the contrast ratio you will need a light meter. The process starts with you measuring the main source of light, or the key light.
Get a reading from the brightest area on the face of your subject. Then, measure the area lit by the secondary light, or fill light. To make sense of what you have just measured you have to understand that the information you have just gathered is in F-stops, a measure of light. With each additional F-stop, for example going one stop from f/1.4 to f/2.0, you create a doubling of light. The reverse is also true; moving one stop from f/8.0 to f/5.6 results in a halving of the light.
Physically-based shading means leaving behind phenomenological models, like the Phong shading model, which are simply built to “look good” subjectively without being based on physics in any real way, and moving to lighting and shading models that are derived from the laws of physics and/or from actual measurements of the real world, and rigorously obey physical constraints such as energy conservation.
For example, in many older rendering systems, shading models included separate controls for specular highlights from point lights and reflection of the environment via a cubemap. You could create a shader with the specular and the reflection set to wildly different values, even though those are both instances of the same physical process. In addition, you could set the specular to any arbitrary brightness, even if it would cause the surface to reflect more energy than it actually received.
In a physically-based system, both the point light specular and the environment reflection would be controlled by the same parameter, and the system would be set up to automatically adjust the brightness of both the specular and diffuse components to maintain overall energy conservation. Moreover you would want to set the specular brightness to a realistic value for the material you’re trying to simulate, based on measurements.
Physically-based lighting or shading includes physically-based BRDFs, which are usually based on microfacet theory, and physically correct light transport, which is based on the rendering equation (although heavily approximated in the case of real-time games).
It also includes the necessary changes in the art process to make use of these features. Switching to a physically-based system can cause some upsets for artists. First of all it requires full HDR lighting with a realistic level of brightness for light sources, the sky, etc. and this can take some getting used to for the lighting artists. It also requires texture/material artists to do some things differently (particularly for specular), and they can be frustrated by the apparent loss of control (e.g. locking together the specular highlight and environment reflection as mentioned above; artists will complain about this). They will need some time and guidance to adapt to the physically-based system.
On the plus side, once artists have adapted and gained trust in the physically-based system, they usually end up liking it better, because there are fewer parameters overall (less work for them to tweak). Also, materials created in one lighting environment generally look fine in other lighting environments too. This is unlike more ad-hoc models, where a set of material parameters might look good during daytime, but it comes out ridiculously glowy at night, or something like that.
Here are some resources to look at for physically-based lighting in games:
SIGGRAPH 2013 Physically Based Shading Course, particularly the background talk by Naty Hoffman at the beginning. You can also check out the previous incarnations of this course for more resources.
And of course, I would be remiss if I didn’t mention Physically-Based Rendering by Pharr and Humphreys, an amazing reference on this whole subject and well worth your time, although it focuses on offline rather than real-time rendering.
As Einstein showed us, light and matter and just aspects of the same thing. Matter is just frozen light. And light is matter on the move. Albert Einstein’s most famous equation says that energy and matter are two sides of the same coin. How does one become the other?
Relativity requires that the faster an object moves, the more mass it appears to have. This means that somehow part of the energy of the car’s motion appears to transform into mass. Hence the origin of Einstein’s equation. How does that happen? We don’t really know. We only know that it does.
Matter is 99.999999999999 percent empty space. Not only do the atom and solid matter consist mainly of empty space, it is the same in outer space
The quantum theory researchers discovered the answer: Not only do particles consist of energy, but so does the space between. This is the so-called zero-point energy. Therefore it is true: Everything consists of energy.
Energy is the basis of material reality. Every type of particle is conceived of as a quantum vibration in a field: Electrons are vibrations in electron fields, protons vibrate in a proton field, and so on. Everything is energy, and everything is connected to everything else through fields.
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.
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