In my announcement of the Green Marble 4 global satellite image mosaic i mentioned that i am moving to a 32 bit per channel color representation in processing of the data. I here want to explain the background of this development a bit.

Color representation basics

Color images in computer systems, for example on websites like this, are commonly represented with 8 bit per channel. That allows for 256 different levels of intensity or for 16.7 million different colors in a color image as it is commonly advertised. That is fairly coarse and only works reasonably well because these intensity levels are defined non-linearly in a way that happens to roughly match the physiology of human color perception. I won’t go into the details of that here – it has to do with the physical characteristics of the CRTs which were used as computer displays.

Anyway – for recording images in cameras this has long been insufficient and most digital cameras use 12 or 14 bit color representations (equivalent to 4096 or 16384 levels), older models sometimes also 10 bit (1024 levels). Earth observation satellites roughly match this development.

These raw values are typically cast into a 16 bit representation for further processing – both in digital photography and with earth observation satellites. When you download optical satellite imagery today for analytic applications this is almost always in the form of 16 bit per channel data.

Reflectance representation conventions

The most common form of distributing optical satellite imagery is as reflectance values. Reflectance is a unit-less quantity where a value of 1.0 means at a certain point in the image as much light is recorded as you’d expect to come from a horizontal surface that is a perfect diffuse reflector under the lighting conditions the image is recorded at.

By almost universal convention these values are scaled with a factor of 10000 for representation in 16 bit values. Sometimes, in addition, an offset is applied as well to be able to represent negative reflectances in unsigned 16 bit values – but that is not of much interest here.

Many readers might ask: Why use factor of only 10000 when the full range of 16 bit values (65536 levels) is available. The reason is that reflectance values routinely exceed 1.0. This can be easily understood based on the definition i gave above. If you have a low sun position a mountain slope facing the sun will reflect significantly more light than a horizontal surface. So even if it is not a perfect diffuse reflector it will frequently exceed a reflectance of 1.0. Hence you practically need significant headroom above a reflectance of 1.0 – which is why a scale factor of 10000 makes sense.

Noise

The next question you might ask: Is this representation of reflectance values (integers with a scale factor of 10000) sufficient for an accurate representation of the recorded data?

The answer to that is yes – as long as

• we are talking about individual images.
• we are talking about data in the visible range of the spectrum.

And most importantly: This is also still going to apply in the future with further improvements in sensor technology.

The reason for that lies in the Earth atmosphere. Whenever a satellite image is recorded it will inevitably contain not only light from the Earth surface but also from the Earth atmosphere. We can try to compensate for the atmosphere part when processing the images – but that compensation is for the bulk effect only. It does not eliminate the noise.

All signal recorded by a satellite image sensor, whether it comes from the Earth surface or from the atmosphere, is subject to noise. And with noise here i do not mean noise from the sensor or from the signal processing in the satellite, i am talking about noise that is already present in the light before it reaches the satellite. This noise is unavoidable and inherently limits the dynamic range of satellite image data. Because of that a dynamic range of 10000 in the data representation is – under the constraints i listed – more than sufficient for an accurate representation of satellite image data.

Aggregation

That is not the end of the story of course. The photon shot noise i discussed follows a well known mathematical characteristic: It is proportional to the square root of the signal. In other words: You can reduce the amount of noise relative to the signal and thereby improve the signal-to-noise ratio and the dynamic range by recording more light. But because of the square root relationship you need a lot more light to have a substantial effect.

There are two potential ways to exploit this possibility:

• You can build larger satellites with larger optics. That is rather costly of course.
• You can combine multiple images.

The latter is what i do when producing a pixel statistics mosaic like the Green Marble. And when combining thousands of individual images in areas with very low surface reflectance you can reach the limits of the standard integer representation of reflectance values with a scale factor of 10000. Here is a practical example to illustrate that. First the area in standard tone mapping.

This shows several fairly dark reefs in an even darker sea area in the Caribbean Sea between Jamaica and Nicaragua/Honduras. With a brighter tone mapping this becomes better visible.

The open ocean away from the reefs is of a very dark blue color with an extremely low red color reflectance. And if we further contrast emphasize this area we can actually get to see the residual noise and work out the difference between the Green Marble 3 and 4 here.

In comparison the Green Marble 4 has a lower noise level overall but in particular note it lacks the posterization in contrast to the Green Marble 3. The banding visible in both images is the result of images with different viewing direction being combined with less-than-perfect compensation for the differences in view geometry.

Conclusions

Practically reaching the limit of standard integer surface reflectance representation in visible range satellite image aggregation – as i have demonstrated here – marks a significant milestone in satellite image processing methodology. So far practical relevance for users of the Green Marble is small. Even users of the linear surface reflectance data who do their own custom color processing will in most cases be able to work with the 16 bit version as before without measurable disadvantages.

What this, however, demonstrates is that pixel statistics mosaicing methods – in addition to the main function of assembling a uniform, representative depiction of the Earth surface from individually incomplete and flawed images due to less-than-perfect viewing conditions – are in principle capable to generate images of higher inherent quality than the original individual images that are used as a source.