When seen from Earth, the distant Kuiper Belt Objects (KBOs or TNOs for Trans-Neptunian Objects) appear as unresolved points of light. Unresolved means that we are unable to measure the size of each object from the image because we lack the resolution. So, we need to come up with different ways to figure out the size of KBOs.
One way is to measure the flux coming from the objects at visible and infrared wavelengths. In the visible we see the KBOs because sunlight is reflected off their surface and travels back to us. So, the visible brightness of a KBOs is proportional to its projected size multiplied by its albedo (A, the fraction of light it reflects back to space). The portion of light that is not reflected (1-A) is absorbed and heats the object. This heat is then re-radiated at longer, infrared wavelengths, between 50 and 100 µm in the case of KBOs. This infrared flux is proportional to the KBO’s projected size times (1-A) which is the fraction of sunlight that was absorbed by the KBO. So, ignoring some of the more complicated details, by measuring the visible and infrared flux from a KBO we can calculate its projected size and its albedo.
Our “TNOs Are Cool” large programme observed about 150 KBOs and Centaurs to measure their infrared flux. These data were combined with visible observations from the ground to obtain sizes and albedos for the objects. The figure below shows the albedo of the objects (how far right along the horizontal axis they lie, and the brightness of the objects) plotted against their colour (redder objects are shown further along the vertical axis). The relative size of each object is also shown. The approximately egg-like shape of some of the objects (e.g. Haumea shown bottom-right) are also drawn.