Notes on Spatial Resolution [Part 1]

Although we think of 3D models as volumetric entities, most of the time they are actually just shells made out of small 2D surfaces. So how can we find the preserved resolution after an intraoral scan is post-processed? Simply counting the number of surfaces can give us a relative degree of detail. In essence: more surfaces equal better resolution.

Visual Inspection

Illustration of different resolutions on the same 3D model. Source:

When we prepare a 3D model for CAM, typically there is a choice to select different levels of resolution. Optimization of output is beyond the scope of this discussion, but suffice to say that we normally want as high a resolution as possible. Essentially, the smaller the individual 2D surfaces (also called polygons), the better.

If we assume that there is no artificial inflation of redundant polygons, then whatever model resolution we started with would represent the maximum spatial resolution possible. So in this investigation I wanted to see what is the maximum polygons per area the 3Shape TRIOS 3 can give me in comparison to the CEREC Omnicam.

First we begin with the totally unscientific method of looking with our eyeballs.

Surface model of a model scanned with 3Shape TRIOS.
Same 3Shape model with mesh structure visualized.
Surface model of a model scanned with CEREC Omnicam.
Same CEREC model with mesh structure visualized.

I would argue that the CEREC models seemed to have denser meshes in general. As we all know, at the moment the 3Shape TRIOS is the king of scanning accuracies, and so this result is somewhat surprising. Now we need to double check with some numbers.

Average Resolution of Models

PPA: points per unit area as a measurement of polygon density.

One thing that I noticed, however, is that the average PPA for the models can be manipulated simply by trimming the models. If I were cut away everything but the abutment, the averages to up to about 77.7 (3Shape) and 87.5 (CEREC). Conversely, if I analyze a full-arch model, the 3Shape average PPA drops to about 46.9. I’m not sure if this is due to programming wizardry or that larger scans tend to have more smoother (and therefore larger polygon) surfaces.

Resolution: Min, Mean, or Max?

So far we’ve only been talking about the PPA, which is an arbitrary unit that I’ve made up. If we know the density (PPA) of the mesh, then simple math and geometry can yield us the average length of the triangular mesh.

  • For our CEREC STL models, the average number of polygons per unit area is 79.
  • So each polygon covers an area of 6329 μm2
  • Assuming equilateral triangles, then the side lengths are about 120 μm.

That number seems large because it is the average, and is entirely dependent on the geometry of the model. If we scan a square box, then the average size of the polygons will be large (low resolution), but it doesn’t give us any information on how good the scanner is. In the figure below, we see a scan that is represented both by very small and extremely large polygons.

View of another CEREC STL file showing that certain areas can be represented by triangles with side lengths as large as 490 μm.

So when 3D printers and milling machine companies talk about their resolution of 100, 50, or even 25 μm, what exactly are they talking about? Average, maximum, or minimum? If we assume that embellishments are part of business routine, then I would bet good money that they’re talking about the maximum resolution (smallest size) achievable.

Going back to our CEREC models, the minimum triangle size is about 27 μm. Full disclaimer though, this was not rigorously calculated, so actual value may be a couple of microns off. Maybe.