I've asked the same question at Math SE, but the suggestion is that probably this question belongs here.
Given a list of point cloud in terms of $(x,y,z)$ how to determine abnormal points?
The motivation is this. We need to reconstruct a terrain surface out from those point cloud, which the surveyors obtain when doing field survey. The surveyors would take an equipment and record a sufficient sample of the $x,y,z$ of a terrain. Those points will be recorded into a CAD program.
The problem is that the CAD file can be corrupted from time to time with the introduction of "abnormal" points. Those points do not fit into the terrain surface generally, and tend to have erroneous $z$ value ( i.e., the $z$ value is outside of the normal range).
I am aware that the definition of abnormal points is a bit loose; and I can't come up with a rigorous definition of it. However, I know what is an abnormal point when I see the drawing.
Given all these constraint, is there any algorithm to detect these kinds of abnormal points?