# Compare a 3D shape measurement with a numerical model?

GROUPS:
 Halo,I have a set of measurements of a 3D shape in the form of a rectangular array (1000 x 1000) with z-values. The matrix location represents the x,y coordinates associated with each z-value. I want to compare these measurements with a numerical (not an analytical) model of this 3D shape. I can easily convert the model to an array of z-values of the same dimension. But the measurements have some uncertainty: the xy-position of the object being measured is not precise and the object might have some tilt or even distortion. How should I fit my model to the measurement data and get a numerical comparison between the measured shape and the model? I assume there are methods around to this: there are machines which measure 3D shapes and compare the measurement to the CAD data. How to do something similar in Mathematica?Thanks a lot for your help. Maarten
4 months ago
4 Replies
 Hi Maarten,just as a little remark: In radiotherapy the comparison of 3D dose distributions (e.g. measurement vs. calculation) is a standard problem. The typical approach here is to use the "gamma evaluation" method (see e.g. this article), because discrepancies may be due to measurement errors or spacial distortions. To me your task seems to be exactly equivalent.When coding gamma evaluation with Mathematica the function Nearest might be most helpful.Regards -- Henrik