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Compare a 3D shape measurement with a numerical model?

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
POSTED BY: Maarten van der Burgt
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Dear Henrik, John,

Thanks a lot. I was already looking into Image3D, but I am afraid the processing could get slow. Thanks for the link to the gamma dose paper. Still hope to get some reply from somebody who is familiar with comparing mechanical CAD models with a 3D measurement data set.

Best regards, Maarten
POSTED BY: Maarten van der Burgt
Anonymous User
Anonymous User
Posted 9 years ago

More briefly: if you use Scaled (make all vertex are reals between 0 and 1) and ImageSize, you can fixate any graphic (relative) to being measurable on-screen and on-paper. If you want to calculate another way: see above or keep looking, Mathematica has many features that can "automate" calculation of area and volume for you.
POSTED BY: Anonymous User
Anonymous User
Anonymous User
Posted 9 years ago
POSTED BY: Anonymous User

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

POSTED BY: Henrik Schachner
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