The nature of coordinate metrology:
Measuring the coordinates of a spatial point goes through several steps of the hardware and software process. Each of the processing steps has its own statistical and probabilistic properties. Gaussian is the statistical and probabilistic model of the overall processing steps because multiple processing steps can be modeled as a single Gaussian process as the number of processing steps increases.
According to the Gaussian process assumed above, a measurement point is the most probable observation of an unknown spatial point closest to the measurement point. The distance between the measurement point and an unknown spatial point is the unknown measurement error.
Substitution of the object surface:
When we measure a 3-D object, we are interested in the shape, size, position, and orientation of the 3-D object. A geometric model substitutes the 3-D object surface. The minimum distances between the measurement points and the geometric model substitute the unknown measurement errors.
Orthogonal distance fitting (maximum likelihood estimation):
The best-fit geometric model minimizes the sum of the squared distances between the geometric model and the measurement points.
The minimum distances between the geometric model and the measurement points are the best discriminator for in- and outliers.
Minimal model description:
A small number of model parameters is preferred. Simple is the best. Simple is better.
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