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I have two sets of 2d-data points which can be transformed in each other by using a certain transformation function (see also this question).

For question 1 I think I should calculate all the point-distances of data1 and then separately of data2. I expect it should be possible to find from this distances-information the additional anomalous points and remove them.

The distance from each point to another point of data1corrected is aproximately the same as for the points of data2corrected.

I have two sets of 2d-data points which can be transformed in each other by using a certain transformation function.

For question 1 I think I should calculate all the point-distances of data1 and then separately of data2. I expect it should be possible to find from this distances-information the additional anomalous points and remove them.

The distance from each point to another point of data1corrected is aproximately the same as for the points of data2corrected.

For what do I need a solution for the upper questions:

I would like to find the best geometric transformation between the remaining points of data1corrected and data2corrected:

trafo = 
  FindGeometricTransform[data2corrected, data1corrected, TransformationClass -> "Affine"];

which gives for each point {x, y} the coordinate transormation:

trafo[[2]][{x, y}]

{1502.56 + 1.00443 x + 0.0069496 y, -13.1299 - 0.00592912 x + 1.00225 y}

Applying this transformation to data1corrected results in:

data1correctedtransformed= trafo[[2]][data1corrected];

And finally I can plot the transormed coordinates of data1correctedtransformed together with the original points data2corrected:

ListPlot[{data2corrected, data1correctedtransformed}, 
 PlotRange -> {{1510, 1600}, {300, 900}}, PlotStyle -> {Blue, Green}, 
 Frame -> True, FrameLabel -> {{"y", ""}, {"x", 
    "data1correctedtransformed (Green), data2corrected (Blue)"}}, 
 BaseStyle -> {FontWeight -> "Bold", FontSize -> 15, 
   FontFamily -> "Calibri"}, ImageSize -> Large]