Identifying the best fitting 3D deformation model using information criteria

Abstract

3D deformation studies are usually based on 12-parameter affine transformation model. Deformation part of this model is expressed with three scale factors and three skew parameters along x, y, z axes. However, actual deformation of the monitored object may have a different structure than the one prescribed by this model. For instance, there may exist skewness along only xy plane, or one dilation along only z-axis. In this sense, we encounter with possible fifteen different deformation models such as 7-parameter (similarity), 8-parameter affine, 10-parameter affine, etc. The question arising is which one fits best to the coordinates. For this aim, we use Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The efficiencies of these criteria are studied within many deformation examples using Monte-Carlo simulations. According to the numerical examples, both criteria can detect the true model successfully with a success rate ranging from 53 to 97% if the deformation parameter is three times bigger than its standard error.