The geometric measurement of parts using a coordinate measuring machine (CMM) has been
generally adapted to the advanced automotive and aerospace industries. However, for the
geometric inspection of deformable free-form parts, special inspection fixtures, in
combination with CMM’s and/or optical data acquisition devices (scanners), are used. As a
result, the geometric inspection of flexible parts is a consuming process in terms of time
and money. The general procedure to eliminate the use of inspection fixtures based on
distance preserving nonlinear dimensionality reduction (NLDR) technique was developed in
our previous works. We sought out geometric properties that are invariant to inelastic
deformations. In this paper we will only present a systematic comparison of some
well-known dimensionality reduction techniques in order to evaluate their accuracy and
potential for non-rigid metrology. We will demonstrate that even though these techniques
may provide acceptable results through artificial data on certain fields like pattern
recognition and machine learning, this performance cannot be extended to all real
engineering metrology problems where high accuracy is needed.