  Deformation estimation of elastic object assuming an internal organ is
important for the computer navigation of surgery. The aim of this study is to
estimate the deformation of an entire three-dimensional elastic object using
displacement information of very few observation points. A learning approach
with a neural network was introduced to estimate the entire deformation of an
object. We applied our method to two elastic objects; a rectangular
parallelepiped model, and a human liver model reconstructed from computed
tomography data. The average estimation error for the human liver model was
0.041 mm when the object was deformed up to 66.4 mm, from only around 3 %
observations. These results indicate that the deformation of an entire elastic
object can be estimated with an acceptable level of error from limited
observations by applying a trained neural network to a new deformation.
