Estimation of elastic deformation by partial observation with kernel method

Abstract

It is expected to support surgical navigation by estimating the deformation of the whole organ from the deformation information of the partially observed organs in the surgical operation. In this study, we estimated the deformation of 3-dimensional elastic body simulated by nonlinear finite element method, assuming the situation of gripping organs with forceps and applying force to deform during endoscopic surgery. As an approach to learn deformation, we estimated the displacement based on the data using the regression with the kernel method. Kernel method allow to learn the displacement without depending on the initial value of parameters for learning and suppress learning time. In actual elastic deformation, observation can only be performed in a partial range, and the displacement of only few points can be tracked. So, we estimated displacement of whole elastic object from the displacement information of only the very few mesh vertices which were observable points.