View Full Version : Strain Tensor Interpolation

07-05-2005, 02:30 AM
Hello Biomech-L,

I am currently working on a Masterís project that involves the
measurement of strain with uCT. I am currently running into a problem
when dealing with my data sets, which are tensor fields on a regular
uniform grid (essentially I have regular nodes in x, y, z and I have the
strain tensor at the nodes). I am wondering how to go about smoothing
and interpolation of my tensor fields. I am not sure how to average
strains, as the addition of strain tensors is not well defined.

I have access to the actual transformation matrices at the nodes, which
I have used to calculate the Lagrangian strain tensor. My current
favoured method of averaging and interpolating is by multiplying local
transformation matrices together and then finding the root of this new
transformation matrix. I take this final result to be the average of the
local transformation matrices. Unfortunately this is not a method that
acts directly on the strain tensor. I am having trouble finding a lot of
literature on this problem. I have only found literature relevant to
this problem within Diffusion Tensor Imaging.

I would be grateful if someone could point me towards some relevant
publications on this subject and/or describe how they solved this
problem and why they chose a particular method.

Michael Hardisty
M.A.Sc Student
University of Toronto
Orthopaedic Biomechanics Laboratory
Sunnybrook & Women's College Health Sciences Centre
(011) 416-480-5056