Hmm could you describe the grain of wood using eigenvectors/values? I think so... take the individual cell as an ellipsoid and the quadratic form eigenvectors will give you axial, radial, and transverse directions. Not sure how to get at the macrostructure like tree rings though.
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You might actually be able to measure that directly using DTI MRI. Or at any rate use the eigenvalues of some effective diffusion tensor to compute it
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