Anisotropic resolution biases estimation of fabric from 3D gray-level images

In the present paper it is investigated how anisotropic resolution, typical for clinical imaging devices like computed tomography, influences detection of principal directions of test structures. The gray-level intensity is derived as a function of position in 3D space for network-like objects under an assumption of anisotropic blurring and then three tensors of structural anisotropy are calculated for the computed gray-level image of the object. The three approaches to compute the tensor of structural anisotropy are based on zero, first and second order derivatives of the gray-level intensity. It is shown that detection of principal directions is biased under anisotropic resolution if zero and first order approaches are used. The computation of principal values is biased for all methods under anisotropic resolution. The analytical results are supported by numerical simulations. The explanation of the observed phenomenon is given. Analogies between gray-level and binary approaches to compute tensors of structural anisotropy are sketched.