Development of an image processing based algorithm to define trabecular bone mechanical properties using the fabric tensor concept
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Bone is as structure that is extensively studied. Many studies attempt to understand the mechanical behaviour of bone tissue. One key factor to fully understand and predict its structural response is the accurate determination of its mechanical properties. As the bone morphology changes (resulting from bone adaptation to external loads), bone tissue mechanical properties change as well. Therefore, its estimation is a never-ending challenging task. In this work, it was developed a methodology that allows, using medical images of micro-CT, to define the mechanical properties of trabecular bone, based on its morphological structure. This methodology uses the fabric tensor concept and a phenomenological material law to estimate the mechanical properties. The developed methodology as overall error of 2% upon the detection of trabecular bone material principal direction.Keywords:
Structure tensor
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The tensor eigenproblem has many important applications.This paper studies the eigenproblem for tensor and tensor transposition,and proves that the mode-pi eigenpair of tensor is the same as the mode-i eigenpair of p-transposition of tensor.It is illustrated by examples that the mode-i eigenvalue of tensor is not necessarily equal to that of p-transposition of tensor,and the eigenvectors corresponding to the mode-i eigenvalue μi and the mode-j eigenvalue μj are not orthogonal when μi≠μj.Therefore,the results show that the properties of eigenvalues of matrix can not be completely extended to tensor.Based on this conclusion,this paper gives a condition that the index vector p should satisfy when the mode-i eigenpair of tensor is equal to that of the p-transposition of tensor.
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We present a novel nonlocal mean (NLM) algorithm using an anisotropic structure tensor to achieve higher accuracy of imaging denoising and better preservation of fine image details. Instead of using the intensity to identify the pixel, the proposed algorithm uses the structure tensor to characterize the boundary information around the pixel more comprehensively. Meanwhile, similarity of the structure tensor is computed in a Riemannian space for more rigorous comparison, and the similarity weight of the pixel (or patch) is determined by the intensity and structure tensor simultaneously. The proposed algorithm is compared with the original NLM algorithm and a modified NLM algorithm that is based on the principle component analysis. Quantitative and qualitative comparisons of the three NLM algorithms are presented as well.
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Unexploded ordnance
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