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24 February 2012 Estimation of trabecular thickness in gray-scale images through granulometric analysis
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Abstract
This paper extends to gray-scale the method proposed by Hildebrand and Rüegsegger for estimating thickness of trabecular bone, which is the most used in trabecular bone research, where local thickness at a point is defined as the diameter of the maximum inscribed ball that includes that point. The proposed extension takes advantage of the equivalence between this method and the opening function computed for the granulometry generated by the opening operation of mathematical morphology with ball-shaped structuring elements of different diameter. The proposed extension (a) uses gray-scale instead of binary mathematical morphology, (b) uses all values of the pattern spectrum of the granulometry instead of the maximum peak as used for binary images, (c) corrects bias on local thickness estimations generated by partial volume effects, and (d) uses the gray-scale as a weighting function for global thickness estimation. The proposed extension becomes equivalent to the original method when it is applied to binary images. A new non-flat structuring element is also proposed in order to reduce the discretization errors generated by traditional flat structuring elements. Translation invariance can be attained by up-sampling the images through interpolation by a factor of two. Results for synthetic and real images show that the quality of the measurements obtained through the original method strongly depends on the binarization process, whereas the measurements obtained through the proposed extension do not. Consequently, the proposed extension is more appropriate for images with limited resolution where binarization is not trivial.
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Rodrigo Moreno, Magnus Borga, and Örjan Smedby "Estimation of trabecular thickness in gray-scale images through granulometric analysis", Proc. SPIE 8314, Medical Imaging 2012: Image Processing, 831451 (24 February 2012); https://doi.org/10.1117/12.906734
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