Image segmentation of trabecular spongiosa by visual inspection of the gradient magnitude

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Abstract
Recent advances in physical models of skeletal dosimetry utilize high-resolution 3-dimensional microscopic computed tomography images of trabecular spongiosa. These images are coupled to radiation transport codes to assess energy deposition within active bone marrow and trabecular endosteum. These transport codes rely primarily on the segmentation of the spongiosa images into bone and marrow voxels. Image thresholding has been the segmentation of choice for bone sample images because of its extreme simplicity. However, the ability of the segmentation to reproduce the physical boundary between bone and marrow depends on the selection of the threshold value. Statistical models, as well as visual inspection of the image, have been employed extensively to determine the correct threshold. Both techniques are affected by partial volume effect and can provide unexpected results if performed without care. In this study, we propose a new technique to threshold trabecular spongiosa images based on visual inspection of the image gradient magnitude. We first show that the gradient magnitude of the image reaches a maximum along a surface that remains almost independent of partial volume effect and that is a good representation of the physical boundary between bone and marrow. A computer program was then developed to allow a user to compare the position of the iso-surface produced by a threshold with the gradient magnitude. The threshold that produces the iso-surface that best coincides with the maximum gradient is chosen. The technique was finally tested with a set of images of a true bone sample with different resolutions, as well as with three images of a cube of Duocell aluminium foam of known mass and density. Both tests demonstrate the ability of the gradient magnitude technique to retrieve sample volumes or media volume fractions with 1% accuracy at 30 microm voxel size.