A variational approach to bone segmentation in CT images

We present a variational approach for segmenting bone structures in Computed Tomography (CT) images. We introduce a novel functional on the space of image segmentations, and subsequently minimize this functional through a gradient descent partial differential equation. The functional we propose provides a measure of similarity of the intensity characteristics of the bone and tissue regions through a comparison of their cumulative distribution functions; minimizing this similarity measure therefore yields the maximal separation between the two regions. We perform the minimization of our proposed functional using level set partial differential equations; in addition to numerical stability, this yields topology independence, which is especially useful in the context of CT bone segmentation where a bone region may consist of several disjoint pieces. Finally, we present an extensive validation of our method against expert manual segmentation on CT images of the wrist, ankle, foot, and pelvis.