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.
Diffusion MRI has become an established research tool for the investigation of tissue structure and orientation from which
has stemmed a number of variations, such as Diffusion Tensor Imaging (DTI) Diffusion Spectrum Imaging (DSI) and QBall
Imaging (QBI). The acquisition and analysis of such data is very challenging due to its complexity. Recently, an
exciting new Kalman filtering framework has been proposed for DTI and QBI reconstructions in real time during the repetition
time (TR) of the acquisition sequence. In this article, we first revisit and thoroughly analyze this approach and show
it is actually sub-optimal and not recursively minimizing the intended criterion due to the Laplace-Beltrami regularization
term. Then, we propose a new approach that implements the QBI reconstruction algorithm in real-time using a fast and
robust Laplace-Beltrami regularization without sacrificing the optimality of the Kalman filter. We demonstrate that our
method solves the correct minimization problem at each iteration and recursively provides the optimal QBI solution. We
validate with real QBI data that our proposed real-time method is equivalent in terms of QBI estimation accuracy to the
standard off-line processing techniques and outperforms the existing solution. This opens new and interesting opportunities
for real-time feedback for clinicians during an acquisition and also for researchers investigating into optimal diffusion
orientation sets and, real-time fiber tracking and connectivity mapping.
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