A Combined Shape-Newton and Topology Optimization Technique in Real-Time Image Segmentation

Recent computational challenges in image segmentation are due to image guided surgery, in particular brain surgery. In a preoperative phase high resolution images, e.g., magnet-resonance images (MRIs), of a patient are taken, enhanced (denoised, deblurred,...) and then used for a 3D rendering of the region of interest which includes a segmentation phase for giving a precise account of tumor boundaries. Based on this reconstruction the surgeon plans the operative intervention. In brain surgery, where high precision is required, any intervention changes the local situation, e.g., the tumor location. Therefore, in modern regimes [8, 19, 20] a correction of the segmented image is attempted intraoperatively by taking new MRI scans and re-doing the image processing part. This should ideally reduce the operation time and accurately guide the surgeon. Besides certain modelling aspects, on the computational side this poses several challenges such as the fast and reliable segmentation. In image segmentation, which is the task of identifying boundary curves (contours) of regions of approximately homogeneous features, there are several paradigm models such as edge detectors, Mumford-Shah model, shape-based approaches, discrete approaches ... which address different aspects in the segmentation. In this

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