Survey on liver CT image segmentation methods <s> Level sets based semi-automatic methods <s> Computer-aided surgery requires the accurate registration of tomographic pre-operative images with intra-operative surface points acquired with 3D spatial localizers. Surface-based registration of these tomographic images with the surface points does, in turn, require a precise and accurate surface representation of the structures to be registered. This paper presents a level set technique for the automatic segmentation of the liver in abdominal CT scans. The main difficulty with level set methods is the design of appropriate speed functions for particular applications. Here we propose a novel speed function that is designed to (1) stop the propagating front at organ boundaries with weak edges, and (2) incorporate a-priori information on the relative position of the liver and other structures. We show that the new speed function we have designed to stop the front a weak edges is superior to other approaches proposed in the literature both on simulated images and on CT images. Results obtained with our approach for the segmentation of the liver in several CT scans are compared to contours obtained manually. <s> BIB001 </s> Survey on liver CT image segmentation methods <s> Level sets based semi-automatic methods <s> We use polyharmonic Radial Basis Functions (RBFs) to reconstruct smooth, manifold surfaces from point-cloud data and to repair incomplete meshes. An object's surface is defined implicitly as the zero set of an RBF fitted to the given surface data. Fast methods for fitting and evaluating RBFs allow us to model large data sets, consisting of millions of surface points, by a single RBF — previously an impossible task. A greedy algorithm in the fitting process reduces the number of RBF centers required to represent a surface and results in significant compression and further computational advantages. The energy-minimisation characterisation of polyharmonic splines result in a “smoothest” interpolant. This scale-independent characterisation is well-suited to reconstructing surfaces from non-uniformly sampled data. Holes are smoothly filled and surfaces smoothly extrapolated. We use a non-interpolating approximation when the data is noisy. The functional representation is in effect a solid model, which means that gradients and surface normals can be determined analytically. This helps generate uniform meshes and we show that the RBF representation has advantages for mesh simplification and remeshing applications. Results are presented for real-world rangefinder data. <s> BIB002 </s> Survey on liver CT image segmentation methods <s> Level sets based semi-automatic methods <s> In this paper, we evaluate a semi-automatic liver segmentation method based on a level-set approach and a dynamically adapted speed func- tion. The approach also relies on a-priori anatomic information to reduce leak- age at the liver-rib interface. The numerical algorithms have been integrated into a complete system that permits loading DICOM images, segmenting these images, and visualizing the liver surface. Although the normal operation of the system assumes manual contour corrections, such corrections were not allowed for this evaluation. Results show that except for cases with large tumors that ex- tend to the liver surface, the method we propose is comparable to a human rater. <s> BIB003 </s> Survey on liver CT image segmentation methods <s> Level sets based semi-automatic methods <s> The automatic segmentation of complex anatomical struc- tures often fails due to low-contrast or missing edges, pathologic alter- ations, or high noise. As an alternative, we propose a novel two-stage semi-automatic algorithm that is able to segment complex structures like the liver shape with moderate user interaction. The first stage of our algorithm is the manual delineation of cross-sections of the anatom- ical structure in 2-D multi-planar reconstruction views. From this set of contours, an initial 3-D surface is reconstructed using radial basis func- tions. In a second step, the surface is evolved using a level set algorithm incorporating a new combination of both image information and shape information, the latter being derived from the initial contours. The al- gorithm has been evaluated for 10 Computed Tomography scans of the liver and has shown promising results. <s> BIB004
Level sets algorithm is involved in the image segmentation problem by asking the user to draw a rough contour outside or inside the object, and then the contour will shrink/extend. When the contour meets the boundary of the object, the shrinking/extending procedure will be ended. The speed function plays the main role in controlling the direction of contour shrinking/growing and finding the end point of the procedure. Liver segmentation methods under this class are divided to two subclasses; 2D level sets methods and 3D level sets methods. BIB003 proposed a liver segmentation method based on 2D level sets with a dynamic speed function. In their method, a rough contour inside the liver tissue is created manually in a number of CT slices. A novel speed function defined by BIB001 was employed. The speed function is adapted dynamically with the pass of each iteration. The basic principle of the designing of the speed function is that the system doesn't have to stop when the speed function is equal to zero over the organ boundary. Instead, the system will track the contour path and use this information in the speed function definition. When the contour passes over isolated pixels that are likely to be a part of the liver boundary, it keeps the propagation process. If it passes over a sequence of several boundary pixels, the propagation process slows down exponentially. The process will continue in that manner until it stopped. Thresholding and morphological operations suggested by  are employed to extract rib cage, subcostal fat and skin before the level sets method implementation; results of the extraction step are used as a blocking regions in the speed function. At the end, when all CT images with user intervention are segmented, results are interpolated to the remaining CT images. The approach described by BIB004 is a 3D level set method which requires a medium level of intervention for the segmentation of liver in CT slices. The user selects a number of 2D contours in image planes re-sampled from various directions (preferably orthogonal to each other). Contours are defined by placing points on the liver boundary, which are interpolated using cubic splines. After the user has set 6-8 contours, radial basis functions proposed by BIB002 are employed to generate a smooth surface passing through all contours and interpolating in between. This surface is used as initialization for an edge-based geodesic active contour. As it is usually close to the true liver boundary, no constant speed forces are required during the level set evolution. The distance of the current level set surface to the user-specified input contours is used as additional shape-preserving term.