The Image Foresting Transform (IFT) is a framework for image partitioning, commonly used for interactive segmentation. Given an image where a subset of the image elements (seed-points) have been assigned correct segmentation labels, the IFT completes the labeling by computing minimal cost paths from all image elements to the seed-points. Each image element is then given the same label as the closest seed-point. Here, we propose the relaxed IFT (RIFT). This modified version of the IFT features an additional parameter to control the smoothness of the segmentation boundary. The RIFT yields more intuitive segmentation results in the presence of noise and
weak edges, while maintaining a low computational complexity. We show an application of the method to the refinement of manual segmentations of a thoracolumbar muscle in magnetic resonance images. The performed study shows that the refined segmentations are qualitatively similar to the manual segmentations, while intra-user variations are reduced by more than 50%.
In this work, we describe and evaluate a semi-automatic method for liver segmentation in CT images using a
3D interface with haptic feedback and stereo graphics. Recently, we reported our fast semi-automatic method
using fast marching segmentation. Four users performed initialization of the method for 52 datasets by manually
drawing seed-regions directly in 3D using the haptic interface. Here, we evaluate our segmentation method
by computing accuracy based on newly obtained manual delineations by two radiologists for 23 datasets. We
also show that by performing subsequent segmentation with an interactive deformable model, we can increase
segmentation accuracy. Our method shows high reproducibility compared to manual delineation. The mean
precision for the manual delineation is 89%, while it is 97% for the fast marching method. With the subsequent
deformable mesh segmentation, we obtain a mean precision of 98%. To assess accuracy, we construct a fuzzy
ground truth by averaging the manual delineations. The mean sensitivity for the fast marching segmentation is
93% and the specificity is close to 100%. When we apply deformable model segmentation, we obtain a sensitivity
increase of three percentage points while the high specificity is maintained. The mean interaction time for the
deformable model segmentation is 1.5 minutes.
We present a fully 3D liver segmentation method where high accuracy and precision is efficiently obtained
via haptic interaction in a 3D user interface. Our method makes it possible to avoid time-consuming manual
delineation, which otherwise is a common option prior to, e.g., hepatic surgery planning.
We demonstrate that the volume enclosed by triangulated surfaces can be computed efficiently in the same elegant way the volume enclosed by digital surfaces is computed by digital surface integration.
Although digital surfaces are good for visualization and volume measurement, their drawback is that surface area measurements are inaccurate. On the other hand, triangulated surfaces give more accurate surface area measurements, but volume measurements and visualization are less efficient.
The T-shell data structure previously proposed retains advantages and overcomes difficulties of both the digital and the triangulated approaches. We create a lookup table with area and volume contributions for each of the 256 Marching Cubes configurations. When scanning the shell (e.g., while creating it), the surface area and volume are incrementally computed by using the lookup table and the current x co-ordinate, where the sign of the x component of the triangle normal indicates the sign of the volume contribution.
We have computed surface area and volume for digital and triangulated surfaces for digitized mathematical phantoms, physical phantoms, and real objects. The computations show that triangulated surface area is more accurate, triangulated volume follows digital volume closely, and that the values get closer to the true value with decreasing voxel size.
We present a method to simplify the structure of the surface skeleton of a 3D object, such that loss of information can be kept under control. Our approach is to prune surface border jaggedness by removing peripheral curves. The surface border is detected and all curves belonging to it are identified. Then, distance information is used to distinguish the short curves, whose voxels are possibly deleted, provided that the topology is not changed. Our method is simple, fast, and can be applied also to two-voxel thick surface skeletons. It prunes only curves which correspond to minor features of the object, without shortening the remaining more significant curves. The structure of the surface skeleton becomes significantly simplified. The simplified set can be used directly for shape representation, or as input to curve skeleton computation. If we extract the curve skeleton from the simplified set, its structure is more manageable than if the curve skeleton is obtained from the non-simplified set.
Magnetic resonance angiography (MRA) images are usually presented as maximum intensity projections (MIP), and the choice of viewing direction is then critical for the detection of stenoses. We propose a presentation method that uses skeletonization and distance transformations, which visualizes variations in vessel width independent of viewing direction. In the skeletonization, the object is reduced to a surface skeleton and further to a curve skeleton. The skeletal voxels are labeled with their distance to the original background. For the curve skeleton, the distance values correspond to the minimum radius of the object at that point, i.e., half the minimum diameter of the blood vessel at that level. The following image processing steps are performed: resampling to cubic voxels, segmentation of the blood vessels, skeletonization ,and reverse distance transformation on the curve skeleton. The reconstructed vessels may be visualized with any projection method. Preliminary results are shown. They indicate that locations of possible stenoses may be identified by presenting the vessels as a structure with the minimum radius at each point.
When interpreting and analyzing magnetic resonance angiography images, the 3D overall tree structure and the thickness of the blood vessels are of interest. This shape information may be easier to obtain from the skeleton of the blood vessels. Skeletonization of digital volume objects denotes either reduction to a 2D structure consisting of 3D surfaces, and curves, or reduction to a 1D structure consisting of 3D curves only. Thin elongated objects, such as blood vessels, are well suited for reduction to curve skeletons. Our results indicate that the tree structure of the vascular system is well represented by the skeleton. Positions for possible artery stenoses may be identified by locating local minima in curve skeletons, where the skeletal voxels are labeled with the distance to the original background.
Three-dimensional objects should be represented by 3D images. So far, most of the evaluation of images of 3D objects have been done visually, either by looking at slices through the volumes or by looking at 3D graphic representations of the data. In many applications a more quantitative evaluation would be valuable. Our application is the analysis of volume images of the causative agent of the acquired immune deficiency syndrome (AIDS), namely human immunodeficiency virus (HIV), produced by electron microscopic tomography (EMT). A structural analysis of the virus is of importance. The representation of some of the interesting structural features will depend on the orientation and the position of the object relative to the digitization grid. We describe a method of defining orientation and position of objects based on the moment of inertia of the objects in the volume image. In addition to a direct quantification of the 3D object a quantitative description of the convex deficiency may provide valuable information about the geometrical properties. The convex deficiency is the volume object subtracted from its convex hull. We describe an algorithm for creating an enclosing polyhedron approximating the convex hull of an arbitrarily shaped object.