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A challenging problem in image segmentation is preventing boundary leakage through poorly resolved edges because not enough local information can be provided along them. In this article, we propose a new directional distance aided image segmentation method, formulated under the level set framework, to prevent the leakage. At each evolution step, the zero level set is extracted and smoothed. For each point on the zero level set, a new directional distance (DD) term, defined as the vector starting from itself and pointing to its counterpart on the smoothed version of the zero level set, is calculated to measure its "degree of protrusion." The evolution speed of the points that are considered to be protruding out will be penalized. Other terms, e.g., curvature and gradient terms and user specified constraints, are used along with the DD term to influence the level set evolution. Our smoothing technique augments traditional Gaussian smoothing with a new antishrinkage operation. The novelty of our method is that the DD term does not depend on intensity or gradient boundaries to regulate the regional shape and, therefore, help prevent leakage and the method incorporates vertex-based curve/surface smoothing into curve evolution under the level set framework. Experimental results show that the new DDA method achieves promising results and reasonable stability in segmenting simulated objects as well as abdominal aortic aneurysms in computed tomography (CT) angiograms, in both 2D and 3D, by preventing leakage into adjacent structures while preserving local shape details.

The tracking of lung nodules across computed tomography(CT) scans acquired at different times for the same patient is helpful for the determination of malignancy. We are developing a nodule registration system to facilitate this process. We propose to use a semi-rigid method that considers principal structures surrounding the nodule and allows relative movements among the structures. The proposed similarity metric, which evaluates both the image correlation and the degree of elastic deformation amongst the structures, is maximized by a two-layered optimization method, employing a simulated annealing framework. We tested our method by simulating five cases that represent physiological deformation as well as different nodule shape/size changes with time. Each case is made up of a source and target scan, where the source scan consists of a nodule-free patient CT volume into which we inserted ten simulated lung nodules, and the target scan is the result of applying a known, physiologically based nonrigid transformation to the nodule-free source scan, into which we inserted modified versions of the corresponding nodules at the same, known locations. Five different modification strategies were used, one for each of the five cases: (1) nodules maintain size and shape, (2) nodules disappear, (3) nodules shrink uniformly by a factor of 2, (4) nodules grow uniformly by a factor of 2, and (5) nodules grow nonuniformly. We also matched 97 real nodules in pairs of scans (acquired at different times) from 12 patients and compared our registration to a radiologist’s visual determination. In the simulation experiments, the mean absolute registration errors were 1.0 ± 0.8 mm (s.d.), 1.1 ± 0.7 mm (s.d.), 1.0 ± 0.7 mm (s.d.), 1.0 ± 0.6 mm (s.d.), and 1.1 ± 0.9 mm (s.d.) for the five cases, respectively. For the 97 nodule pairs in 12 patient scans, the mean absolute registration error was 1.4 ± 0.8 mm (s.d.).

We present a system for segmenting the human aortic aneurysm in CT angiograms (CTA), which, in turn, allows measurements of volume and morphological aspects useful for treatment planning. The system estimates a rough "initial surface," and then refines it using a level set segmentation scheme augmented with two external analyzers: The global region analyzer, which incorporates a priori knowledge of the intensity, volume, and shape of the aorta and other structures, and the local feature analyzer, which uses voxel location, intensity, and texture features to train and drive a support vector machine classifier. Each analyzer outputs a value that corresponds to the likelihood that a given voxel is part of the aneurysm, which is used during level set iteration to control the evolution of the surface. We tested our system using a database of 20 CTA scans of patients with aortic aneurysms. The mean and worst case values of volume overlap, volume error, mean distance error, and maximum distance error relative to human tracing were 95.3% +/- 1.4% (s.d.); worst case = 92.9%, 3.5% +/- 2.5% (s.d.); worst case = 7.0%, 0.6 +/- 0.2 mm (s.d.); worst case = 1.0 mm, and 5.2 +/- 2.3 mm (s.d.); worst case = 9.6 mm, respectively. When implemented on a 2.8 GHz Pentium IV personal computer, the mean time required for segmentation was 7.4 +/- 3.6 min (s.d.). We also performed experiments that suggest that our method is insensitive to parameter changes within 10% of their experimentally determined values. This preliminary study proves feasibility for an accurate, precise, and robust system for segmentation of the abdominal aneurysm from CTA data, and may be of benefit to patients with aortic aneurysms.

A challenging problem in image segmentation is preventing boundary leakage through poorly resolved edges because not enough local information can be provided along them. In this article, we propose a new directional distance aided image segmentation method, formulated under the level set framework, to prevent the leakage. At each evolution step, the zero level set is extracted and smoothed. For each point on the zero level set, a new directional distance (DD) term, defined as the vector starting from itself and pointing to its counterpart on the smoothed version of the zero level set, is calculated to measure its "degree of protrusion." The evolution speed of the points that are considered to be protruding out will be penalized. Other terms, e.g., curvature and gradient terms and user specified constraints, are used along with the DD term to influence the level set evolution. Our smoothing technique augments traditional Gaussian smoothing with a new antishrinkage operation. The novelty of our method is that the DD term does not depend on intensity or gradient boundaries to regulate the regional shape and, therefore, help prevent leakage and the method incorporates vertex-based curve/surface smoothing into curve evolution under the level set framework. Experimental results show that the new DDA method achieves promising results and reasonable stability in segmenting simulated objects as well as abdominal aortic aneurysms in computed tomography (CT) angiograms, in both 2D and 3D, by preventing leakage into adjacent structures while preserving local shape details.

The tracking of lung nodules across computed tomography (CT) scans acquired at different times for the same patient is helpful for the determination of malignancy. We are developing a nodule registration system to facilitate this process. We propose to use a semi-rigid method that considers principal structures surrounding the nodule and allows relative movements among the structures. The proposed similarity metric, which evaluates both the image correlation and the degree of elastic deformation amongst the structures, is maximized by a two-layered optimization method, employing a simulated annealing framework. We tested our method by simulating five cases that represent physiological deformation as well as different nodule shape/size changes with time. Each case is made up of a source and target scan, where the source scan consists of a nodule-free patient CT volume into which we inserted ten simulated lung nodules, and the target scan is the result of applying a known, physiologically based nonrigid transformation to the nodule-free source scan, into which we inserted modified versions of the corresponding nodules at the same, known locations. Five different modification strategies were used, one for each of the five cases: (1) nodules maintain size and shape, (2) nodules disappear, (3) nodules shrink uniformly by a factor of 2, (4) nodules grow uniformly by a factor of 2, and (5) nodules grow nonuniformly. We also matched 97 real nodules in pairs of scans (acquired at different times) from 12 patients and compared our registration to a radiologist's visual determination. In the simulation experiments, the mean absolute registration errors were 1.0+/-0.8 mm (s.d.), 1.1+/-0.7 mm (s.d.), 1.0+/-0.7 mm (s.d.), 1.0+/-0.6 mm (s.d.), and 1.1+/- 0.9 mm (s.d.) for the five cases, respectively. For the 97 nodule pairs in 12 patient scans, the mean absolute registration error was 1.4+/-0.8 mm (s.d.).