Virtual colonoscopy (VC) has gained popularity as a new colon diagnostic method over the last decade. VC is a new,
less invasive alternative to the usually practiced optical colonoscopy for colorectal polyp and cancer screening, the
second major cause of cancer related deaths in industrial nations. Haustral (colonic) folds serve as important landmarks
for virtual endoscopic navigation in the existing computer-aided-diagnosis (CAD) system. In this paper, we propose and
compare two different methods of haustral fold detection from volumetric computed tomographic virtual colonoscopy
images. The colon lumen is segmented from the input using modified region growing and fuzzy connectedness. The first
method for fold detection uses a level set that evolves on a mesh representation of the colon surface. The colon surface is
obtained from the segmented colon lumen using the Marching Cubes algorithm. The second method for fold detection,
based on a combination of heat diffusion and fuzzy c-means algorithm, is employed on the segmented colon volume.
Folds obtained on the colon volume using this method are then transferred to the corresponding colon surface. After
experimentation with different datasets, results are found to be promising. The results also demonstrate that the first
method has a tendency of slight under-segmentation while the second method tends to slightly over-segment the folds.
The Iterative Closest Point (ICP) algorithm is an efficient and popular technique for surface registration. It however
suffers from the well-known problem of local minima that make the algorithm stop before it reaches the desired global
solution. ICP can be improved by the use of landmarks or features. We recently developed a level set capable of evolving on the surface of an object represented by a triangular mesh. This level set permits the segmentation of portions of a surface based on curvature features. The boundary of a segmented portion forms a ridgeline/crestline. We show that the ridgelines/crestlines and corresponding enclosed surfaces extracted by the algorithm can substantially improve ICP registration. We compared the performance of an ICP algorithm in three setups: 1) ICP without landmarks. 2) ICP using ridgelines. 3) ICP using ridgelines and corresponding enclosed surfaces. Our material consists of vertebral body surfaces
extracted for a study about the progression of Ankylosing Spondylitis. Same vertebrae scanned at intervals of one or two
years were rigidly registered. Vertebral body rims and the end plate surfaces they enclose were used as landmarks. The performance measure was the mean error distance between the registered surfaces. From the one hundred registrations that we performed the average mean error was respectively 0.503mm, 0.335mm and 0.254mm for the three setups. Setup 3 almost halved the average error of setup 1. Moreover the error range is dramatically reduced from [0.0985, 2.19]mm to just [0.0865, 0.532]mm, making the algorithm very robust.
Knowledge of the acetabular rim and surface can be invaluable for hip surgery planning and dysplasia evaluation. The acetabular rim can also be used as a landmark for registration purposes. At the present time acetabular features are mostly extracted manually at great cost of time and human labor. Using a recent level set algorithm that can evolve on the surface of a 3D object represented by a triangular mesh we automatically extracted rims and surfaces of acetabulae.
The level set is guided by curvature features on the mesh. It can segment portions of a surface that are bounded by a line of extremal curvature (ridgeline or crestline). The rim of the acetabulum is such an extremal curvature line. Our material consists of eight hemi-pelvis surfaces. The algorithm is initiated by putting a small circle (level set seed) at the center of the acetabular surface. Because this surface distinctively has the form of a cup we were able to use the Shape Index feature to automatically extract an approximate center. The circle then expands and deforms so as to take the shape of the acetabular rim. The results were visually inspected. Only minor errors were detected. The algorithm also proved to be robust. Seed placement was satisfactory for the eight hemi-pelvis surfaces without changing any parameters. For the level set evolution we were able to use a single set of parameters for seven out of eight surfaces.
Validating segmentation algorithms remains a difficult problem. Manual segmentation taken as gold standard is timeconsuming
and can still be contentious especially in the case of complex 3D objects and in the presence of important partial volume effect (PVE). In contrast digital phantoms have well-defined built-in boundaries even when PVE is simulated. However their degree of realism is questionable. In particular the rich natural structures inside an object that constitute one of the most difficult obstacles to segmentation are to this day too complex to model. A new method for
constructing semi-synthetic digital phantoms was recently proposed that incorporates natural structured noise and
boundary inhomogeneities. However only one phantom was presented and validation was lacking. In the present work we constructed 5 phantoms of vertebral bodies. Validation of phantoms should test their ability to predict how an algorithm will perform when confronted to real data. Our phantoms were used to compare the performance of two level set based segmentation algorithms and find the parameters that optimize their performances. We validated the phantoms by correlating the results obtained on them with those obtained on 50 real vertebrae. We show that: 1) the phantoms accurately predict which segmentation algorithm will perform better with real clinical data. 2) by combining the results obtained by the 5 different phantoms we can extract useful predictions about the performance of different sets of parameters on real data. Because the phantoms possess the high variability of real data predictions based on only one phantom would fail.
We describe an algorithm for evolving a level set on a non-planar manifold like the isosurface of a 3D object. The
surface is represented by a triangular mesh and the feature that guides our level set via a speed function is its curvature.
We overcome the difficulty of computing the gradient and curvature of the level set distance function on a non-planar,
non-Cartesian mesh by performing the calculations locally in neighborhoods small enough to be considered planar.
Moreover we use a least squares estimation of derivatives to replace finite differences and achieve better accuracy. The
algorithm was motivated by our need to detect the ridge lines of vertebral bodies. The advantage of using level sets is
that they are capable of producing a continuous ridge line despite noise and gaps in the ridge. We tested our algorithm on
40 vertebral bodies (80 ridge lines). 76 ridge lines showed no noticeable mistakes. The same set of parameters was used.
For the remaining 4, we had to change the parameters of the speed function sigmoid to correct small under- or over-segmenting.
To further test our algorithm we designed a synthetic surface with large curvature and to which we added
noise and a ridge. The level set was able to evolve on the surface and stop at the ridge. Tests on synthetic cylinders with
a ground truth ridge and to which we added noise indicate that the level set has good accuracy.
Ankylosing Spondylitis is a disease of the vertebra where abnormal bone structures (syndesmophytes) grow at intervertebral disk spaces. Because this growth is so slow as to be undetectable on plain radiographs taken over years, it is necessary to resort to computerized techniques to complement qualitative human judgment with precise quantitative measures on 3-D CT images. Very fine segmentation of the vertebral body is required to capture the small structures caused by the pathology. We propose a segmentation algorithm based on a cascade of three level set stages and requiring no training or prior knowledge. First, the noise inside the vertebral body that often blocks the proper evolution of level set surfaces is attenuated by a sigmoid function whose parameters are determined automatically. The 1st level set (geodesic active contour) is designed to roughly segment the interior of the vertebra despite often highly inhomogeneous and even discontinuous boundaries. The result is used as an initial contour for the 2nd level set (Laplacian level set) that closely captures the inner boundary of the cortical bone. The last level set (reversed Laplacian level set) segments the outer boundary of the cortical bone and also corrects small flaws of the previous stage. We carried out extensive tests on 30 vertebrae (5 from each of 6 patients). Two medical experts scored the results at intervertebral disk spaces focusing on end plates and syndesmophytes. Only two minor segmentation errors at vertebral end plates were reported and two syndesmophytes were considered slightly under-segmented.
A technique for the experimental implementation of fully complex filters with commercially available spatial light modulators (SLMs) is reported. The filters are incorporated into an all-optical correlator and a hybrid digital-optical correlator, the relative merits of each configuration being considered. Various filter functions requiring complex modulation are demonstrated, consideration being given to the degradation of filter performance due to the limited quantization and dynamic range with which they can be implemented using current SLM technology.