A shape-based approach to the segmentation of medical imagery using level sets

Abstract

Abstract-We propose a shape-based approach to curve evolution for the segmentation of medical images containing known object types. In particular, motivated by the work of Leventon, Grimson, and Faugeras [15], we derive a parametric model for an implicit representation of the segmenting curve by applying principal component analysis to a collection of signed distance representations of the training data. The parameters of this representation are then manipulated to minimize an objective function for segmentation. The resulting algorithm is able to handle multidimensional data, can deal with topological changes of the curve, is robust to noise and initial contour placements, and is computationally efficient. At the same time, it avoids the need for point correspondences during the training phase of the algorithm. We demonstrate this technique by applying it to two medical applications; two-dimensional segmentation of cardiac magnetic resonance imaging (MRI) and three-dimensional segmentation of prostate MRI.Index Terms-Active contours, binary image alignment, cardiac MRI segmentation, curve evolution, deformable model, distance transforms, eigenshapes, implicit shape representation, medical image segmentation, parametric shape model, principal component analysis, prostate segmentation, shape prior, statistical shape model.

Statistical shape learning for 3D tracking

“…This can be seen in Figure 1. Interestingly, if one were to use a purely 2D shape based learning methodology like that of [17], one would have to learn every possible projection of the 3D object object onto to the 2D image plane (if no prior knowledge is given about the aspect of the projection). Moreover, and more importantly, we are able to return the 3D pose of the object, which is a drawback to the method proposed in typical 2D tracking algorithms [11].…”

“…Specifically, here we will follow the work of [6], [17]. Accordingly, we let ϕ i represent the signed distance function corresponding to a 3D surface X i .…”

“…Rearranging the column vectors back into the structure of ϕ i , we can then estimate a novel 3D shapeφ = ϕ + i=k i=0 w i ψ i , where w i is the shape weight and k is the number of principal modes used (see [17] for details). It is important to note here that we are concerned only with the zero level surface of the derived shape.…”

Edge‐detection of the radiation field in double exposure portal images using a curve propagation algorithm

“…Their algorithms compensate for the disappearance of the contour shape in images by relying on the known data. Tsai et al (21) used prior shape variation knowledge to deduce the initial contour for the Level Set method. To minimize the influence of noise, they used an energy function based on global characteristics of the image instead of the local gradient information.…”

Statistics of Pose and Shape in Multi-object Complexes Using Principal Geodesic Analysis

“…A description of the change of the object set might help to explain underlying neurobiological processes affecting brain circuits. Whereas Tsai et al [4] and Yang et al [5] describe statistical Martin Styner, Kevin Gorczowski, Tom Fletcher, Ja Yeon Jeong, Stephen M. Pizer, Guido Gerig, Multi-Object Statistics using Principal Geodesic Analysis in a Longitudinal Pediatric Study, Springer Lecture Notes in Computer Science LNCS, Proc. MIAR conference, to appear August 2006 object modeling by level-sets, we propose explicit deformable shape modeling with a sampled medial mesh representation called m-rep, introduced by Pizer et al [6].…”