Deformable models are generally applied to simple images with smooth region boundaries. Segmentation of objects with high curvature shapes (corners) is limited by the models' finite node density and their intrinsic smoothness constraint. Previous solutions to segmentation of objects with corners are based on relating the smoothness constraint at the candidate corner nodes. While allowing a contour to bend at those nodes, these solutions do not provide a force to propel nodes into corners. In this paper, we propose a deformable model algorithm for segmenting objects containing high curvature shapes with subresolution accuracy, which provides a driving force for nodes to slide into corners along object boundaries. The algorithm can be applied to both 2D and 3D deformable models.

The problem of fitting a mesh to a surface, whether defined analytically or by image data, requires consideration of accuracy and attendant computational cost. The accuracy of the surface fit depends on the size of mesh elements. Distributing large mesh elements to surface parts with low curvature and small ones to those with high curvature enables efficient use of mesh elements. In this paper, we propose an algorithm which adapts mesh size to local surface smoothness. Changes in mesh size are accomplished by adaptively adjusting thresholds for division and merger of mesh elements. The primary motivation for developing this algorithm is image segmentation using deformable models and the algorithm was implemented in that context. Tests on a synthetic shape demonstrate the extent to which the local surface smoothness affects the mesh size.

In this paper, we propose fully 3D active surface models for image segmentation. Our models are capable of fitting a diverse range of region shapes. They have low sensitivity to initial shape and position. We design self-inflation/deflation forces, which cooperate naturally with gradient forces. They permit the active surface to travel a long distance without the aid of any external forces. They are easily controlled in both their direction and magnitude. The models produce accurate segmentation when tested with synthetic and real images. They manifest robustness to image noise and imperfect image data. Importantly, they are capable of converging to the correct boundary even if the initial estimate is not close.

This article presents a detailed description of an algorithm for the automatic detection of the mid-sagittal plane in three-dimensional (3-D) brain images. The algorithm seeks the plane with respect to which the image exhibits maximum symmetry. For a given plane, symmetry is measured by the cross-correlation between the image sections lying on either side. The search for the plane of maximum symmetry is performed by using a multiresolution approach which substantially decreases computational time. The choice of the starting plane was found to be an important issue in optimization. A method for selecting the initial plane is presented. The algorithm has been tested on brain images from various imaging modalities in both humans and animals. Results were evaluated by visual inspection by neuroradiologists and were judged to be consistently correct.

Phase unwrapping refers to the determination of phase from modulo 2pi data, some of which may not be reliable. In 2D, this is equivalent to confining the support of the phase function to one or more arbitrarily shaped regions. A phase unwrapping algorithm is presented which works for 2D data known only within a set of nonconnected regions with possibly nonconvex boundaries. The algorithm includes the following steps: segmentation to identify connectivity, phase unwrapping within each segment using a Taylor series expansion, phase unwrapping between disconnected segments along an optimum path, and filling of phase information voids. The optimum path for intersegment unwrapping is determined by a minimum spanning tree algorithm. Although the algorithm is applicable to any 2D data, the main application addressed is magnetic resonance imaging (MRI) where phase maps are useful.