Segmentation and Restoration of Images on Surfaces by Parametric Active Contours with Topology Changes

In this article, a new method for segmentation and restoration of images on two-dimensional surfaces is given. Active contour models for image segmentation are extended to images on surfaces. The evolving curves on the surfaces are mathematically described using a parametric approach. For image restoration, a diffusion equation with Neumann boundary conditions is solved in a postprocessing step in the individual regions. Numerical schemes are presented which allow to efficiently compute segmentations and denoised versions of images on surfaces. Also topology changes of the evolving curves are detected and performed using a fast sub-routine. Finally, several experiments are presented where the developed methods are applied on different artificial and real images defined on different surfaces

Segmentation of Three-dimensional Images with Parametric Active Surfaces and Topology Changes

In this paper, we introduce a novel parametric method for segmentation of three-dimensional images. We consider a piecewise constant version of the Mumford-Shah and the Chan-Vese functionals and perform a region-based segmentation of 3D image data. An evolution law is derived from energy minimization problems which push the surfaces to the boundaries of 3D objects in the image. We propose a parametric scheme which describes the evolution of parametric surfaces. An efficient finite element scheme is proposed for a numerical approximation of the evolution equations. Since standard parametric methods cannot handle topology changes automatically, an efficient method is presented to detect, identify and perform changes in the topology of the surfaces. One main focus of this paper are the algorithmic details to handle topology changes like splitting and merging of surfaces and change of the genus of a surface. Different artificial images are studied to demonstrate the ability to detect the different types of topology changes. Finally, the parametric method is applied to segmentation of medical 3D images

Estimation of vector fields in unconstrained and inequality constrained variational problems for segmentation and registration

Vector fields arise in many problems of computer vision, particularly in non-rigid registration. In this paper, we develop coupled partial differential equations (PDEs) to estimate vector fields that define the deformation between objects, and the contour or surface that defines the segmentation of the objects as well.We also explore the utility of inequality constraints applied to variational problems in vision such as estimation of deformation fields in non-rigid registration and tracking. To solve inequality constrained vector field estimation problems, we apply tools from the Kuhn-Tucker theorem in optimization theory. Our technique differs from recently popular joint segmentation and registration algorithms, particularly in its coupled set of PDEs derived from the same set of energy terms for registration and segmentation. We present both the theory and results that demonstrate our approach

Shape Priors in Medical Image Analysis: Extensions of the Level Set Method

The 3D medical image segmentation problem typically involves assigning labels to 3D pixels, called voxels, which comprise a given medical volume. In its simplest form the segmentation problem involves assigning the labels part of the structure of interest or not part of the structure to each voxel using locally measured properties and prior knowledge of human anatomy. Robust segmentation remains an open research problem today due to the significant challenges in the task including: partial volume averaging, overlapping intensity distributions and image noise. In the face of these challenges prior knowledge needs to be added to make the segmentation methods more robust. Active contours were introduced in the late 1980\u27s mainly to address situations in which the object to be segmented had a single closed boundary. To address situations in which the object(s) to be segmented have unknown topology the level set framework was recently introduced to segment medical images. Unlike active contours, the level set method relies on an implicit shape representation rather than an explicit shape representation and hence new methods to impose prior knowledge about expected shape have to be devised for the new framework. This paper explores recent segmentation methods from four research groups which address the task of imposing prior knowledge of shape for object boundary segmentation. Three of the methods impose priors onto the level set technique and one employs a medial axis shape representation and Statistical shape information to guide a model-based segmentation. All of the methods include a notion of a statistical shape distribution. Each method is described, analyzed for its strengths and weaknesses. The paper concludes with a comparison of all four methods and recommendations for their applicability