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

Gaussian mixture model based probabilistic modeling of images for medical image segmentation

In this paper, we propose a novel image segmentation algorithm that is based on the probability distributions of the object and background. It uses the variational level sets formulation with a novel region based term in addition to the edge-based term giving a complementary functional, that can potentially result in a robust segmentation of the images. The main theme of the method is that in most of the medical imaging scenarios, the objects are characterized by some typical characteristics such a color, texture, etc. Consequently, an image can be modeled as a Gaussian mixture of distributions corresponding to the object and background. During the procedure of curve evolution, a novel term is incorporated in the segmentation framework which is based on the maximization of the distance between the GMM corresponding to the object and background. The maximization of this distance using differential calculus potentially leads to the desired segmentation results. The proposed method has been used for segmenting images from three distinct imaging modalities i.e. magnetic resonance imaging (MRI), dermoscopy and chromoendoscopy. Experiments show the effectiveness of the proposed method giving better qualitative and quantitative results when compared with the current state-of-the-art. INDEX TERMS Gaussian Mixture Model, Level Sets, Active Contours, Biomedical Engineerin

GIST: an interactive, GPU-based level set segmentation tool for 3D medical images

technical reportWhile level sets have demonstrated a great potential for 3D medical image segmentation, their usefulness has been limited by two problems. First, 3D level sets are relatively slow to compute. Second, their formulation usually entails several free parameters which can be very difficult to correctly tune for specific applications. The second problem is compounded by the first. This paper describes a new tool for 3D segmentation that addresses these problems by computing level-set surface models at interactive rates. This tool employs two important, novel technologies. First is the mapping of a 3D level-set solver onto a commodity graphics card (GPU). This mapping relies on a novel mechanism for GPU memory management. The interactive rates level-set PDE solver give the user immediate feedback on the parameter settings, and thus users can tune free parameters and control the shape of the model in real time. The second technology is the use of region-based speed functions, which allow a user to quickly and intuitively specify the behavior of the deformable model. We have found that the combination of these interactive tools enables users to produce good, reliable segmentations. To support this observation, this paper presents qualitative results from several different datasets as well as a quantitative evaluation from a study of brain tumor segmentations

A Multiresolution PDE-Based Deformable Surface for Medical Imaging Applications

We recently developed a multiresolution PDE-based deformable surface whose deformation behavior is governed by partial differential equations (PDEs) such as the weighted minimal surface flow. Comparing with the level-set approach, our new model has better control of the mesh quality and model resolution, and is much simpler to implement since all the computations are local. The new deformable model is very useful for a variety of medical imaging applications including boundary reconstruction, surface visualization, data segmentation, and topology discovery. In this paper, we demonstrate both the accuracy and robustness of our model on areas such as medical image segmentation through a number of experiments on both real (MRI/CT) and synthetic volumetric datasets

PDE-based preprocessing of medical images

Medical imaging often requires a preprocessing step where filters are applied that remove noise while preserving semantically important structures such as edges. This may help to simplify subsequent tasks such as segmentation. One class of recent adaptive denoising methods consists of methods based on nonlinear partial differential equations (PDEs). In the present paper we survey our recent results on PDE-based preprocessing methods that may be applied to medical imaging problems. We focus on nonlinear diffusion filters and variational restoration methods. We explain the basic ideas, sketch some algorithmic aspects, illustrate the concepts by applying them to medical images such as mammograms, computerized tomography (CT), and magnetic resonance (MR) images. In particular we show the use of these filters as preprocessing steps for segmentation algorithms