Nonlinear optimisation method for image segmentation and noise reduction using geometrical intrinsic properties

This paper considers the optimisation of a nonlinear functional for image segmentation and noise reduction. Equations optimising this functional are derived and employed to detect edges using geometrical intrinsic properties such as metric and Riemann curvature tensor of a smooth differentiable surface approximating the original image. Images are then smoothed using a Helmholtz type partial differential equation. The proposed approach is shown to be very efficient and robust in the presence of noise, and the reported results demonstrate better performance than the conventional derivative based edge detectors

Image Segmentation Using Active Contours Driven by the Bhattacharyya Gradient Flow

©2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.DOI: 10.1109/TIP.2007.908073This paper addresses the problem of image segmentation by means of active contours, whose evolution is driven by the gradient flow derived froman energy functional that is based on the Bhattacharyya distance. In particular, given the values of a photometric variable (or of a set thereof), which is to be used for classifying the image pixels, the active contours are designed to converge to the shape that results in maximal discrepancy between the empirical distributions of the photometric variable inside and outside of the contours. The above discrepancy is measured by means of the Bhattacharyya distance that proves to be an extremely useful tool for solving the problem at hand. The proposed methodology can be viewed as a generalization of the segmentation methods, in which active contours maximize the difference between a finite number of empirical moments of the "inside" and "outside" distributions. Furthermore, it is shown that the proposed methodology is very versatile and flexible in the sense that it allows one to easily accommodate a diversity of the image features based on which the segmentation should be performed. As an additional contribution, a method for automatically adjusting the smoothness properties of the empirical distributions is proposed. Such a procedure is crucial in situations when the number of data samples (supporting a certain segmentation class) varies considerably in the course of the evolution of the active contour. In this case, the smoothness properties of the empirical distributions have to be properly adjusted to avoid either over- or underestimation artifacts. Finally, a number of relevant segmentation results are demonstrated and some further research directions are discussed

Nonparametric statistics of image neighborhoods for unsupervised texture segmentation

technical reportIn this paper, we present a novel approach to unsupervised texture segmentation that is based on a very general statistical model of image neighborhoods. We treat image neighborhoods as samples from an underlying, high-dimensional probability density function (PDF). We obtain an optimal segmentation via the minimization of an entropy-based metric on the neighborhood PDFs conditioned on the classification. Unlike previous work in this area, we model image neighborhoods directly without preprocessing or the construction of intermediate features. We represent the underlying PDFs nonparametrically, using Parzen windowing, thus enabling the method to model a wide variety of textures. The entropy minimization drives a level-set evolution that provides a degree of spatial homogeneity. We show that the proposed approach easily generalizes, from the two-class case, to an arbitrary number of regions by incorporating an efficient multi-phase level-set framework. This paper presents results on synthetic and real images from the literature, including segmentations of electron microscopy images of cellular structures

Coupled non-parametric shape and moment-based inter-shape pose priors for multiple basal ganglia structure segmentation

This paper presents a new active contour-based, statistical method for simultaneous volumetric segmentation of multiple subcortical structures in the brain. In biological tissues, such as the human brain, neighboring structures exhibit co-dependencies which can aid in segmentation, if properly analyzed and modeled. Motivated by this observation, we formulate the segmentation problem as a maximum a posteriori estimation problem, in which we incorporate statistical prior models on the shapes and inter-shape (relative) poses of the structures of interest. This provides a principled mechanism to bring high level information about the shapes and the relationships of anatomical structures into the segmentation problem. For learning the prior densities we use a nonparametric multivariate kernel density estimation framework. We combine these priors with data in a variational framework and develop an active contour-based iterative segmentation algorithm. We test our method on the problem of volumetric segmentation of basal ganglia structures in magnetic resonance (MR) images. We present a set of 2D and 3D experiments as well as a quantitative performance analysis. In addition, we perform a comparison to several existent segmentation methods and demonstrate the improvements provided by our approach in terms of segmentation accuracy

Unsupervised Multi Class Segmentation of 3D Images with Intensity Inhomogeneities

Intensity inhomogeneities in images constitute a considerable challenge in image segmentation. In this paper we propose a novel biconvex variational model to tackle this task. We combine a total variation approach for multi class segmentation with a multiplicative model to handle the inhomogeneities. Our method assumes that the image intensity is the product of a smoothly varying part and a component which resembles important image structures such as edges. Therefore, we penalize in addition to the total variation of the label assignment matrix a quadratic difference term to cope with the smoothly varying factor. A critical point of our biconvex functional is computed by a modified proximal alternating linearized minimization method (PALM). We show that the assumptions for the convergence of the algorithm are fulfilled by our model. Various numerical examples demonstrate the very good performance of our method. Particular attention is paid to the segmentation of 3D FIB tomographical images which was indeed the motivation of our work