Statistical Model of Shape Moments with Active Contour Evolution for Shape Detection and Segmentation

This paper describes a novel method for shape representation and robust image segmentation. The proposed method combines two well known methodologies, namely, statistical shape models and active contours implemented in level set framework. The shape detection is achieved by maximizing a posterior function that consists of a prior shape probability model and image likelihood function conditioned on shapes. The statistical shape model is built as a result of a learning process based on nonparametric probability estimation in a PCA reduced feature space formed by the Legendre moments of training silhouette images. A greedy strategy is applied to optimize the proposed cost function by iteratively evolving an implicit active contour in the image space and subsequent constrained optimization of the evolved shape in the reduced shape feature space. Experimental results presented in the paper demonstrate that the proposed method, contrary to many other active contour segmentation methods, is highly resilient to severe random and structural noise that could be present in the data

Learning the dynamics and time-recursive boundary detection of deformable objects

We propose a principled framework for recursively segmenting deformable objects across a sequence of frames. We demonstrate the usefulness of this method on left ventricular segmentation across a cardiac cycle. The approach involves a technique for learning the system dynamics together with methods of particle-based smoothing as well as non-parametric belief propagation on a loopy graphical model capturing the temporal periodicity of the heart. The dynamic system state is a low-dimensional representation of the boundary, and the boundary estimation involves incorporating curve evolution into recursive state estimation. By formulating the problem as one of state estimation, the segmentation at each particular time is based not only on the data observed at that instant, but also on predictions based on past and future boundary estimates. Although the paper focuses on left ventricle segmentation, the method generalizes to temporally segmenting any deformable object

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

Shape and data-driven texture segmentation using local binary patterns

We propose a shape and data driven texture segmentation method using local binary patterns (LBP) and active contours. In particular, we pass textured images through a new LBP-based filter, which produces non-textured images. In this “filtered” domain each textured region of the original image exhibits a characteristic intensity distribution. In this domain we pose the segmentation problem as an optimization problem in a Bayesian framework. The cost functional contains a data-driven term, as well as a term that brings in information about the shapes of the objects to be segmented. We solve the optimization problem using level set-based active contours. Our experimental results on synthetic and real textures demonstrate the effectiveness of our approach in segmenting challenging textures as well as its robustness to missing data and occlusions

Statistical Region Based Segmentation of Ultrasound Images

Segmentation of ultrasound images is a challenging problem due to speckle, which corrupts the image and can result in weak or missing image boundaries, poor signal to noise ratio, and diminished contrast resolution. Speckle is a random interference pattern that is characterized by an asymmetric distribution as well as significant spatial correla- tion. These attributes of speckle are challenging to model in a segmentation approach, so many previous ultrasound segmentation methods simplify the problem by assuming that the speckle is white and/or Gaussian distributed. Unlike these methods, in this paper we present an ultrasound-specific segmentation approach that addresses both the spatial correlation of the data as well as its intensity distribution. We first decorrelate the image and then apply a region-based active contour whose motion is derived from an appropri- ate parametric distribution for maximum likelihood image segmentation. We consider zero-mean complex Gaussian, Rayleigh, and Fisher-Tippett flows, which are designed to model fully formed speckle in the in-phase/quadrature (IQ), envelope detected, and display (log compressed) images, respectively. We present experimental results demon- strating the effectiveness of our method, and compare the results to other parametric and non-parametric active contours

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

Colour, texture, and motion in level set based segmentation and tracking

This paper introduces an approach for the extraction and combination of different cues in a level set based image segmentation framework. Apart from the image grey value or colour, we suggest to add its spatial and temporal variations, which may provide important further characteristics. It often turns out that the combination of colour, texture, and motion permits to distinguish object regions that cannot be separated by one cue alone. We propose a two-step approach. In the first stage, the input features are extracted and enhanced by applying coupled nonlinear diffusion. This ensures coherence between the channels and deals with outliers. We use a nonlinear diffusion technique, closely related to total variation flow, but being strictly edge enhancing. The resulting features are then employed for a vector-valued front propagation based on level sets and statistical region models that approximate the distributions of each feature. The application of this approach to two-phase segmentation is followed by an extension to the tracking of multiple objects in image sequences

Statistical region based active contour using a fractional entropy descriptor: Application to nuclei cell segmentation in confocal microscopy images

We propose an unsupervised statistical region based active contour approach integrating an original fractional entropy measure for image segmentation with a particular application to single channel actin tagged fluorescence confocal microscopy image segmentation. Following description of statistical based active contour segmentation and the mathematical definition of the proposed fractional entropy descriptor, we demonstrate comparative segmentation results between the proposed approach and standard Shannon’s entropy on synthetic and natural images. We also show that the proposed unsupervised statistical based approach, integrating the fractional entropy measure, leads to very satisfactory segmentation of the cell nuclei from which shape characterization can be calculated

Tubular Surface Evolution for Segmentation of the Cingulum Bundle From DW-MRI

Presented at the 2nd MICCAI Workshop on Mathematical Foundations of Computational Anatomy: Geometrical and Statistical Methods for Biological Shape Variability Modeling, September 6th, 2008, Kimmel Center, New York, USA.This work provides a framework for modeling and extracting the Cingulum Bundle (CB) from Diffusion-Weighted Imagery (DW-MRI) of the brain. The CB is a tube-like structure in the brain that is of potentially of tremendous importance to clinicians since it may be helpful in diagnosing Schizophrenia. This structure consists of a collection of fibers in the brain that have locally similar diffusion patterns, but vary globally. Standard region-based segmentation techniques adapted to DW-MRI are not suitable here because the diffusion pattern of the CB cannot be described by a global set of simple statistics. Active surface models extended to DW-MRI are not suitable since they allow for arbitrary deformations that give rise to unlikely shapes, which do not respect the tubular geometry of the CB. In this work, we explicitly model the CB as a tube-like surface and construct a general class of energies defined on tube-like surfaces. An example energy of our framework is optimized by a tube that encloses a region that has locally similar diffusion patterns, which differ from the diffusion patterns immediately outside. Modeling the CB as a tube-like surface is a natural shape prior. Since a tube is characterized by a center-line and a radius function, the method is reduced to a 4D (center-line plus radius) curve evolution that is computationally much less costly than an arbitrary surface evolution. The method also provides the center-line of CB, which is potentially of clinical significance