Nonparametric statistical methods for image segmentation and shape analysis

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Page 131 blank.Includes bibliographical references (p. 125-130).Image segmentation, the process of decomposing an image into meaningful regions, is a fundamental problem in image processing and computer vision. Recently, image segmentation techniques based on active contour models with level set implementation have received considerable attention. The objective of this thesis is in the development of advanced active contour-based image segmentation methods that incorporate complex statistical information into the segmentation process, either about the image intensities or about the shapes of the objects to be segmented. To this end, we use nonparametric statistical methods for modeling both the intensity distributions and the shape distributions. Previous work on active contour-based segmentation considered the class of images in which each region can be distinguished from others by second order statistical features such as the mean or variance of image intensities of that region. This thesis addresses the problem of segmenting a more general class of images in which each region has a distinct arbitrary intensity distribution. To this end, we develop a nonparametric information-theoretic method for image segmentation. In particular, we cast the segmentation problem as the maximization of the mutual information between the region labels and the image pixel intensities. The resulting curve evolution equation is given in terms of nonparametric density estimates of intensity distributions, and the segmentation method can deal with a variety of intensity distributions in an unsupervised fashion. The second component of this thesis addresses the problem of estimating shape densities from training shapes and incorporating such shape prior densities into the image segmentation process.(cont.) To this end, we propose nonparametric density estimation methods in the space of curves and the space of signed distance functions. We then derive a corresponding curve evolution equation for shape-based image segmentation. Finally, we consider the case in which the shape density is estimated from training shapes that form multiple clusters. This case leads to the construction of complex, potentially multi-modal prior densities for shapes. As compared to existing methods, our shape priors can: (a) model more complex shape distributions; (b) deal with shape variability in a more principled way; and (c) represent more complex shapes.by Junmo Kim.Ph.D

Multi-object segmentation using coupled nonparametric shape and relative pose priors

We present a new method for multi-object segmentation in a maximum a posteriori estimation framework. Our method is motivated by the observation that neighboring or coupling objects in images generate configurations and co-dependencies which could potentially aid in segmentation if properly exploited. Our approach employs coupled shape and inter-shape pose priors that are computed using training images in a nonparametric multi-variate kernel density estimation framework. The coupled shape prior is obtained by estimating the joint shape distribution of multiple objects and the inter-shape pose priors are modeled via standard moments. Based on such statistical models, we formulate an optimization problem for segmentation, which we solve by an algorithm based on active contours. Our technique provides significant improvements in the segmentation of weakly contrasted objects in a number of applications. In particular for medical image analysis, we use our method to extract brain Basal Ganglia structures, which are members of a complex multi-object system posing a challenging segmentation problem. We also apply our technique to the problem of handwritten character segmentation. Finally, we use our method to segment cars in urban scenes

Segmentation of the evolving left ventricle by learning the dynamics

We propose a method for recursive segmentation of the left ventricle (LV) across a temporal sequence of magnetic resonance (MR) images. The approach involves a technique for learning the LV boundary dynamics together with a particle-based inference algorithm 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 boundary estimation involves incorporating curve evolution into 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. We assess and demonstrate the effectiveness of the proposed framework on a large data set of breath-hold cardiac MR image sequences

Coupled nonparametric shape priors for segmentation of multiple basal ganglia structures

This paper presents a new method for multiple structure segmentation, using a maximum a posteriori (MAP) estimation framework, based on prior shape densities involving nonparametric multivariate kernel density estimation of multiple shapes. Our method is motivated by the observation that neighboring or coupling structures in medical images generate configurations and co-dependencies which could potentially aid in segmentation if properly exploited. Our technique allows simultaneous segmentation of multiple objects, where highly contrasted, easy-to-segment structures can help improve the segmentation of weakly contrasted objects. We demonstrate the effectiveness of our method on both synthetic images and real magnetic resonance images (MRI) for segmentation of basal ganglia structures

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

Volumetric segmentation of multiple basal ganglia structures

We present a new active contour-based, statistical method for simultaneous volumetric segmentation of multiple subcortical structures in the brain. Neighboring anatomical structures in the human brain 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 based on training data, 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 compare our technique with existing methods and demonstrate the improvements it provides in terms of segmentation accuracy

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

Shape-driven segmentation of the arterial wall in intravascular ultrasound images

Segmentation of arterial wall boundaries from intravascular images is an important problem for many applications in the study of plaque characteristics, mechanical properties of the arterial wall, its 3D reconstruction, and its measurements such as lumen size, lumen radius, and wall radius. We present a shape-driven approach to segmentation of the arterial wall from intravascular ultrasound images in the rectangular domain. In a properly built shape space using training data, we constrain the lumen and media-adventitia contours to a smooth, closed geometry, which increases the segmentation quality without any tradeoff with a regularizer term. In addition to a shape prior, we utilize an intensity prior through a non-parametric probability density based image energy, with global image measurements rather than pointwise measurements used in previous methods. Furthermore, a detection step is included to address the challenges introduced to the segmentation process by side branches and calcifications. All these features greatly enhance our segmentation method. The tests of our algorithm on a large dataset demonstrate the effectiveness of our approach