Location Dependent Dirichlet Processes

Dirichlet processes (DP) are widely applied in Bayesian nonparametric modeling. However, in their basic form they do not directly integrate dependency information among data arising from space and time. In this paper, we propose location dependent Dirichlet processes (LDDP) which incorporate nonparametric Gaussian processes in the DP modeling framework to model such dependencies. We develop the LDDP in the context of mixture modeling, and develop a mean field variational inference algorithm for this mixture model. The effectiveness of the proposed modeling framework is shown on an image segmentation task

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

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

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

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

A Latent Source Model for Patch-Based Image Segmentation

Despite the popularity and empirical success of patch-based nearest-neighbor and weighted majority voting approaches to medical image segmentation, there has been no theoretical development on when, why, and how well these nonparametric methods work. We bridge this gap by providing a theoretical performance guarantee for nearest-neighbor and weighted majority voting segmentation under a new probabilistic model for patch-based image segmentation. Our analysis relies on a new local property for how similar nearby patches are, and fuses existing lines of work on modeling natural imagery patches and theory for nonparametric classification. We use the model to derive a new patch-based segmentation algorithm that iterates between inferring local label patches and merging these local segmentations to produce a globally consistent image segmentation. Many existing patch-based algorithms arise as special cases of the new algorithm.Comment: International Conference on Medical Image Computing and Computer Assisted Interventions 201