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

Nonparametric Bayesian Image Segmentation

Image segmentation algorithms partition the set of pixels of an image into a specific number of different, spatially homogeneous groups. We propose a nonparametric Bayesian model for histogram clustering which automatically determines the number of segments when spatial smoothness constraints on the class assignments are enforced by a Markov Random Field. A Dirichlet process prior controls the level of resolution which corresponds to the number of clusters in data with a unique cluster structure. The resulting posterior is efficiently sampled by a variant of a conjugate-case sampling algorithm for Dirichlet process mixture models. Experimental results are provided for real-world gray value images, synthetic aperture radar images and magnetic resonance imaging dat

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

Nonparametric clustering for image segmentation

open1openMenardi, GiovannaMenardi, Giovann

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

Structured Learning of Tree Potentials in CRF for Image Segmentation

We propose a new approach to image segmentation, which exploits the advantages of both conditional random fields (CRFs) and decision trees. In the literature, the potential functions of CRFs are mostly defined as a linear combination of some pre-defined parametric models, and then methods like structured support vector machines (SSVMs) are applied to learn those linear coefficients. We instead formulate the unary and pairwise potentials as nonparametric forests---ensembles of decision trees, and learn the ensemble parameters and the trees in a unified optimization problem within the large-margin framework. In this fashion, we easily achieve nonlinear learning of potential functions on both unary and pairwise terms in CRFs. Moreover, we learn class-wise decision trees for each object that appears in the image. Due to the rich structure and flexibility of decision trees, our approach is powerful in modelling complex data likelihoods and label relationships. The resulting optimization problem is very challenging because it can have exponentially many variables and constraints. We show that this challenging optimization can be efficiently solved by combining a modified column generation and cutting-planes techniques. Experimental results on both binary (Graz-02, Weizmann horse, Oxford flower) and multi-class (MSRC-21, PASCAL VOC 2012) segmentation datasets demonstrate the power of the learned nonlinear nonparametric potentials.Comment: 10 pages. Appearing in IEEE Transactions on Neural Networks and Learning System

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