Segmentation is a fundamental task for extracting semantically meaningful regions from an image. The goal of segmentation algorithms is to accurately assign object labels to each image location. However, image-noise, shortcomings of algorithms, and image ambiguities cause uncertainty in label assignment. Estimating the uncertainty in label assignment is important in multiple application domains, such as segmenting tumors from medical images for radiation treatment planning. One way to estimate these uncertainties is through the computation of posteriors of Bayesian models, which is computationally prohibitive for many practical applications. On the other hand, most computationally efficient methods fail to estimate label uncertainty. We therefore propose in this paper the Active Mean Fields (AMF) approach, a technique based on Bayesian modeling that uses a mean-field approximation to efficiently compute a segmentation and its corresponding uncertainty. Based on a variational formulation, the resulting convex model combines any label-likelihood measure with a prior on the length of the segmentation boundary. A specific implementation of that model is the Chan-Vese segmentation model (CV), in which the binary segmentation task is defined by a Gaussian likelihood and a prior regularizing the length of the segmentation boundary. Furthermore, the Euler-Lagrange equations derived from the AMF model are equivalent to those of the popular Rudin-Osher-Fatemi (ROF) model for image denoising. Solutions to the AMF model can thus be implemented by directly utilizing highly-efficient ROF solvers on log-likelihood ratio fields. We qualitatively assess the approach on synthetic data as well as on real natural and medical images. For a quantitative evaluation, we apply our approach to the icgbench dataset.

We propose two new algorithms for the sparse reinforcement learning problem based on different formulations. The first algorithm is an off-line method based on the alternating direction method of multipliers for solving a constrained formulation that explicitly controls the projected Bellman residual. The second algorithm is an online stochastic approximation algorithm that employs the regularized dual averaging technique, using the Lagrangian formulation. The convergence of both algorithms are established. We demonstrate the performance of these algorithms through two classical examples.

Identifying patterns from the neuroimaging recordings of brain activity related to the unobservable psychological or mental state of an individual can be treated as a unsupervised pattern recognition problem. The main challenges, however, for such an analysis of fMRI data are: a) defining a physiologically meaningful feature-space for representing the spatial patterns across time; b) dealing with the high-dimensionality of the data; and c) robustness to the various artifacts and confounds in the fMRI time-series. In this paper, we present a network-aware feature-space to represent the states of a general network, that enables comparing and clustering such states in a manner that is a) meaningful in terms of the network connectivity structure; b)computationally efficient; c) low-dimensional; and d) relatively robust to structured and random noise artifacts. This feature-space is obtained from a spherical relaxation of the transportation distance metric which measures the cost of transporting ``mass'' over the network to transform one function into another. Through theoretical and empirical assessments, we demonstrate the accuracy and efficiency of the approximation, especially for large problems. While the application presented here is for identifying distinct brain activity patterns from fMRI, this feature-space can be applied to the problem of identifying recurring patterns and detecting outliers in measurements on many different types of networks, including sensor, control and social networks.

Abstract Classically, analysis of the time‐varying data acquired during fMRI experiments is done using static activation maps obtained by testing voxels for the presence of significant activity using statistical methods. The models used in these analysis methods have a number of parameters, which profoundly impact the detection of active brain areas. Also, it is hard to study the temporal dependencies and cascading effects of brain activation from these static maps. In this paper, we propose a methodology to visually analyze the time dimension of brain function with a minimum amount of processing, allowing neurologists to verify the correctness of the analysis results, and develop a better understanding of temporal characteristics of the functional behaviour. The system allows studying time‐series data through specific volumes‐of‐interest in the brain‐cortex, the selection of which is guided by a hierarchical clustering algorithm performed in the wavelet domain. We also demonstrate the utility of this tool by presenting results on a real data‐set.

Abstract Neuronal dendrites and their spines affect the connectivity of neural networks, and play a significant role in many neurological conditions. Neuronal function is observed to be closely correlated with the appearance, disappearance and morphology of the spines. Automatic 3‐D reconstruction of neurons from light microscopy images, followed by the identification, classification and visualization of dendritic spines is therefore essential for studying neuronal physiology and biophysical properties. In this paper, we present a method to reconstruct dendrites using a surface representation of the dendrite. The 1‐D skeleton of the dendritic surface is then extracted by a medial geodesic function that is robust and topologically correct. This is followed by a Bayesian identification and classification of the spines. The dendrite and spines are visualized in a manner that displays the spines' types and the inherent uncertainty in identification and classification. We also describe a user study conducted to validate the accuracy of the classification and the efficacy of the visualization.

In this paper, we propose a technique for detecting pockets on a surface-of-interest. A sequence of propagating fronts converging to the target surface is used as the basis for inspection. We compute a correspondence function between the initial and the target surface. This leads to a natural definition of the local feature size measured as the evolution distance between mapped points. Surface pockets are then extracted as salient clusters embedded in the feature space. The level-set initialization also determines the scale-space of the extracted pockets. Results are presented on a case-study in which the focus is to chronicle the phenotyping differences in genetically modified mouse placenta. Our results are validated based on manually verified ground-truth.