Shape complexes: the intersection of label orderings and star convexity constraints in continuous max-flow medical image segmentation.

Optimization-based segmentation approaches deriving from discrete graph-cuts and continuous max-flow have become increasingly nuanced, allowing for topological and geometric constraints on the resulting segmentation while retaining global optimality. However, these two considerations, topological and geometric, have yet to be combined in a unified manner. The concept of shape complexes, which combine geodesic star convexity with extendable continuous max-flow solvers, is presented. These shape complexes allow more complicated shapes to be created through the use of multiple labels and super-labels, with geodesic star convexity governed by a topological ordering. These problems can be optimized using extendable continuous max-flow solvers. Previous approaches required computationally expensive coordinate system warping, which are ill-defined and ambiguous in the general case. These shape complexes are demonstrated in a set of synthetic images as well as vessel segmentation in ultrasound, valve segmentation in ultrasound, and atrial wall segmentation from contrast-enhanced CT. Shape complexes represent an extendable tool alongside other continuous max-flow methods that may be suitable for a wide range of medical image segmentation problems

Optimization-based interactive segmentation interface for multiregion problems.

Interactive segmentation is becoming of increasing interest to the medical imaging community in that it combines the positive aspects of both manual and automated segmentation. However, general-purpose tools have been lacking in terms of segmenting multiple regions simultaneously with a high degree of coupling between groups of labels. Hierarchical max-flow segmentation has taken advantage of this coupling for individual applications, but until recently, these algorithms were constrained to a particular hierarchy and could not be considered general-purpose. In a generalized form, the hierarchy for any given segmentation problem is specified in run-time, allowing different hierarchies to be quickly explored. We present an interactive segmentation interface, which uses generalized hierarchical max-flow for optimization-based multiregion segmentation guided by user-defined seeds. Applications in cardiac and neonatal brain segmentation are given as example applications of its generality

Contributions of Continuous Max-Flow Theory to Medical Image Processing

Discrete graph cuts and continuous max-flow theory have created a paradigm shift in many areas of medical image processing. As previous methods limited themselves to analytically solvable optimization problems or guaranteed only local optimizability to increasingly complex and non-convex functionals, current methods based now rely on describing an optimization problem in a series of general yet simple functionals with a global, but non-analytic, solution algorithms. This has been increasingly spurred on by the availability of these general-purpose algorithms in an open-source context. Thus, graph-cuts and max-flow have changed every aspect of medical image processing from reconstruction to enhancement to segmentation and registration. To wax philosophical, continuous max-flow theory in particular has the potential to bring a high degree of mathematical elegance to the field, bridging the conceptual gap between the discrete and continuous domains in which we describe different imaging problems, properties and processes. In Chapter 1, we use the notion of infinitely dense and infinitely densely connected graphs to transfer between the discrete and continuous domains, which has a certain sense of mathematical pedantry to it, but the resulting variational energy equations have a sense of elegance and charm. As any application of the principle of duality, the variational equations have an enigmatic side that can only be decoded with time and patience. The goal of this thesis is to show the contributions of max-flow theory through image enhancement and segmentation, increasing incorporation of topological considerations and increasing the role played by user knowledge and interactivity. These methods will be rigorously grounded in calculus of variations, guaranteeing fuzzy optimality and providing multiple solution approaches to addressing each individual problem

A graph-based mathematical morphology reader

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research

Dynamic PRA: an Overview of New Algorithms to Generate, Analyze and Visualize Data

State of the art PRA methods, i.e. Dynamic PRA (DPRA) methodologies, largely employ system simulator codes to accurately model system dynamics. Typically, these system simulator codes (e.g., RELAP5 ) are coupled with other codes (e.g., ADAPT, RAVEN that monitor and control the simulation. The latter codes, in particular, introduce both deterministic (e.g., system control logic, operating procedures) and stochastic (e.g., component failures, variable uncertainties) elements into the simulation. A typical DPRA analysis is performed by: 1. Sampling values of a set of parameters from the uncertainty space of interest 2. Simulating the system behavior for that specific set of parameter values 3. Analyzing the set of simulation runs 4. Visualizing the correlations between parameter values and simulation outcome Step 1 is typically performed by randomly sampling from a given distribution (i.e., Monte-Carlo) or selecting such parameter values as inputs from the user (i.e., Dynamic Event Tre