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

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

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

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

Directed Acyclic Graph Continuous Max-Flow Image Segmentation for Unconstrained Label Orderings

Label ordering, the specification of subset–superset relationships for segmentation labels, has been of increasing interest in image segmentation as they allow for complex regions to be represented as a collection of simple parts. Recent advances in continuous max-flow segmentation have widely expanded the possible label orderings from binary background/foreground problems to extendable frameworks in which the label ordering can be specified. This article presents Directed Acyclic Graph Max-Flow image segmentation which is flexible enough to incorporate any label ordering without constraints. This framework uses augmented Lagrangian multipliers and primal–dual optimization to develop a highly parallelized solver implemented using GPGPU. This framework is validated on synthetic, natural, and medical images illustrating its general applicability

Topological Equivalence and Similarity in Multi-Representation Geographic Databases

Geographic databases contain collections of spatial data representing the variety of views for the real world at a specific time. Depending on the resolution or scale of the spatial data, spatial objects may have different spatial dimensions, and they may be represented by point, linear, or polygonal features, or combination of them. The diversity of data that are collected over the same area, often from different sources, imposes a question of how to integrate and to keep them consistent in order to provide correct answers for spatial queries. This thesis is concerned with the development of a tool to check topological equivalence and similarity for spatial objects in multi-representation databases. The main question is what are the components of a model to identify topological consistency, based on a set of possible transitions for the different types of spatial representations. This work develops a new formalism to model consistently spatial objects and spatial relations between several objects, each represented at multiple levels of detail. It focuses on the topological consistency constraints that must hold among the different representation of objects, but it is not concerned about generalization operations of how to derive one representation level from another. The result of this thesis is a?computational tool to evaluate topological equivalence and similarity across multiple representations. This thesis proposes to organize a spatial scene -a set of spatial objects and their embeddings in space- directly as a relation-based model that uses a hierarchical graph representation. The focus of the relation-based model is on relevant object representations. Only the highest-dimensional object representations are explicitly stored, while their parts are not represented in the graph

Interpretable statistics for complex modelling: quantile and topological learning

As the complexity of our data increased exponentially in the last decades, so has our need for interpretable features. This thesis revolves around two paradigms to approach this quest for insights. In the first part we focus on parametric models, where the problem of interpretability can be seen as a “parametrization selection”. We introduce a quantile-centric parametrization and we show the advantages of our proposal in the context of regression, where it allows to bridge the gap between classical generalized linear (mixed) models and increasingly popular quantile methods. The second part of the thesis, concerned with topological learning, tackles the problem from a non-parametric perspective. As topology can be thought of as a way of characterizing data in terms of their connectivity structure, it allows to represent complex and possibly high dimensional through few features, such as the number of connected components, loops and voids. We illustrate how the emerging branch of statistics devoted to recovering topological structures in the data, Topological Data Analysis, can be exploited both for exploratory and inferential purposes with a special emphasis on kernels that preserve the topological information in the data. Finally, we show with an application how these two approaches can borrow strength from one another in the identification and description of brain activity through fMRI data from the ABIDE project