Optimal Multiresolution 3D Level-Set Method for Liver Segmentation incorporating Local Curvature Constraints

Advanced liver surgery requires a precise pre-operative planning, where liver segmentation and remnant liver volume are key elements to avoid post-operative liver failure. In that context, level-set algorithms have achieved better results than others, especially with altered liver parenchyma or in cases with previous surgery. In order to improve functional liver parenchyma volume measurements, in this work we propose two strategies to enhance previous level-set algorithms: an optimal multi-resolution strategy with fine details correction and adaptive curvature, as well as an additional semiautomatic step imposing local curvature constraints. Results show more accurate segmentations, especially in elongated structures, detecting internal lesions and avoiding leakages to close structures

Level Set Segmentation with Shape and Appearance Models Using Affine Moment Descriptors

We propose a level set based variational approach that incorporates shape priors into edge-based and region-based models. The evolution of the active contour depends on local and global information. It has been implemented using an efficient narrow band technique. For each boundary pixel we calculate its dynamic according to its gray level, the neighborhood and geometric properties established by training shapes. We also propose a criterion for shape aligning based on affine transformation using an image normalization procedure. Finally, we illustrate the benefits of the our approach on the liver segmentation from CT images.

A Semi-Lagrangian Particle Level Set Finite Element Method for Interface Problems

We present a quasi-monotone semi-Lagrangian particle level set (QMSL-PLS) method for moving interfaces. The QMSL method is a blend of first order monotone and second order semi-Lagrangian methods. The QMSL-PLS method is easy to implement, efficient, and well adapted for unstructured, either simplicial or hexahedral, meshes. We prove that it is unconditionally stable in the maximum discrete norm, � · �h,∞, and the error analysis shows that when the level set solution u(t) is in the Sobolev space Wr+1,∞(D), r ≥ 0, the convergence in the maximum norm is of the form (KT/Δt)min(1,Δt � v �h,∞ /h)((1 − α)hp + hq), p = min(2, r + 1), and q = min(3, r + 1),where v is a velocity. This means that at high CFL numbers, that is, when Δt > h, the error is O( (1−α)hp+hq) Δt ), whereas at CFL numbers less than 1, the error is O((1 − α)hp−1 + hq−1)). We have tested our method with satisfactory results in benchmark problems such as the Zalesak’s slotted disk, the single vortex flow, and the rising bubble.

A level set approach for the analysis of flow and compaction during resin infusion in composite materials

Fluid flow and fabric compaction during vacuum assisted resin infusion (VARI) of composite materials was simulated using a level set-based approach. Fluid infusion through the fiber preform was modeled using Darcy’s equations for the fluid flow through a porous media. The stress partition between the fluid and the fiber bed was included by means of Terzaghi’s effective stress theory. Tracking the fluid front during infusion was introduced by means of the level set method. The resulting partial differential equations for the fluid infusion and the evolution of flow front were discretized and solved approximately using the finite differences method with a uniform grid discretization of the spatial domain. The model results were validated against uniaxial VARI experiments through an [0]8 E-glass plain woven preform. The physical parameters of the model were also independently measured. The model results (in terms of the fabric thickness, pressure and fluid front evolution during filling) were in good agreement with the numerical simulations, showing the potential of the level set method to simulate resin infusion

A fast marching level set method for monotonically advancing fronts.

A fast marching level set method is presented for monotonically advancing fronts, which leads to an extremely fast scheme for solving the Eikonal equation. Level set methods are numerical techniques for computing the position of propagating fronts. They rely on an initial value partial differential equation for a propagating level set function and use techniques borrowed from hyperbolic conservation laws. Topological changes, corner and cusp development, and accurate determination of geometric properties such as curvature and normal direction are naturally obtained in this setting. This paper describes a particular case of such methods for interfaces whose speed depends only on local position. The technique works by coupling work on entropy conditions for interface motion, the theory of viscosity solutions for Hamilton-Jacobi equations, and fast adaptive narrow band level set methods. The technique is applicable to a variety of problems, including shape-from-shading problems, lithographic development calculations in microchip manufacturing, and arrival time problems in control theory.

Image processing via level set curvature flow.

We present a controlled image smoothing and enhancement method based on a curvature flow interpretation of the geometric heat equation. Compared to existing techniques, the model has several distinct advantages. (i) It contains just one enhancement parameter. (ii) The scheme naturally inherits a stopping criterion from the image; continued application of the scheme produces no further change. (iii) The method is one of the fastest possible schemes based on a curvature-controlled approach.

Incorporating level set methods in Geographical Information Systems (GIS) for land-surface process modelling

Land-surface processes include a broad class of models that operate at a landscape scale. Current modelling approaches tend to be specialised towards one type of process, yet it is the interaction of processes that is increasing seen as important to obtain a more integrated approach to land management. This paper presents a technique and a tool that may be applied generically to landscape processes. The technique tracks moving interfaces across landscapes for processes such as water flow, biochemical diffusion, and plant dispersal. Its theoretical development applies a Lagrangian approach to motion over a Eulerian grid space by tracking quantities across a landscape as an evolving front. An algorithm for this technique, called level set method, is implemented in a geographical information system (GIS). It fits with a field data model in GIS and is implemented as operators in map algebra. The paper describes an implementation of the level set methods in a map algebra programming language, called MapScript, and gives example program scripts for applications in ecology and hydrology.

Simultaneous optimisation of structural topology and material grading using level set method

Peer reviewed

Modelling of water removal during a paper vacuum dewatering process using a Level-Set method

Water removal in paper manufacturing is an energy-intensive process. The dewatering process generally consists of four stages of which the first three stages include mechanical water removal through gravity filtration, vacuum dewatering and wet pressing. In the fourth stage, water is removed thermally, which is the most expensive stage in terms of energy use. In order to analyse water removal during a vacuum dewatering process, a numerical model was created by using a Level-Set method. Various different 2D structures of the paper model were created in MATLAB code with randomly positioned circular fibres with identical orientation. The model considers the influence of the forming fabric which supports the paper sheet during the dewatering process, by using volume forces to represent flow resistance in the momentum equation. The models were used to estimate the dry content of the porous structure for various dwell times. The relation between dry content and dwell time was compared to laboratory data for paper sheets with basis weights of 20 and 50 g/m2 exposed to vacuum levels between 20 kPa and 60 kPa. The comparison showed reasonable results for dewatering and air flow rates. The random positioning of the fibres influences the dewatering rate slightly. In order to achieve more accurate comparisons, the random orientation of the fibres needs to be considered, as well as the deformation and displacement of the fibres during the dewatering process.

Uma nova abordagem do método Level Set baseada em conhecimento a e priori da forma

The analysis of fluid behavior in multiphase flow is very relevant to guarantee system safety. The use of equipment to describe such behavior is subjected to factors such as the high level of investments and of specialized labor. The application of image processing techniques to flow analysis can be a good alternative, however, very little research has been developed. In this subject, this study aims at developing a new approach to image segmentation based on Level Set method that connects the active contours and prior knowledge. In order to do that, a model shape of the targeted object is trained and defined through a model of point distribution and later this model is inserted as one of the extension velocity functions for the curve evolution at zero level of level set method. The proposed approach creates a framework that consists in three terms of energy and an extension velocity function λLg(θ)+vAg(θ)+muP(0)+θf. The first three terms of the equation are the same ones introduced in (LI CHENYANG XU; FOX, 2005) and the last part of the equation θf is based on the representation of object shape proposed in this work. Two method variations are used: one restricted (Restrict Level Set - RLS) and the other with no restriction (Free Level Set - FLS). The first one is used in image segmentation that contains targets with little variation in shape and pose. The second will be used to correctly identify the shape of the bubbles in the liquid gas two phase flows. The efficiency and robustness of the approach RLS and FLS are presented in the images of the liquid gas two phase flows and in the image dataset HTZ (FERRARI et al., 2009). The results confirm the good performance of the proposed algorithm (RLS and FLS) and indicate that the approach may be used as an efficient method to validate and/or calibrate the various existing equipment used as meters for two phase flow properties, as well as in other image segmentation problems.

Discrete-event Simulation and Optimization to Improve the Performance of a Healthcare System

Thesis (Ph.D.)--University of Washington, 2016-08

Linguistic models for decision support

Linguistic modelling is a rather new branch of mathematics that is still undergoing rapid development. It is closely related to fuzzy set theory and fuzzy logic, but knowledge and experience from other fields of mathematics, as well as other fields of science including linguistics and behavioral sciences, is also necessary to build appropriate mathematical models. This topic has received considerable attention as it provides tools for mathematical representation of the most common means of human communication - natural language. Adding a natural language level to mathematical models can provide an interface between the mathematical representation of the modelled system and the user of the model - one that is sufficiently easy to use and understand, but yet conveys all the information necessary to avoid misinterpretations. It is, however, not a trivial task and the link between the linguistic and computational level of such models has to be established and maintained properly during the whole modelling process. In this thesis, we focus on the relationship between the linguistic and the mathematical level of decision support models. We discuss several important issues concerning the mathematical representation of meaning of linguistic expressions, their transformation into the language of mathematics and the retranslation of mathematical outputs back into natural language. In the first part of the thesis, our view of the linguistic modelling for decision support is presented and the main guidelines for building linguistic models for real-life decision support that are the basis of our modeling methodology are outlined. From the theoretical point of view, the issues of representation of meaning of linguistic terms, computations with these representations and the retranslation process back into the linguistic level (linguistic approximation) are studied in this part of the thesis. We focus on the reasonability of operations with the meanings of linguistic terms, the correspondence of the linguistic and mathematical level of the models and on proper presentation of appropriate outputs. We also discuss several issues concerning the ethical aspects of decision support - particularly the loss of meaning due to the transformation of mathematical outputs into natural language and the issue or responsibility for the final decisions. In the second part several case studies of real-life problems are presented. These provide background and necessary context and motivation for the mathematical results and models presented in this part. A linguistic decision support model for disaster management is presented here – formulated as a fuzzy linear programming problem and a heuristic solution to it is proposed. Uncertainty of outputs, expert knowledge concerning disaster response practice and the necessity of obtaining outputs that are easy to interpret (and available in very short time) are reflected in the design of the model. Saaty’s analytic hierarchy process (AHP) is considered in two case studies - first in the context of the evaluation of works of art, where a weak consistency condition is introduced and an adaptation of AHP for large matrices of preference intensities is presented. The second AHP case-study deals with the fuzzified version of AHP and its use for evaluation purposes – particularly the integration of peer-review into the evaluation of R&D outputs is considered. In the context of HR management, we present a fuzzy rule based evaluation model (academic faculty evaluation is considered) constructed to provide outputs that do not require linguistic approximation and are easily transformed into graphical information. This is achieved by designing a specific form of fuzzy inference. Finally the last case study is from the area of humanities - psychological diagnostics is considered and a linguistic fuzzy model for the interpretation of outputs of multidimensional questionnaires is suggested. The issue of the quality of data in mathematical classification models is also studied here. A modification of the receiver operating characteristics (ROC) method is presented to reflect variable quality of data instances in the validation set during classifier performance assessment. Twelve publications on which the author participated are appended as a third part of this thesis. These summarize the mathematical results and provide a closer insight into the issues of the practicalapplications that are considered in the second part of the thesis.

A discontinuous-Galerkin-based immersed boundary method with non-homogeneous boundary conditions and its application to elasticity

We propose a discontinuous-Galerkin-based immersed boundary method for elasticity problems. The resulting numerical scheme does not require boundary fitting meshes and avoids boundary locking by switching the elements intersected by the boundary to a discontinuous Galerkin approximation. Special emphasis is placed on the construction of a method that retains an optimal convergence rate in the presence of non-homogeneous essential and natural boundary conditions. The role of each one of the approximations introduced is illustrated by analyzing an analog problem in one spatial dimension. Finally, extensive two- and three-dimensional numerical experiments on linear and nonlinear elasticity problems verify that the proposed method leads to optimal convergence rates under combinations of essential and natural boundary conditions. (C) 2009 Elsevier B.V. All rights reserved.

A discontinuous-Galerkin-based immersed boundary method

A numerical method to approximate partial differential equations on meshes that do not conform to the domain boundaries is introduced. The proposed method is conceptually simple and free of user-defined parameters. Starting with a conforming finite element mesh, the key ingredient is to switch those elements intersected by the Dirichlet boundary to a discontinuous-Galerkin approximation and impose the Dirichlet boundary conditions strongly. By virtue of relaxing the continuity constraint at those elements. boundary locking is avoided and optimal-order convergence is achieved. This is shown through numerical experiments in reaction-diffusion problems. Copyright (c) 2008 John Wiley & Sons, Ltd.

Estimating and quantifying uncertainties on level sets using the Vorob'ev expectation and deviation with Gaussian process models

Several methods based on Kriging have recently been proposed for calculating a probability of failure involving costly-to-evaluate functions. A closely related problem is to estimate the set of inputs leading to a response exceeding a given threshold. Now, estimating such a level set—and not solely its volume—and quantifying uncertainties on it are not straightforward. Here we use notions from random set theory to obtain an estimate of the level set, together with a quantification of estimation uncertainty. We give explicit formulae in the Gaussian process set-up and provide a consistency result. We then illustrate how space-filling versus adaptive design strategies may sequentially reduce level set estimation uncertainty.