Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 42 for “"level sets"”.
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Uniform Sampling over Level Sets
… method to extract near-uniform samples from a level set of a provided function 𝑓 : Rᵈ → Rᵏ . We propose a sequence of unnormalized distributions over Rᵈ with asymptotic convergence to the Hausdorff measure of the level set, therefore resulting in uniform samples. Beyond our formulation’s …
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Algebraic level sets for CAD/CAE integration and moving boundary problems
… measure, also referred to as the <em>Algebraic Level Sets</em>, gives a volumetric representation of the B-rep geometry constructed by purely non-iterative algebraic operations on the geometry. This in turn enables both the implicit boolean operations and analysis operations on B-rep geometries …
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Linear Dimension Reduction Approximately Preserving Level-Sets of the 1-Norm
<p>We choose a family of matrices F : \R^D \to \R^k and a metric \rho on \R^k such that with high</p><p>probability, \rho(F (x), F (y)) is a strictly concave increasing function of ||x − y||_1 > 8 \epsilon^2</p><p>for x, y \in \R^D , up to a multiplicative error of 1 ±\epsilon. In particular, if X …
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Meshless methods: theory and application in 3D fracture modelling with level sets
… using the element-free Galerkin method and the level set method. The former contributes to some fundamental issues related to accuracy and error control in meshless methods needing to be addressed for fracture modelling developed later namely, the modified weak form for imposition of essential …
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Lelong Numbers and Geometric Properties of Upper Level Sets of Currents on Projective Space
… more about the geometric properties of the sets of highly singular points of the current $T$. Lelong numbers will be the main tool used for determining how singular a point of a current is. For the first main result of this thesis, we let $T$ be a positive closed current of bidimension …
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Bayesian level sets and texture models for image segmentation and classification with application to non-invasive stem cell monitoring
… by this and other applications, the Bayesian Level Set (BLS) algorithm is developed for automated segmentation and classification that computes smooth, regular segmenting contours in a manner similar to level sets while possessing a simple, probabilistic implementation similar to that of the …
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Regularity of the Level Set Equation for Mean Curvature Flow with an Axis of Symmetry
… the regularity of viscosity solutions to the level set equation for mean curvature flow. We describe a set of hypotheses under which we can prove that the level sets of these solutions are C¹,¹ submanifolds of spacetime with well understood behavior near singular times. We then relate the …
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Segmentation of medical images under topological constraints
… of digital segmentations. Second, we design a level set framework that offers a subtle control over the topology of the level set components. Our method constitutes a trade-off between traditional level sets and topology-preserving level sets.
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A new guidance trajectory generation algorithm for unmanned systems incorporating vehicle dynamics and constraints
… in real time using onboard sensors and compute level sets on the map reflecting the minimal cost of traversal from the current vehicle location to the goal. We convert the trajectory generation problem into a finite-time-horizon optimal control problem using the computed level sets as terminal …
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Fast Path Planning in Uncertain Environments: Theory and Experiments
… control path planning algorithm that is based on level-set methods. The hybrid method uses global or local level sets in the formulation of the receding horizon control problem. The decision to select a new level set is made based on certain matching conditions that guarantee the optimality of the …
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Sparse Fourier restriction for the cone
… inequalities allow us to probe the shape of level sets. In this thesis, we describe a new weighted Fourier extension estimate for the cone and its connection with the Mizohata–Takeuchi conjecture. The main result Theorem 3.1 builds on techniques from geometry originally explored by Tom Wolff …
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Symmetry and Other Structures: Topics in Nonparametric Regression
… This framework exploits the structure of the level sets of the regression function. If we know the level set [x]_f = {u ∈ [0, 1]^d ∶ f(x) = f(u)} then we can average any sufficiently local estimator fn over this level set to obtain an estimator with a pointwise risk that is bounded in terms of …
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Hadwiger Integration of Definable Functions
… intrinsic volumes are valuations on "tame" subsets of R^n, and by easy extension, valuations on functionals on R^n with nitely many level sets, each a "tame" subset of R^n. We extend these valuations, which we call Hadwiger integrals, to denable functionals on R^n, and present some important …
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An Implicit Level Set Model for Firespread
<p>The level set method is a mathematical and computational, technique for tracking a moving interface over time. It can naturally handle topological changes such as merging or breaking interfaces. Intrinsic geometric properties of the interface, such as curvature and normal direction, are easily …
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Navigation in an unfamiliar environment using signal intensity
… be symmetric; the main requirement is that the level sets are concentric images of simple closed curves, i.e. topological circles. Convergence analysis and distance bounds are established for the presented approach. The algorithm is then experimentally verified using a differential drive robot …
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Stochastic acoustic ray tracing with dynamically orthogonal equations
… of the Parabolic Equation, Ray Theory, and Level Sets methods for ocean acoustic computation. We investigate methods for evolving stochastic fields using direct Monte Carlo, Empirical Orthogonal Functions, and adaptive Dynamically Orthogonal (DO) differential equations.
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Large-scale optimization Methods for data-science applications
… function, that measures how quickly the level sets grow relative to the function value, and that plays a fundamental role in the complexity analysis. Based on such measure, we present new computational guarantees for both smooth and non-smooth convex optimization, that can improve …
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Supervised manifold distance segmentation
… quantitative results to other algorithms like Level Sets and Random Walks. Analysis of sensitivity to parameters is presented. Comparison between segmentation results and ground-truth images is also provided to validate of the robustness of this method.
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A free boundary problem inspired by a conjecture of De Giorgi
… are bounded and monotone in one direction have levell sets that are hyperplanes, at least up to dimension 8. Recently, Del Pino, Kowalczyk and Wei gave an intricate fixed-point-argument construction of a counterexample in dimension 9, whose level sets "follow" the entire minimal non-planar …
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