Hierarchical Gradient Domain Vector Field Processing

Simple item page
dc.contributor.authorLee, Sing Chun
dc.date.accessioned2024-01-15T08:36:42Z
dc.date.available2024-01-15T08:36:42Z
dc.date.issued2023-07-31
dc.description.abstractVector fields are a fundamental mathematical construct for describing flow-field-related problems in science and engineering. To solve these types of problems effectively on a discrete surface, various vector field representations are proposed using finite dimensional bases, a discrete connection, and an operator approach. Furthermore, for computational efficiency, quadratic Dirichlet energy is preferred to measure the smoothness of the vector field in the gradient domain. However, while quadratic energy gives a simple linear system, it does not support real-time vector field processing on a high-resolution mesh without extensive GPU parallelization. To this end, this dissertation describes an efficient hierarchical solver for vector field processing. Our method extends the successful multigrid design for interactive signal processing on meshes using an induced vector field prolongation combing it with novel speedup techniques. We formulate a general way for extending scalar field prolongation to vector fields. Focusing on triangle meshes, our convergence study finds that a standard multigrid does not achieve fast convergence due to the poorly-conditioned system matrix. We observe a similar performance in standard single-level iterative methods such as the Jacobi, Gauss-Seidel, and conjugate gradient methods. Therefore, we compare three speedup techniques -- successive over-relaxation, smoothed prolongation, and Krylov subspace update, and incorporate them into our solver. Finally, we demonstrate our solver on useful applications such as logarithmic map computation and discuss the applications to other hierarchies such as texture grids, followed by the conclusion and future work.en_US
dc.identifier.urihttps://diglib.eg.org:443/handle/10.2312/3543933
dc.language.isoen_USen_US
dc.publisherJohns Hopkins Universityen_US
dc.subjectHierarchicalen_US
dc.subjectVector Fielden_US
dc.subject1-Formen_US
dc.subjectDifferential Formen_US
dc.subjectMultigriden_US
dc.titleHierarchical Gradient Domain Vector Field Processingen_US
dc.typeThesisen_US
Files
Original bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
LEE-DISSERTATION-2023.pdf
Size:
68.24 MB
Format:
Adobe Portable Document Format
Description:
Download
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
1.79 KB
Format:
Item-specific license agreed upon to submission
Description:
Download
Collections
2023