New ETHZ masters thesis project available: Optimizing Bounded Biharmonic Weights Computation
Alec Jacobson
January 29, 2013
Olga Sorkine and I will be hosting a master's thesis project. The project, entitled Optimizing Bounded Biharmonic Weights Computation is now available, and we are eagerly awaiting applications.
Bounded biharmonic weights (BBW) are compactly supported, smooth functions defined over a 2D or 3D shape. Their primary use is for blending transformations to achieve shape deformation in real time. However, computing them requires optimizing a quadratic program (QP) over a finite-element discretization of the shape's volume. This is costly (~minutes) and limits applications to those where it is acceptable to precompute such weights once and reuse them. Dynamically adapting BBWs by recomputing them interactively would greatly enhance its list of applications: physically-based simulation, interactive modeling, even many-to-many image registration.
In this thesis, the student will explore algorithmic and pragmatic optimization of the computation of bounded biharmonic weights. Current solutions lean on black-box QP solvers, which do not take advantage of the geometry-specific and problem-specific nature of the BBW energy minimization problem. We will explore algorithmic and data-structure optimizations such as multi-resolution hierarchies (both geometric and algebraic). Then we will explore performance optimizations that make the most of modern multi-core SIMD CPUs.
Please don't hesitate to contact me for more details.
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