Related papers: Domain Mapping for Volumetric Parameterization usi…
We present a volumetric mesh-based algorithm for parameterizing the placenta to a flattened template to enable effective visualization of local anatomy and function. MRI shows potential as a research tool as it provides signals directly…
Many tasks in geometry processing are modeled as variational problems solved numerically using the finite element method. For solid shapes, this requires a volumetric discretization, such as a boundary conforming tetrahedral mesh.…
In the optimization of convex domains under a PDE constraint numerical difficulties arise in the approximation of convex domains in $\mathbb{R}^3$. Previous research used a restriction to rotationally symmetric domains to reduce shape…
Seamless global parametrization of surfaces is a key operation in geometry processing, e.g. for high-quality quad mesh generation. A common approach is to prescribe the parametric domain structure, in particular the locations of…
This paper presents a shape optimisation system to design the shape of an acoustically-hard object in the three-dimensional open space. Boundary element method (BEM) is suitable to analyse such an exterior field. However, the conventional…
We consider the variational problem of minimizing an anisotropic perimeter functional under a volume constraint in a Euclidean convex domain. We extend to this setting analytical properties of the isoperimetric profile, topological features…
Convolution is an efficient technique to obtain abstract feature representations using hierarchical layers in deep networks. Although performing convolution in Euclidean geometries is fairly straightforward, its extension to other…
This article presents a new high-order accurate algorithm for finding a particular solution to a linear, constant-coefficient partial differential equation (PDE) by means of a convolution of the volumetric source function with the Green's…
Convexity prior is one of the main cue for human vision and shape completion with important applications in image processing, computer vision. This paper focuses on characterization methods for convex objects and applications in image…
Boundary conforming coordinates are commonly used in plasma physics to describe the geometry of toroidal domains, for example, in three-dimensional magnetohydrodynamic equilibrium solvers. The magnetohydrodynamic equilibrium configuration…
The advancements in neural rendering have increased the need for techniques that enable intuitive editing of 3D objects represented as neural implicit surfaces. This paper introduces a novel neural algorithm for parameterizing neural…
Conformal surface parameterization is useful in graphics, imaging and visualization, with applications to texture mapping, atlas construction, registration, remeshing and so on. With the increasing capability in scanning and storing data,…
In an attempt to characterize the distribution of forms and shapes of nodal domains in wave functions, we define a geometric parameter - the ratio $\rho$ between the area of a domain and its perimeter, measured in units of the wavelength…
We develop a volume penalization method for inhomogeneous Neumann boundary conditions, generalizing the flux-based volume penalization method for homogeneous Neumann boundary condition proposed by Kadoch et al. [J. Comput. Phys. 231 (2012)…
This paper presents Volume-DROID, a novel approach for Simultaneous Localization and Mapping (SLAM) that integrates Volumetric Mapping and Differentiable Recurrent Optimization-Inspired Design (DROID). Volume-DROID takes camera images…
Recent work has demonstrated that volumetric scene representations combined with differentiable volume rendering can enable photo-realistic rendering for challenging scenes that mesh reconstruction fails on. However, these methods entangle…
Regularization approaches have demonstrated their effectiveness for solving ill-posed problems. However, in the context of variational restoration methods, a challenging question remains, which is how to find a good regularizer. While total…
We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…
We present two techniques novel in numerical methods. The first technique compiles the domain of the numerical methods as a discretized volume. Congruent elements are glued together to compile the domain over which the solution of a…
The rapid advances in 3D scanning and acquisition techniques have given rise to the explosive increase of volumetric digital models in recent years. This dissertation systematically trailblazes a novel volumetric modeling framework to…