Related papers: Efficient conformal parameterization of multiply-c…
Particle-based shape modeling (PSM) is a family of approaches that automatically quantifies shape variability across anatomical cohorts by positioning particles (pseudo landmarks) on shape surfaces in a consistent configuration. Recent…
We are interested in geometric approximation by parameterization of two-dimensional multiple-component shapes, in particular when the number of components is a priori unknown. Starting a standard method based on successive shape…
The invariant theory for conformal hypersurfaces is studied by treating these as the conformal infinity of a conformally compact manifold: For a given conformal hypersurface embedding, a distinguished ambient metric is found (within its…
In this paper, we present a surface remeshing method with high approximation quality based on Principal Component Analysis. Given a triangular mesh and a user assigned polygon/vertex budget, traditional methods usually require the extra…
Construction of spline surfaces from given boundary curves is one of the classical problems in computer aided geometric design, which regains much attention in isogeometric analysis in recent years and is called domain parameterization.…
In this paper we propose an approach for computing multiple high-quality near-isometric dense correspondences between a pair of 3D shapes. Our method is fully automatic and does not rely on user-provided landmarks or descriptors. This…
Multiple lidars are prevalently used on mobile vehicles for rendering a broad view to enhance the performance of localization and perception systems. However, precise calibration of multiple lidars is challenging since the feature…
In this paper, we introduce complex functional maps, which extend the functional map framework to conformal maps between tangent vector fields on surfaces. A key property of these maps is their orientation awareness. More specifically, we…
Deep learning on non-Euclidean domains is important for analyzing complex geometric data that lacks common coordinate systems and familiar Euclidean properties. A central challenge in this field is to define convolution on domains, which…
Recently, the mapping approach to surface hopping (MASH) was proposed as a method to simulate the non-adiabatic dynamics of two-level systems. It was shown that the method possesses many desirable qualities, both theoretically and through…
We consider the problem of improving kernel approximation via randomized feature maps. These maps arise as Monte Carlo approximation to integral representations of kernel functions and scale up kernel methods for larger datasets. Based on…
We propose a conformal prediction method for constructing tight simultaneous prediction intervals for multiple, potentially related, numerical outputs given a single input. This method can be combined with any multi-target regression model…
The application of transformation optics to the development of intriguing electromagnetic devices can produce weakly anisotropic or isotropic media with the assistance of quasi-conformal and/or conformal mapping, as opposed to the strongly…
We address the problem of determining correspondences between two images in agreement with a geometric model such as an affine or thin-plate spline transformation, and estimating its parameters. The contributions of this work are…
We discuss solutions of several questions concerning the geometry of conformal planes.
Motivated by geometry processing for surfaces with non-trivial topology, we study discrete harmonic maps between closed surfaces of genus at least two. Harmonic maps provide a natural framework for comparing surfaces by minimizing…
We recently found that the electromagnetic scattering problem can be very fast in an approach expressing the fields in terms of orthonormal basis functions. In this paper we apply computational conformal geometry with the conformal energy…
Optical metasurfaces are planar arrangements of subwavelength meta-atoms that implement a wide range of transformations on incident light. The design of efficient metasurfaces requires that the responses of and interactions among meta-atoms…
Geometry processing presents a variety of difficult numerical problems, each seeming to require its own tailored solution. This breadth is largely due to the expansive list of geometric primitives, e.g., splines, triangles, and hexahedra,…
We propose a novel learning-based approach for robust 3D shape matching. Our method builds upon deep functional maps and can be trained in a fully unsupervised manner. Previous deep functional map methods mainly focus on predicting…