Related papers: Conformal Surface Morphing with Applications on Fa…

The concept of an adapted homology basis for a prime order conformal automorphism of a compact Riemann surface extends to arbitrary finite groups of conformal automorphisms. Here we compute some examples of adapted homology bases for some…

We introduce a simple procedure to integrate differential forms with arbitrary holomorphic poles on Riemann surfaces. It gives rise to an intrinsic regularization of such singular integrals in terms of the underlying conformal geometry.…

We investigate discrete spin transformations, a geometric framework to manipulate surface meshes by controlling mean curvature. Applications include surface fairing -- flowing a mesh onto say, a reference sphere -- and mesh extrusion --…

The paper presents a novel concept of a 3D structural metasurface with mechanically morphing capability that can be used as a transmit- or reflect-array to manipulate electromagnetic beams for applications in RF sensing and communications…

We establish a uniformization result for metric surfaces - metric spaces that are topological surfaces with locally finite Hausdorff 2-measure. Using the geometric definition of quasiconformality, we show that a metric surface that can be…

Registration is an essential tool in image analysis. Deep learning based alternatives have recently become popular, achieving competitive performance at a faster speed. However, many contemporary techniques are limited to volumetric…

We fully generalize a previously-developed computational geometry tool [1] to perform large-scale simulations of arbitrary two-dimensional faceted surfaces $z = h(x,y)$. Our method uses a three-component facet/edge/junction storage model,…

In this paper, we present a novel open-source pipeline for face registration based on Gaussian processes as well as an application to face image analysis. Non-rigid registration of faces is significant for many applications in computer…

Anatomical structures such as the hippocampus, liver, and bones can be analyzed as orientable, closed surfaces. This permits the computation of volume, surface area, mean curvature, Gaussian curvature, and the Euler-Poincar\'e…

In the present paper, an integrated paradigm for topology optimization on complex surfaces with arbitrary genus is proposed. The approach is constructed based on the two-dimensional (2D) Moving Morphable Component (MMC) framework, where a…

Many recent works have reconstructed distinctive 3D face shapes by aggregating shape parameters of the same identity and separating those of different people based on parametric models (e.g., 3D morphable models (3DMMs)). However, despite…

This is an elementary introduction to a method for studying harmonic maps into symmetric spaces, and in particular for studying constant mean curvature (CMC) surfaces, that was developed by J. Dorfmeister, F. Pedit and H. Wu. There already…

We present a variety of geometrical and combinatorial tools that are used in the study of geometric structures on surfaces: volume, contact, symplectic, complex and almost complex structures. We start with a series of local rigidity results…

In this work, we present a practical approach to the problem of facial landmark detection. The proposed method can deal with large shape and appearance variations under the rich shape deformation. To handle the shape variations we equip our…

In this article we give a complete description of the evolution of an area decreasing map $f:M\to N$ induced by its mean curvature in the situation where $M$ and $N$ are complete Riemann surfaces with bounded geometry, $M$ being compact,…

The advent of high resolution imaging has made data on surface shape widespread. Methods for the analysis of shape based on landmarks are well established but high resolution data require a functional approach. The starting point is a…

We present an algorithm that automatically establishes dense correspondences between a large number of 3D faces. Starting from automatically detected sparse correspondences on the outer boundary of 3D faces, the algorithm triangulates…

Any three-dimensional Riemannian metric can be locally obtained by deforming a constant curvature metric along one direction. The general interest of this result, both in geometry and physics, and related open problems are stressed.

In this paper, we present an end-to-end learning framework for detailed 3D face reconstruction from a single image. Our approach uses a 3DMM-based coarse model and a displacement map in UV-space to represent a 3D face. Unlike previous work…

We propose a framework that can deform an object in a 2D image as it exists in 3D space. Most existing methods for 3D-aware image manipulation are limited to (1) only changing the global scene information or depth, or (2) manipulating an…