Related papers: Divergence-Free Shape Interpolation and Correspond…
We present a novel method for computing correspondences across 3D shapes using unsupervised learning. Our method computes a non-linear transformation of given descriptor functions, while optimizing for global structural properties of the…
We present a novel learning-based approach for computing correspondences between non-rigid 3D shapes. Unlike previous methods that either require extensive training data or operate on handcrafted input descriptors and thus generalize poorly…
We introduce a new paradigm for immersed finite element and isogeometric methods based on interpolating function spaces from an unfitted background mesh into Lagrange finite element spaces defined on a foreground mesh that captures the…
Learning 3D shape representation with dense correspondence for deformable objects is a fundamental problem in computer vision. Existing approaches often need additional annotations of specific semantic domain, e.g., skeleton poses for human…
We present a new technique for the interpolation of discretely-sampled non-negat ive scalar fields across regions of missing data. Any set of basis functions can be used, though the method is fastest when they are close to orthogonal. We…
While dealing with matching shapes to their parts, we often apply a tool known as functional maps. The idea is to translate the shape matching problem into "convenient" spaces by which matching is performed algebraically by solving a least…
Efficient shape morphing techniques play a crucial role in the approximation of partial differential equations defined in parametrized domains, such as for fluid-structure interaction or shape optimization problems. In this paper, we focus…
This note introduces a novel paradigm for conformal defects with continuously adjustable dimensions. Just as the standard $\varepsilon$ expansion interpolates between integer spacetime dimensions, a new parameter, $\delta$, is used to…
The Karhunen-Lo\`eve series expansion (KLE) decomposes a stochastic process into an infinite series of pairwise uncorrelated random variables and pairwise $L^2$-orthogonal functions. For any given truncation order of the infinite series the…
We present implicit displacement fields, a novel representation for detailed 3D geometry. Inspired by a classic surface deformation technique, displacement mapping, our method represents a complex surface as a smooth base surface plus a…
Dense 3D shape correspondence remains a central challenge in computer vision and graphics as many deep learning approaches still rely on intermediate geometric features or handcrafted descriptors, limiting their effectiveness under…
We introduce and discuss shape-based models for finding the best interpolation data in the compression of images with noise. The aim is to reconstruct missing regions by means of minimizing a data fitting term in the $L^2$-norm between the…
Although shape correspondence is a central problem in geometry processing, most methods for this task apply only to two-dimensional surfaces. The neglected task of volumetric correspondence--a natural extension relevant to shapes extracted…
We present a nonlinear interpolation technique for parametric fields that exploits optimal transportation of coherent structures of the solution to achieve accurate performance. The approach generalizes the nonlinear interpolation procedure…
Accurately reconstructing continuous flow fields from sparse or indirect measurements remains an open challenge, as existing techniques often suffer from oversmoothing artifacts, reliance on heterogeneous architectures, and the…
Topological transforms have been very useful in statistical analysis of shapes or surfaces without restrictions that the shapes are diffeomorphic and requiring the estimation of correspondence maps. In this paper we introduce two…
In this note, we consider the truncated Karhunen-Lo\`eve expansion for approximating solutions to infinite dimensional inverse problems. We show that, under certain conditions, the bound of the error between a solution and its…
We study the dimensional continuation of the sphere free energy in conformal field theories. In continuous dimension $d$ we define the quantity $\tilde F=\sin (\pi d/2)\log Z$, where $Z$ is the path integral of the Euclidean CFT on the…
We detail how to use Newton's method for distortion-based curved $r$-adaption to a discrete high-order metric field while matching a target geometry. Specifically, we combine two terms: a distortion measuring the deviation from the target…
Correspondence-based shape models are key to various medical imaging applications that rely on a statistical analysis of anatomies. Such shape models are expected to represent consistent anatomical features across the population for…