相关论文: Local Morphometry of Closed, Implicit Surfaces

The isometric immersion of two-dimensional Riemannian manifolds or surfaces in the three-dimensional Euclidean space is a fundamental problem in differential geometry. When the Gauss curvature is negative, the isometric immersion problem is…

The computer vision task of reconstructing 3D images, i.e., shapes, from their single 2D image slices is extremely challenging, more so in the regime of limited data. Deep learning models typically optimize geometric loss functions, which…

Neural implicit surface representations have recently emerged as popular alternative to explicit 3D object encodings, such as polygonal meshes, tabulated points, or voxels. While significant work has improved the geometric fidelity of these…

Efficient and fast reconstruction of anatomical structures plays a crucial role in clinical practice. Minimizing retrieval and processing times not only potentially enhances swift response and decision-making in critical scenarios but also…

We propose approaches based on deep learning to localize objects in images when only a small training dataset is available and the images have low quality. That applies to many problems in medical image processing, and in particular to the…

We obtain improved local well-posedness results for the Lorentzian timelike minimal surface equation. In dimension $d=3$, for a surface of arbitrary co-dimension, we show a gain of $1/3$ derivative regularity compared to a generic equation…

Hypersurfaces embedded in conformal manifolds appear frequently as boundary data in boundary-value problems in cosmology and string theory. Viewed as the non-null conformal infinity of a spacetime, we consider hypersurfaces embedded in a…

Tube-like surfaces are widely encountered in geometry processing, engineering structures, and medical anatomy, yet their intrinsic longitudinal and circumferential topology is not well preserved by conventional planar annular or rectangular…

To reconstruct a 3D human surface from a single image, it is crucial to simultaneously consider human pose, shape, and clothing details. Recent approaches have combined parametric body models (such as SMPL), which capture body pose and…

In this article, we first show that for all compact Riemannian manifolds with non-empty smooth boundary and dimension at least 3, there exists a metric, pointwise conformal to the original metric, with constant scalar curvature in the…

Morphing is a long-standing problem in vision and computer graphics, requiring a time-dependent warping for feature alignment and a blending for smooth interpolation. Recently, multilayer perceptrons (MLPs) have been explored as implicit…

We propose a visualization method to understand the effect of multidimensional projection on local subspaces, using implicit function differentiation. Here, we understand the local subspace as the multidimensional local neighborhood of data…

We develop a new approach to the conformal geometry of embedded hypersurfaces by treating them as conformal infinities of conformally compact manifolds. This involves the Loewner--Nirenberg-type problem of finding on the interior a metric…

We prove the following localized version of a classical ellipsoid characterization: Let $B\subset\mathbb R^3$ be convex body with a smooth strictly convex boundary and 0 in the interior, and suppose that there is an open set of planes…

Interferometric closure invariants encode calibration-independent details of an object's morphology. Excepting simple cases, a direct backward transformation from closure invariants to morphologies is not well established. We demonstrate…

This paper is devoted to $C^2$ a priori estimates for strictly locally convex radial graphs with prescribed Weingarten curvature and boundary in space forms. By constructing two-step continuity process and applying degree theory arguments,…

In this paper we deduce a local deformation lemma for uniform embeddings in a metric covering space over a compact manifold from the deformation lemma for embeddings of a compact subspace in a manifold. This implies the local…

Accurate detection and segmentation of anatomical structures from ultrasound images are crucial for clinical diagnosis and biometric measurements. Although ultrasound imaging has been widely used with superiorities such as low cost and…

We address the problem of integrability of the sub-Riemannian mean curvature of an embedded hypersurface around isolated characteristic points. The main contribution of this note is the introduction of a concept of mildly degenerate…

This paper extends parts of the results from [P.W.Michor and D. Mumford, \emph{Appl. Comput. Harmon. Anal.,} 23 (2007), pp. 74--113] for plane curves to the case of hypersurfaces in $\mathbb R^n$. Let $M$ be a compact connected oriented…