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In man-made environments such as indoor scenes, when point-based 3D reconstruction fails due to the lack of texture, lines can still be detected and used to support surfaces. We present a novel method for watertight piecewise-planar surface…

3D geometry is a very informative cue when interacting with and navigating an environment. This writing proposes a new approach to 3D reconstruction and scene understanding, which implicitly learns 3D geometry from depth maps pairing a deep…

In this study, we address the challenge of 3D scene structure recovery from monocular depth estimation. While traditional depth estimation methods leverage labeled datasets to directly predict absolute depth, recent advancements advocate…

Deep learning approaches to 3D shape segmentation are typically formulated as a multi-class labeling problem. Existing models are trained for a fixed set of labels, which greatly limits their flexibility and adaptivity. We opt for top-down…

We propose an end-to-end deep learning architecture that produces a 3D shape in triangular mesh from a single color image. Limited by the nature of deep neural network, previous methods usually represent a 3D shape in volume or point cloud,…

We present a generic framework for gradient reconstruction schemes on unstructured meshes using the notion of a dyadic sum-vector product. The proposed formulation reconstructs centroidal gradients of a scalar from its directional…

Nonlinear manifold learning from unorganized data points is a very challenging unsupervised learning and data visualization problem with a great variety of applications. In this paper we present a new algorithm for manifold learning and…

Interfacial reconstruction between two-dimensional (2D) materials and metal substrates fundamentally governs heterostructure properties, yet conventional flat substrates fail to capture the continuous crystallographic landscape. Here, we…

A levelset free but a hybrid image segmentation approach based on a modified version of the piece wise constant shape gradient of an Mumford Shah shape functional and a repulsive function is considered. The segmentation is performed a…

Reconstructing the underlying 3D surface of an object from a single image is a challenging problem that has received extensive attention from the computer vision community. Many learning-based approaches tackle this problem by learning a 3D…

3D dense reconstruction refers to the process of obtaining the complete shape and texture features of 3D objects from 2D planar images. 3D reconstruction is an important and extensively studied problem, but it is far from being solved. This…

We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…

Random geometric graphs are random graph models defined on metric spaces. Such a model is defined by first sampling points from a metric space and then connecting each pair of sampled points with probability that depends on their distance,…

In this paper, a novel learning-based network, named DeepDT, is proposed to reconstruct the surface from Delaunay triangulation of point cloud. DeepDT learns to predict inside/outside labels of Delaunay tetrahedrons directly from a point…

We propose a Semi-Lagrangian scheme coupled with Radial Basis Function interpolation for approximating a curvature-related level set model, which has been proposed by Zhao et al. in \cite{ZOMK} to reconstruct unknown surfaces from sparse,…

Choosing the right representation for geometry is crucial for making 3D models compatible with existing applications. Focusing on piecewise-smooth man-made shapes, we propose a new representation that is usable in conventional CAD modeling…

Reconstructions of sea level prior to the satellite altimeter era are usually derived from tide gauge records; however most algorithms for this assume that modes of sea level variability are stationary which is not true over several…

This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…

We present a unified framework tackling two problems: class-specific 3D reconstruction from a single image, and generation of new 3D shape samples. These tasks have received considerable attention recently; however, existing approaches rely…

We review the theory of, and develop algorithms for transforming a finite point set in ${\bf R}^d$ into a set in \emph{radial isotropic position} by a nonsingular linear transformation followed by rescaling each image point to the unit…