Related papers: Geometry Fidelity for Spherical Images
I propose a spatial-mode demultiplexing (SPADE) measurement scheme for the far-field imaging of spatially incoherent optical sources. For any object too small to be resolved by direct imaging under the diffraction limit, I show that SPADE…
Shape metrics for objects in high dimensions remain sparse. Those that do exist, such as hyper-volume, remain limited to objects that are better understood such as Platonic solids and $n$-Cubes. Further, understanding objects of ill-defined…
One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…
The geometry of a two-dimensional surface in a curved space can be most easily visualized by using an isometric embedding in flat three-dimensional space. Here we present a new method for embedding surfaces with spherical topology in flat…
3D scene reconstruction is fundamental for spatial intelligence applications such as AR, robotics, and digital twins. Traditional multi-view stereo struggles with sparse viewpoints or low-texture regions, while neural rendering approaches,…
We introduce a differential visual similarity metric to train deep neural networks for 3D reconstruction, aimed at improving reconstruction quality. The metric compares two 3D shapes by measuring distances between multi-view images…
Reconstructing object deformation from a single image remains a significant challenge in computer vision and graphics. Existing methods typically rely on multi-view video to recover deformation, limiting their applicability under…
In absence of a lens to form an image, incoherent or partially coherent light scattering off an obstructive or reflective object forms a broad intensity distribution in the far field with only feeble spatial features. We show here that…
Gaussian Splatting (GS), a recent technique for converting discrete points into continuous spatial representations, has shown promising results in 3D scene modeling and 2D image super-resolution. In this paper, we explore its untapped…
Neural signed distance functions (SDFs) have been a vital representation to represent 3D shapes or scenes with neural networks. An SDF is an implicit function that can query signed distances at specific coordinates for recovering a 3D…
We address the problems of measuring geometric similarity between 3D scenes, represented through point clouds or range data frames, and associating them. Our approach leverages macro-scale 3D structural geometry - the relative configuration…
Given a surface $S$ in a 3D contact sub-Riemannian manifold $M$, we investigate the metric structure induced on $S$ by $M$, in the sense of length spaces. First, we define a coefficient $\widehat K$ at characteristic points that determines…
Semantic segmentation stands as a pivotal research focus in computer vision. In the context of industrial image inspection, conventional semantic segmentation models fail to maintain the segmentation consistency of fixed components across…
The geodesic total curvature of rectifiable spherical curves is analyzed. We extend to the case of high dimension spheres the explicit formula that holds true for curves supported into the 2-sphere. For this purpose, we take advantage of…
In spherical surface wave tomography, one measures the integrals of a function defined on the sphere along great circle arcs. This forms a generalization of the Funk--Radon transform, which assigns to a function its integrals along full…
We present a novel data set made up of omnidirectional video of multiple objects whose centroid positions are annotated automatically. Omnidirectional vision is an active field of research focused on the use of spherical imagery in video…
We study the statistical geometry of random chords on n-dimensional spheres by deriving explicit analytical expressions for the chord length distribution and its associated structural properties. A critical threshold emerges at dimension…
Qualifying the discrepancy between 3D geometric models, which could be represented with either point clouds or triangle meshes, is a pivotal issue with board applications. Existing methods mainly focus on directly establishing the…
Accurate surface estimation is critical for downstream tasks in scientific simulation, and quantifying uncertainty in implicit neural 3D representations still remains a substantial challenge due to computational inefficiencies, scalability…
In addition to color and textural information, geometry provides important cues for 3D scene reconstruction. However, current reconstruction methods only include geometry at the feature level thus not fully exploiting the geometric…