Related papers: Globally Consistent Normal Orientation for Point C…

For a smooth map $g: X \to U(N)$, where $X$ is a three-dimensional, oriented, and closed manifold, the winding number is defined as $W_3 = \frac{1}{24\pi^2} \int_{X} \mathrm{Tr}\left[(g^{-1}dg)^3\right]$. We present a discrete formulation…

In this paper we address the task of finding representative subsets of points in a 3D point cloud by means of a point-wise ordering. Only a few works have tried to address this challenging vision problem, all with the help of hard to obtain…

This paper presents a consensus algorithm under misaligned orientations, which is defined as (i) misalignment to global coordinate frame of local coordinate frames, (ii) biases in control direction or sensing direction, or (iii) misaligned…

Point Cloud Registration (PCR) is a fundamental and significant issue in photogrammetry and remote sensing, aiming to seek the optimal rigid transformation between sets of points. Achieving efficient and precise PCR poses a considerable…

The conventional pose estimation of a 3D object usually requires the knowledge of the 3D model of the object. Even with the recent development in convolutional neural networks (CNNs), a 3D model is often necessary in the final estimation.…

In the field of data-driven 3D shape analysis and generation, the estimation of global topological features from localized representations such as point clouds, voxels, and neural implicit fields is a longstanding challenge. This paper…

This paper presents the linear Global stability analysis of the incompressible axisymmetric boundary layer on a circular cone. The base flow is considered parallel to the axis of cone at the inlet. The angle of attack is zero and hence the…

Deep neural networks endow the downsampled superpoints with highly discriminative feature representations. Previous dominant point cloud registration approaches match these feature representations as the first step, e.g., using the Sinkhorn…

Point cloud processing poses two fundamental challenges: establishing consistent point ordering and effectively learning fine-grained geometric features. Current architectures rely on complex operations that limit expressivity while…

We present a global optimization approach to optical flow estimation. The approach optimizes a classical optical flow objective over the full space of mappings between discrete grids. No descriptor matching is used. The highly regular…

One-class learning is the classic problem of fitting a model to data for which annotations are available only for a single class. In this paper, we propose a novel objective for one-class learning. Our key idea is to use a pair of…

Many approaches have been proposed to estimate camera poses by directly minimizing photometric error. However, due to the non-convex property of direct alignment, proper initialization is still required for these methods. Many robust norms…

Let $M^m$ be an oriented manifold, let $N^{m-1}$ be an oriented closed manifold, and let $p$ be a point in $M^m$. For a smooth map $f:N^{m-1} \to M^m, p \not\in Im f,$ we introduce an invariant $awin_p(f)$ that can be regarded as a…

Point cloud filtering and normal estimation are two fundamental research problems in the 3D field. Existing methods usually perform normal estimation and filtering separately and often show sensitivity to noise and/or inability to preserve…

Real-time registration of partially overlapping point clouds has emerging applications in cooperative perception for autonomous vehicles and multi-agent SLAM. The relative translation between point clouds in these applications is higher…

The winding number is a concept in complex analysis which has, in the presence of chiral symmetry, a physics interpretation as the topological index belonging to gapped phases of fermions. We study statistical properties of this topological…

Targets are essential in problems such as object tracking in cluttered or textureless environments, camera (and multi-sensor) calibration tasks, and simultaneous localization and mapping (SLAM). Target shapes for these tasks typically are…

Point cloud is the most fundamental representation of 3D geometric objects. Analyzing and processing point cloud surfaces is important in computer graphics and computer vision. However, most of the existing algorithms for surface analysis…

Despite the growing demand for accurate surface normal estimation models, existing methods use general-purpose dense prediction models, adopting the same inductive biases as other tasks. In this paper, we discuss the inductive biases needed…

We present a complete mean field theory for a balanced state of a simple model of an orientation hypercolumn. The theory is complemented by a description of a numerical procedure for solving the mean-field equations quantitatively. With our…