相关论文: Advances in Global Solvers for 3D Vision

Automated three-dimensional (3D) object reconstruction is the task of building a geometric representation of a physical object by means of sensing its surface. Even though new single view reconstruction techniques can predict the surface,…

Geodesic convexity generalizes the notion of (vector space) convexity to nonlinear metric spaces. But unlike convex optimization, geodesically convex (g-convex) optimization is much less developed. In this paper we contribute to the…

Although 3D Gaussian Splatting has been widely studied because of its realistic and efficient novel-view synthesis, it is still challenging to extract a high-quality surface from the point-based representation. Previous works improve the…

Piecewise constant curvature is a popular kinematics framework for continuum robots. Computing the model parameters from the desired end pose, known as the inverse kinematics problem, is fundamental in manipulation, tracking and planning…

Geometry problem solving, a crucial aspect of mathematical reasoning, is vital across various domains, including education, the assessment of AI's mathematical abilities, and multimodal capability evaluation. The recent surge in deep…

Generalist neural routing solvers have shown great potential in solving diverse vehicle routing problems (VRPs) with a unified model. However, existing solvers are typically limited to symmetric settings or degrade in performance when…

This paper presents an accurate and fast 3D global localization method, 3D-BBS, that extends the existing branch-and-bound (BnB)-based 2D scan matching (BBS) algorithm. To reduce memory consumption, we utilize a sparse hash table for…

3D Gaussian Splatting (3DGS) enables efficient rendering, yet accurate surface reconstruction remains challenging due to unreliable geometric supervision. Existing approaches predominantly rely on depth-based reprojection to infer…

The benefits of cutting planes based on the perspective function are well known for many specific classes of mixed-integer nonlinear programs with on/off structures. However, we are not aware of any empirical studies that evaluate their…

Is a geometric model required to synthesize novel views from a single image? Being bound to local convolutions, CNNs need explicit 3D biases to model geometric transformations. In contrast, we demonstrate that a transformer-based model can…

Visual segmentation seeks to partition images, video frames, or point clouds into multiple segments or groups. This technique has numerous real-world applications, such as autonomous driving, image editing, robot sensing, and medical…

Many resource allocation tasks are challenging global (i.e., non-convex) optimization problems. The main issue is that the computational complexity of these problems grows exponentially in the number of variables instead of polynomially as…

We propose a containment query that is robust to the watertightness of regions bound by trimmed NURBS surfaces, as this property is difficult to guarantee for in-the-wild CAD models. Containment is determined through the generalized winding…

High-order tensor methods that employ Taylor-based local models (of degree $p\ge 3$) within adaptive regularization frameworks have been recently proposed for both convex and nonconvex optimization problems. They have been shown to have…

In recent years, the nuclear norm minimization (NNM) problem has been attracting much attention in computer vision and machine learning. The NNM problem is capitalized on its convexity and it can be solved efficiently. The standard nuclear…

Constrained Optimization solution algorithms are restricted to point based solutions. In practice, single or multiple objectives must be satisfied, wherein both the objective function and constraints can be non-convex resulting in multiple…

In this paper we show that visual diffusion models can serve as effective geometric solvers: they can directly reason about geometric problems by working in pixel space. We first demonstrate this on the Inscribed Square Problem, a…

We present a new approach for computing approximate global minimizers to a large class of non-local pairwise interaction problems defined over probability distributions. The approach predicts candidate global minimizers, with a recovery…

3D Gaussian Splatting (3DGS) has emerged as a prominent technique with the potential to become a mainstream method for 3D representations. It can effectively transform multi-view images into explicit 3D Gaussian through efficient training,…

This paper presents a piecewise convexification method for solving non-convex multi-objective optimization problems with box constraints. Based on the ideas of the $\alpha$-based Branch and Bound (${\rm \alpha BB}$) method of global…