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We present the Branch-and-Bound Performance Estimation Programming (BnB-PEP), a unified methodology for constructing optimal first-order methods for convex and nonconvex optimization. BnB-PEP poses the problem of finding the optimal…
This paper proposes a novel and exact method to reconstruct line-based 3D structure from a single image using Manhattan world assumption. This problem is a distinctly unsolved problem because there can be multiple 3D reconstructions from a…
Numerous applications require algorithms that can align partially overlapping point sets while maintaining invariance to geometric transformations (e.g., similarity, affine, rigid). This paper introduces a novel global optimization method…
This paper presents a method of estimating the geometry of a room and the 3D pose of objects from a single 360-degree panorama image. Assuming Manhattan World geometry, we formulate the task as a Bayesian inference problem in which we…
In this paper, a robust RGB-D SLAM system is proposed to utilize the structural information in indoor scenes, allowing for accurate tracking and efficient dense mapping on a CPU. Prior works have used the Manhattan World (MW) assumption to…
Extracting planes from a 3D scene is useful for downstream tasks in robotics and augmented reality. In this paper we tackle the problem of estimating the planar surfaces in a scene from posed images. Our first finding is that a surprisingly…
Finding an optimal alignment connecting two end-points in a specified corridor is a complex problem that requires solving three interrelated sub-problems, namely the horizontal alignment, vertical alignment and earthwork optimization…
Map based visual inertial localization is a crucial step to reduce the drift in state estimation of mobile robots. The underlying problem for localization is to estimate the pose from a set of 3D-2D feature correspondences, of which the…
This article considers nonconvex global optimization problems subject to uncertainties described by continuous random variables. Such problems arise in chemical process design, renewable energy systems, stochastic model predictive control,…
In recent years, several branch-and-bound (BnB) algorithms have been proposed to globally optimize rigid registration problems. In this paper, we suggest a general framework to improve upon the BnB approach, which we name Quasi BnB. Quasi…
In this paper, a statistically optimal solution to the Perspective-n-Point (PnP) problem is presented. Many solutions to the PnP problem are geometrically optimal, but do not consider the uncertainties of the observations. In addition, it…
We propose an algorithm to predict room layout from a single image that generalizes across panoramas and perspective images, cuboid layouts and more general layouts (e.g. L-shape room). Our method operates directly on the panoramic image,…
Online augmentation of an oblique aerial image sequence with structural information is an essential aspect in the process of 3D scene interpretation and analysis. One key aspect in this is the efficient dense image matching and depth…
Estimating consistently oriented normals for point clouds enables a number of important applications in computer graphics. While local normal estimation is possible with simple techniques like PCA, orienting them to be globally consistent…
Optimal transport on a graph focuses on finding the most efficient way to transfer resources from one distribution to another while considering the graph's structure. This paper introduces a new distributed algorithm that solves the optimal…
Significant geometric structures can be compactly described by global wireframes in the estimation of 3D room layout from a single panoramic image. Based on this observation, we present an alternative approach to estimate the walls in 3D…
The estimation of 3D human motion from video has progressed rapidly but current methods still have several key limitations. First, most methods estimate the human in camera coordinates. Second, prior work on estimating humans in global…
Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…
In this work, we construct a novel numerical method for solving the multi-marginal optimal transport problems with Coulomb cost. This type of optimal transport problems arises in quantum physics and plays an important role in understanding…
Recent developments in generative models and large-scale datasets have substantially advanced 3D world generation, facilitating a broad range of domains including spatial intelligence, embodied intelligence, and autonomous driving. While…