Related papers: PLG-IN: Pluggable Geometric Consistency Loss with …

We present Wasserstein Embedding for Graph Learning (WEGL), a novel and fast framework for embedding entire graphs in a vector space, in which various machine learning models are applicable for graph-level prediction tasks. We leverage new…

Wasserstein metrics are increasingly being used as similarity scores for images treated as discrete measures on a grid, yet their behavior under noise remains poorly understood. In this work, we consider the sensitivity of the signed…

Wasserstein distances are increasingly used in a wide variety of applications in machine learning. Sliced Wasserstein distances form an important subclass which may be estimated efficiently through one-dimensional sorting operations. In…

Reconstruction of geometric structures from images using supervised learning suffers from limited available amount of accurate data. One type of such data is accurate real-world RGB-D images. A major challenge in acquiring such ground truth…

We address the problem of efficiently computing Wasserstein distances for multiple pairs of distributions drawn from a meta-distribution. To this end, we propose a fast estimation method based on regressing Wasserstein distance on sliced…

This paper focuses on a similarity measure, known as the Wasserstein distance, with which to compare images. The Wasserstein distance results from a partial differential equation (PDE) formulation of Monge's optimal transport problem. We…

Monocular depth estimation aims at predicting depth from a single image or video. Recently, self-supervised methods draw much attention since they are free of depth annotations and achieve impressive performance on several daytime…

Motivated by the 2D class averaging problem in single-particle cryo-electron microscopy (cryo-EM), we present a k-means algorithm based on a rotationally-invariant Wasserstein metric for images. Unlike existing methods that are based on…

Depth map estimation from images is an important task in robotic systems. Existing methods can be categorized into two groups including multi-view stereo and monocular depth estimation. The former requires cameras to have large overlapping…

Monocular 3D scene understanding tasks, such as object size estimation, heading angle estimation and 3D localization, is challenging. Successful modern day methods for 3D scene understanding require the use of a 3D sensor. On the other…

The sliced Wasserstein (SW) distances between two probability measures are defined as the expectation of the Wasserstein distance between two one-dimensional projections of the two measures. The randomness comes from a projecting direction…

Self-supervised monocular depth estimation has been widely investigated to estimate depth images and relative poses from RGB images. This framework is attractive for researchers because the depth and pose networks can be trained from just…

In this paper, we propose Wasserstein Isometric Mapping (Wassmap), a nonlinear dimensionality reduction technique that provides solutions to some drawbacks in existing global nonlinear dimensionality reduction algorithms in imaging…

Monocular image-based 3D perception has become an active research area in recent years owing to its applications in autonomous driving. Approaches to monocular 3D perception including detection and tracking, however, often yield inferior…

Self-supervised multi-frame monocular depth estimation relies on the geometric consistency between successive frames under the assumption of a static scene. However, the presence of moving objects in dynamic scenes introduces inevitable…

In this paper, we propose a pipeline to generate 3D point cloud of an object from a single-view RGB image. Most previous work predict the 3D point coordinates from single RGB images directly. We decompose this problem into depth estimation…

Consider a set of points sampled independently near a smooth compact submanifold of Euclidean space. We provide mathematically rigorous bounds on the number of sample points required to estimate both the dimension and the tangent spaces of…

Wasserstein distance (WD) and the associated optimal transport plan have been proven useful in many applications where probability measures are at stake. In this paper, we propose a new proxy of the squared WD, coined min-SWGG, that is…

Monocular depth prediction plays a crucial role in understanding 3D scene geometry. Although recent methods have achieved impressive progress in evaluation metrics such as the pixel-wise relative error, most methods neglect the geometric…

Learning to predict scene depth and camera motion from RGB inputs only is a challenging task. Most existing learning based methods deal with this task in a supervised manner which require ground-truth data that is expensive to acquire. More…