Related papers: PLG-IN: Pluggable Geometric Consistency Loss with …
The Wasserstein distance has become increasingly important in machine learning and deep learning. Despite its popularity, the Wasserstein distance is hard to approximate because of the curse of dimensionality. A recently proposed approach…
We study the structure of the support of a doubling measure by analyzing its self-similarity properties, which we estimate using a variant of the $L^1$ Wasserstein distance. We show that measure satisfying certain self-similarity conditions…
Persistence diagrams are a useful tool from topological data analysis which can be used to provide a concise description of a filtered topological space. What makes them even more useful in practice is that they come with a notion of a…
Change Point Detection (CPD) aims to identify moments of abrupt distribution shifts in data streams. Real-world high-dimensional CPD remains challenging due to data pattern complexity and violation of common assumptions. Resorting to…
Computer vision systems that are deployed in safety-critical applications need to quantify their output uncertainty. We study regression from images to parameter values and here it is common to detect uncertainty by predicting probability…
Monocular depth estimation is often described as an ill-posed and inherently ambiguous problem. Estimating depth from 2D images is a crucial step in scene reconstruction, 3Dobject recognition, segmentation, and detection. The problem can be…
Many applications of computer vision rely on the alignment of similar but non-identical images. We present a fast algorithm for aligning heterogeneous images based on optimal transport. Our approach combines the speed of fast Fourier…
This paper presents a unified computational framework for the estimation of distances, geodesics and barycenters of merge trees. We extend recent work on the edit distance [106] and introduce a new metric, called the Wasserstein distance…
3D detection is a critical task that enables machines to identify and locate objects in three-dimensional space. It has a broad range of applications in several fields, including autonomous driving, robotics and augmented reality. Monocular…
Monocular depth estimation has improved significantly in recent years, driven by increasingly powerful models and large-scale training data. Predicted depth is increasingly used as an input signal for downstream tasks such as…
Deducing a 3D human pose from a single 2D image is inherently challenging because multiple 3D poses can correspond to the same 2D representation. 3D data can resolve this pose ambiguity, but it is expensive to record and requires an…
We propose a projected Wasserstein gradient descent method (pWGD) for high-dimensional Bayesian inference problems. The underlying density function of a particle system of WGD is approximated by kernel density estimation (KDE), which faces…
Reconstructing dynamic 3D scenes from monocular video has broad applications in AR/VR, robotics, and autonomous navigation, but often fails due to severe motion blur caused by camera and object motion. Existing methods commonly follow a…
Geometry Projection is a powerful depth estimation method in monocular 3D object detection. It estimates depth dependent on heights, which introduces mathematical priors into the deep model. But projection process also introduces the error…
Monocular depth inference has gained tremendous attention from researchers in recent years and remains as a promising replacement for expensive time-of-flight sensors, but issues with scale acquisition and implementation overhead still…
Sliced Wasserstein (SW) distances offer an efficient method for comparing high-dimensional probability measures by projecting them onto multiple 1-dimensional probability distributions. However, identifying informative slicing directions…
Learning to predict multi-label outputs is challenging, but in many problems there is a natural metric on the outputs that can be used to improve predictions. In this paper we develop a loss function for multi-label learning, based on the…
Depth estimation is essential for various important real-world applications such as autonomous driving. However, it suffers from severe performance degradation in high-velocity scenario since traditional cameras can only capture blurred…
Optimization over the space of probability measures endowed with the Wasserstein-2 geometry is central to modern machine learning and mean-field modeling. However, traditional methods relying on full Wasserstein gradients often suffer from…
Optimal Transport has sparked vivid interest in recent years, in particular thanks to the Wasserstein distance, which provides a geometrically sensible and intuitive way of comparing probability measures. For computational reasons, the…