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Mistakes/uncertainties in object detection could lead to catastrophes when deploying robots in the real world. In this paper, we measure the uncertainties of object localization to minimize this kind of risk. Uncertainties emerge upon…
Bounding box regression (BBR) has been widely used in object detection and instance segmentation, which is an important step in object localization. However, most of the existing loss functions for bounding box regression cannot be…
Recently, the Wasserstein loss function has been proven to be effective when applied to deterministic full-waveform inversion (FWI) problems. We consider the application of this loss function in Bayesian FWI so that the uncertainty can be…
The Gromov-Wasserstein (GW) distance is frequently used in machine learning to compare distributions across distinct metric spaces. Despite its utility, it remains computationally intensive, especially for large-scale problems. Recently, a…
Intersection over Union (IoU) is the most popular evaluation metric used in the object detection benchmarks. However, there is a gap between optimizing the commonly used distance losses for regressing the parameters of a bounding box and…
Understanding the 3D geometry and semantics of driving scenes is critical for safe autonomous driving. Recent advances in 3D occupancy prediction have improved scene representation but often suffer from visual inconsistencies, leading to…
We present an efficient 3D object detection framework based on a single RGB image in the scenario of autonomous driving. Our efforts are put on extracting the underlying 3D information in a 2D image and determining the accurate 3D bounding…
This paper proposes a new theoretical lens to view Wasserstein generative adversarial networks (WGANs). To minimize the Wasserstein-1 distance between the true data distribution and our estimate of it, we derive a distribution-dependent…
Modeling observations as random distributions embedded within Wasserstein spaces is becoming increasingly popular across scientific fields, as it captures the variability and geometric structure of the data more effectively. However, the…
The Wasserstein distance and its variations, e.g., the sliced-Wasserstein (SW) distance, have recently drawn attention from the machine learning community. The SW distance, specifically, was shown to have similar properties to the…
Optimal transport with quadratic cost provides a geometric framework for steering an ensemble, modeled by a probability law, with minimal effort. Yet ambient-space formulations become unwieldy in high dimensions, and sensing or actuation in…
Weak Gaussian perturbations on a plane wave background could trigger lots of rogue waves, due to modulational instability. Numerical simulations showed that these rogue waves seemed to have similar unit structure. However, to the best of…
As 3D Gaussian Splatting (3D-GS) gains significant attention and its commercial usage increases, the need for watermarking technologies to prevent unauthorized use of the 3D-GS models and rendered images has become increasingly important.…
While theoretically appealing, the application of the Wasserstein distance to large-scale machine learning problems has been hampered by its prohibitive computational cost. The sliced Wasserstein distance and its variants improve the…
The emergence of neural and Gaussian-based radiance field methods has led to considerable advancements in novel view synthesis and 3D object reconstruction. Nonetheless, specular reflection and refraction continue to pose significant…
Anomaly detection in time-series data is a critical challenge with significant implications for network security. Recent quantum machine learning approaches, such as quantum kernel methods and variational quantum circuits, have shown…
The Gromov-Wasserstein (GW) distance is an effective measure of alignment between distributions supported on distinct ambient spaces. Calculating essentially the mutual departure from isometry, it has found vast usage in domain translation…
Simultaneously localizing camera poses and constructing Gaussian radiance fields in dynamic scenes establish a crucial bridge between 2D images and the 4D real world. Instead of removing dynamic objects as distractors and reconstructing…
3D object detection has been widely studied due to its potential applicability to many promising areas such as robotics and augmented reality. Yet, the sparse nature of the 3D data poses unique challenges to this task. Most notably, the…
Used as priors for Bayesian inverse problems, diffusion models have recently attracted considerable attention in the literature. Their flexibility and high variance enable them to generate multiple solutions for a given task, such as…