Elliptically symmetric distributions for directional data of arbitrary dimension

We formulate a class of angular Gaussian distributions that allows different degrees of isotropy for directional random variables of arbitrary dimension. Through a series of novel reparameterization, this distribution family is indexed by parameters with meaningful statistical interpretations that can range over the entire real space of an adequate dimension. The new parameterization greatly simplifies maximum likelihood estimation of all model parameters, which in turn leads to theoretically sound and numerically stable inference procedures to infer key features of the distribution. Byproducts from the likelihood-based inference are used to develop graphical and numerical diagnostic tools for assessing goodness of fit of this distribution in a data application. Simulation study and application to data from a hydrogeology study are used to demonstrate implementation and performance of the inference procedures and diagnostics methods.Comment: 22 pages, 15 figure

Learnable Graph Matching: A Practical Paradigm for Data Association

Data association is at the core of many computer vision tasks, e.g., multiple object tracking, image matching, and point cloud registration. Existing methods usually solve the data association problem by network flow optimization, bipartite matching, or end-to-end learning directly. Despite their popularity, we find some defects of the current solutions: they mostly ignore the intra-view context information; besides, they either train deep association models in an end-to-end way and hardly utilize the advantage of optimization-based assignment methods, or only use an off-the-shelf neural network to extract features. In this paper, we propose a general learnable graph matching method to address these issues. Especially, we model the intra-view relationships as an undirected graph. Then data association turns into a general graph matching problem between graphs. Furthermore, to make optimization end-to-end differentiable, we relax the original graph matching problem into continuous quadratic programming and then incorporate training into a deep graph neural network with KKT conditions and implicit function theorem. In MOT task, our method achieves state-of-the-art performance on several MOT datasets. For image matching, our method outperforms state-of-the-art methods with half training data and iterations on a popular indoor dataset, ScanNet. Code will be available at https://github.com/jiaweihe1996/GMTracker.Comment: Submitted to TPAMI on Mar 21, 2022. arXiv admin note: substantial text overlap with arXiv:2103.1617

Object as Query: Lifting any 2D Object Detector to 3D Detection

3D object detection from multi-view images has drawn much attention over the past few years. Existing methods mainly establish 3D representations from multi-view images and adopt a dense detection head for object detection, or employ object queries distributed in 3D space to localize objects. In this paper, we design Multi-View 2D Objects guided 3D Object Detector (MV2D), which can lift any 2D object detector to multi-view 3D object detection. Since 2D detections can provide valuable priors for object existence, MV2D exploits 2D detectors to generate object queries conditioned on the rich image semantics. These dynamically generated queries help MV2D to recall objects in the field of view and show a strong capability of localizing 3D objects. For the generated queries, we design a sparse cross attention module to force them to focus on the features of specific objects, which suppresses interference from noises. The evaluation results on the nuScenes dataset demonstrate the dynamic object queries and sparse feature aggregation can promote 3D detection capability. MV2D also exhibits a state-of-the-art performance among existing methods. We hope MV2D can serve as a new baseline for future research.Comment: technical repor

TSTTC: A Large-Scale Dataset for Time-to-Contact Estimation in Driving Scenarios

Time-to-Contact (TTC) estimation is a critical task for assessing collision risk and is widely used in various driver assistance and autonomous driving systems. The past few decades have witnessed development of related theories and algorithms. The prevalent learning-based methods call for a large-scale TTC dataset in real-world scenarios. In this work, we present a large-scale object oriented TTC dataset in the driving scene for promoting the TTC estimation by a monocular camera. To collect valuable samples and make data with different TTC values relatively balanced, we go through thousands of hours of driving data and select over 200K sequences with a preset data distribution. To augment the quantity of small TTC cases, we also generate clips using the latest Neural rendering methods. Additionally, we provide several simple yet effective TTC estimation baselines and evaluate them extensively on the proposed dataset to demonstrate their effectiveness. The proposed dataset is publicly available at https://open-dataset.tusen.ai/TSTTC.Comment: 19 pages, 9 figure

Mip-Splatting: Alias-free 3D Gaussian Splatting

Recently, 3D Gaussian Splatting has demonstrated impressive novel view synthesis results, reaching high fidelity and efficiency. However, strong artifacts can be observed when changing the sampling rate, \eg, by changing focal length or camera distance. We find that the source for this phenomenon can be attributed to the lack of 3D frequency constraints and the usage of a 2D dilation filter. To address this problem, we introduce a 3D smoothing filter which constrains the size of the 3D Gaussian primitives based on the maximal sampling frequency induced by the input views, eliminating high-frequency artifacts when zooming in. Moreover, replacing 2D dilation with a 2D Mip filter, which simulates a 2D box filter, effectively mitigates aliasing and dilation issues. Our evaluation, including scenarios such a training on single-scale images and testing on multiple scales, validates the effectiveness of our approach.Comment: Project page: https://niujinshuchong.github.io/mip-splatting