OC3D: Weakly Supervised Outdoor 3D Object Detection with Only Coarse Click Annotation

LiDAR-based outdoor 3D object detection has received widespread attention. However, training 3D detectors from the LiDAR point cloud typically relies on expensive bounding box annotations. This paper presents OC3D, an innovative weakly supervised method requiring only coarse clicks on the bird' s eye view of the 3D point cloud. A key challenge here is the absence of complete geometric descriptions of the target objects from such simple click annotations. To address this problem, our proposed OC3D adopts a two-stage strategy. In the first stage, we initially design a novel dynamic and static classification strategy and then propose the Click2Box and Click2Mask modules to generate box-level and mask-level pseudo-labels for static and dynamic instances, respectively. In the second stage, we design a Mask2Box module, leveraging the learning capabilities of neural networks to update mask-level pseudo-labels, which contain less information, to box level pseudo-labels. Experimental results on the widely used KITTI and nuScenes datasets demonstrate that our OC3D with only coarse clicks achieves state-of-the-art performance compared to weakly-supervised 3D detection methods. Combining OC3D with a missing click mining strategy, we propose a OC3D++ pipeline, which requires only 0.2% annotation cost in the KITTI dataset to achieve performance comparable to fully supervised methods.

Functional Network: A Novel Framework for Interpretability of Deep Neural Networks

The layered structure of deep neural networks hinders the use of numerous analysis tools and thus the development of its interpretability. Inspired by the success of functional brain networks, we propose a novel framework for interpretability of deep neural networks, that is, the functional network. We construct the functional network of fully connected networks and explore its small-worldness. In our experiments, the mechanisms of regularization methods, namely, batch normalization and dropout, are revealed using graph theoretical analysis and topological data analysis. Our empirical analysis shows the following: (1) Batch normalization enhances model performance by increasing the global e ciency and the number of loops but reduces adversarial robustness by lowering the fault tolerance. (2) Dropout improves generalization and robustness of models by improving the functional specialization and fault tolerance. (3) The models with dierent regularizations can be clustered correctly according to their functional topological dierences, re ecting the great potential of the functional network and topological data analysis in interpretability.

High-Dimensional Data Set Simplification by Laplace-Beltrami Operator

With the development of the Internet and other digital technologies, the speed of data generation has become considerably faster than the speed of data processing. Because big data typically contain massive redundant information, it is possible to significantly simplify a big data set while maintaining the key information it contains. In this paper, we develop a big data simplification method based on the eigenvalues and eigenfunctions of the Laplace-Beltrami operator (LBO). Specifically, given a data set that can be considered as an unorganized data point set in high-dimensional space, a discrete LBO defined on the big data set is constructed and its eigenvalues and eigenvectors are calculated. Then, the local extremum and the saddle points of the eigenfunctions are proposed to be the feature points of a data set in high-dimensional space, constituting a simplified data set. Moreover, we develop feature point detection methods for the functions defined on an unorganized data point set in high-dimensional space, and devise metrics for measuring the fidelity of the simplified data set to the original set. Finally, examples and applications are demonstrated to validate the efficiency and effectiveness of the proposed methods, demonstrating that data set simplification is a method for processing a maximum-sized data set using a limited data processing capability.

Persistence B-Spline Grids: Stable Vector Representation of Persistence Diagrams Based on Data Fitting

Over the last decades, many attempts have been made to optimally integrate machine learning (ML) and topological data analysis. A prominent problem in applying persistent homology to ML tasks is finding a vector representation of a persistence diagram (PD), which is a summary diagram for representing topological features. From the perspective of data fitting, a stable vector representation, persistence B-spline grid (PB), is proposed based on the efficient technique of progressive-iterative approximation for least-squares B-spline surface fitting. Meanwhile, we theoretically prove that the PB method is stable with respect to the metrics defined on the PD space, i.e., the $p$-Wasserstein distance and the bottleneck distance. The proposed method was tested on a synthetic dataset, datasets of randomly generated PDs, data of a dynamical system, and 3D CAD models.