Point cloud data augmentation is critical to improving the generalization of 3D deep learning models. However, existing methods often fail to preserve the underlying manifold structure, leading to semantic distortion or topology violation. This causes models to learn untrustworthy features, thereby limiting the representational ability of the model. To overcome these limitations, we propose ManiPoint, a novel point cloud augmentation framework based on diffeomorphism that explicitly preserves manifold structure during deformation. ManiPoint constructs diffeomorphic transformations via continuous differentiable mappings, ensuring topological consistency and geometric continuity between original and augmented data. To prevent excessive distortion and ensure semantic consistency, we introduce a controllable deformation mechanism that quantitatively constrains the augmentation magnitude and enables fine-grained control over the deformation space. We further provide theoretical analysis, indicating that, compared with topologically inconsistent methods, ManiPoint reduces empirical and vicinal risks by generating diverse and structurally reliable samples. Extensive experiments and visualizations on object-level datasets demonstrate that ManiPoint produces high-quality augmentations and consistently improves model robustness over existing baselines. Meanwhile, the scalability of our method was further verified on the scene-level datasets.

With the rapid advancement of 3D scanning technology, point clouds have become a crucial data type in computer vision and machine learning. However, learning robust representations for point clouds remains a significant challenge due to their irregularity and sparsity. In this paper, we propose a novel Dual Manifold Regularization (DMR) framework that makes full use of the properties of positive and negative curvature in manifolds to improve the representation of point clouds. Specifically, we leverage DMR based on hyperbolic and hyperspherical manifolds to address the limitations of traditional single-manifold regularization techniques, including inadequate generalization ability and adaptability to data diversity, as well as the difficulty of capturing complex relationships between data. To begin, we utilize the tree-like structure of the hyperbolic manifold to model the part-whole hierarchical relationships within point clouds. This allows for a more comprehensive representation of the data, improving the model's capability to understand complex shapes. Additionally, we construct positive samples through topological consistency augmentation and employ contrastive learning techniques in the hyperspherical manifold to capture more discriminative features within the data. Our experimental results show that our method outperforms traditional supervised learning and single-manifold regularization techniques in point cloud analysis. Specifically, for shape classification, DMR achieves a new State-Of-The-Art (SOTA) performance with 94.8% Overall Accuracy (OA) on ModelNet40 and 90.7% OA on ScanObjectNN, surpassing the recent SOTA model without increasing the baseline parameters.

Data augmentation has been widely used in machine learning. Its main goal is to transform and expand the original data using various techniques, creating a more diverse and enriched training dataset. However, due to the disorder and irregularity of point clouds, existing methods struggle to enrich geometric diversity and maintain topological consistency, leading to imprecise point cloud understanding. In this paper, we propose SinPoint, a novel method designed to preserve the topological structure of the original point cloud through a homeomorphism. It utilizes the Sine function to generate smooth displacements. This simulates object deformations, thereby producing a rich diversity of samples. In addition, we propose a Markov chain Augmentation Process to further expand the data distribution by combining different basic transformations through a random process. Our extensive experiments demonstrate that our method consistently outperforms existing Mixup and Deformation methods on various benchmark point cloud datasets, improving performance for shape classification and part segmentation tasks. Specifically, when used with PointNet++ and DGCNN, our method achieves a state-of-the-art accuracy of 90.2 in shape classification with the real-world ScanObjectNN dataset. We release the code at https://github.com/CSBJian/SinPoint.

The Moderate Resolution Imaging Spectroradiometer (MODIS) Leaf Area Index (LAI) product is critical for global terrestrial carbon monitoring and ecosystem modeling. However, MODIS LAI is calculated on a pixel-by-pixel and day-by-day basis without using spatial or temporal correlation information, which leads to its high sensitivity of LAI to uncertainties in observed reflectance resulting in an increased noise level in time series. While exploiting prior knowledge is a common practice to fill gaps in observations, little research has been conducted on reducing noisy fluctuations and improving the overall quality of the MODIS LAI product. To address this issue, we proposed a Spatio-Temporal Information Composition Algorithm (STICA), which directly introduces prior Spatio-temporal correlation and Multiple Quality Assessment (MQA) information into the existing MODIS LAI product. STICA reduces the noise level and improves the quality of the product while maintaining the original physically-based (Radiative Transfer Model, RTM) LAI production process. In our analysis, the R2 increased from 0.79 to 0.81, and the RMSE decreased from 0.81 to 0.68 compared to the ground-based LAI reference. The improvement was more pronounced with the degradation of the data quality. STICA reduced noisy fluctuations in the LAI time series to varying degrees among eight biome types. In the Amazon Forest, STICA significantly improved the time-series stability of LAI. Moreover, STICA can effectively eliminate abnormal declines in time series and correct for extreme outliers in LAI. We expect that the MODIS LAI Reanalyzed product generated by this method will better support the application of high-quality LAI datasets.