Noise removal is a critical stage in the preprocessing of point clouds, exerting a significant impact on subsequent processes such as point cloud classification, segmentation, feature extraction, and 3D reconstruction. The exploration of methods capable of adapting to and effectively handling the noise in point clouds from real-world outdoor scenes remains an open and practically significant issue. Addressing this issue, this study proposes an adaptive kernel approach based on local density and global statistics (AKA-LDGS). This method constructs the overall framework for point cloud denoising using Bayesian estimation theory. It dynamically sets the prior probabilities of real and noise points according to the spatial function relationship, which varies with the distance from the points to the center of the LiDAR. The probability density function (PDF) for real points is constructed using a multivariate Gaussian distribution, while the PDF for noise points is established using a data-driven, non-parametric adaptive kernel density estimation (KDE) approach. Experimental results demonstrate that this method can effectively remove noise from point clouds in real-world outdoor scenes while maintaining the overall structural features of the point cloud.

With the rapid advancement of remote-sensing technology, the spectral information obtained from hyperspectral remote-sensing imagery has become increasingly rich, facilitating detailed spectral analysis of Earth’s surface objects. However, the abundance of spectral information presents certain challenges for data processing, such as the “curse of dimensionality” leading to the “Hughes phenomenon”, “strong correlation” due to high resolution, and “nonlinear characteristics” caused by varying surface reflectances. Consequently, dimensionality reduction of hyperspectral data emerges as a critical task. This paper begins by elucidating the principles and processes of hyperspectral image dimensionality reduction based on manifold theory and learning methods, in light of the nonlinear structures and features present in hyperspectral remote-sensing data, and formulates a dimensionality reduction process based on manifold learning. Subsequently, this study explores the capabilities of feature extraction and low-dimensional embedding for hyperspectral imagery using manifold learning approaches, including principal components analysis (PCA), multidimensional scaling (MDS), and linear discriminant analysis (LDA) for linear methods; and isometric mapping (Isomap), locally linear embedding (LLE), Laplacian eigenmaps (LE), Hessian locally linear embedding (HLLE), local tangent space alignment (LTSA), and maximum variance unfolding (MVU) for nonlinear methods, based on the Indian Pines hyperspectral dataset and Pavia University dataset. Furthermore, the paper investigates the optimal neighborhood computation time and overall algorithm runtime for feature extraction in hyperspectral imagery, varying by the choice of neighborhood k and intrinsic dimensionality d values across different manifold learning methods. Based on the outcomes of feature extraction, the study examines the classification experiments of various manifold learning methods, comparing and analyzing the variations in classification accuracy and Kappa coefficient with different selections of neighborhood k and intrinsic dimensionality d values. Building on this, the impact of selecting different bandwidths t for the Gaussian kernel in the LE method and different Lagrange multipliers λ for the MVU method on classification accuracy, given varying choices of neighborhood k and intrinsic dimensionality d, is explored. Through these experiments, the paper investigates the capability and effectiveness of different manifold learning methods in feature extraction and dimensionality reduction within hyperspectral imagery, as influenced by the selection of neighborhood k and intrinsic dimensionality d values, identifying the optimal neighborhood k and intrinsic dimensionality d value for each method. A comparison of classification accuracies reveals that the LTSA method yields superior classification results compared to other manifold learning approaches. The study demonstrates the advantages of manifold learning methods in processing hyperspectral image data, providing an experimental reference for subsequent research on hyperspectral image dimensionality reduction using manifold learning methods.

With the continuous advancements in three-dimensional scanning technology, point clouds are fundamental data in various fields such as autonomous driving, 3D urban modeling, and the preservation of cultural heritage. However, inherent inaccuracies in instruments and external environmental interference often introduce noise and outliers into point cloud data, posing numerous challenges for advanced processing tasks such as registration, segmentation, classification, and 3D reconstruction. To effectively address these issues, this study proposes a hierarchical denoising strategy based on finite measurable segmentation in spherical space, taking into account the performance differences in horizontal and vertical resolutions of LiDAR systems. The effectiveness of this method was validated through a denoising experiment conducted on point cloud data collected from real outdoor environments. The experimental result indicates that this denoising strategy not only effectively eliminates noise but also more accurately preserves the original detail features of the point clouds, demonstrating significant advantages over conventional denoising techniques. Overall, this study introduces a novel and effective method for denoising point cloud data in outdoor real-world scenes.

With the rapid advancements in remote sensing technology, the spectral information from hyperspectral remote sensing images has become increasingly rich, facilitating detailed spectral analysis of the Earth's surface objects. However, this abundance of spectral data poses significant challenges in data processing, such as the curse of dimensionality leading to the “Hughes” phenomenon, "strong correlation" due to high resolution, and "non-linear characteristics" caused by varied surface reflectance rates. Therefore, dimensionality reduction of hyperspectral data has become a crucial task. This paper, grounded in manifold theory and manifold learning techniques, and considering the non-linear structures and features in hyperspectral remote sensing data, elucidates the principles and processes of dimensionality reduction in hyperspectral remote sensing images using manifold learning, with a formalized expression of the process. This article introduces spectral information divergence (SID) into the nearest neighbor graph computation of manifold learning algorithms. The principles and computational processes of nearest neighbor graph algorithms based on Euclidean distance (ED), spectral angle mapping (SAM), and SID are studied, and a comparative analysis of the dimensionality reduction effects under these three metrics in hyperspectral data is conducted. Experiments on feature extraction under different metrics were performed using the publicly available Indian Pines hyperspectral dataset. The intrinsic features obtained post-dimensionality reduction were used as inputs for classification algorithms in ground objects classification experiments, with algorithm runtime, overall accuracy, and Kappa coefficient as evaluation metrics for dimensionality reduction quality. The results demonstrate that nearest neighbor graph computation based on SAM and SID outperforms traditional ED methods; SAM-based computation has the lowest time complexity, while SID-based manifold learning yields the highest accuracy in ground objects classification. Thus, manifold learning based on SAM and SID metrics proves to be an effective method for feature extraction in hyperspectral remote sensing data, underscoring the potential of manifold learning techniques in the dimensionality reduction of hyperspectral remote sensing images.

Simultaneous localization and mapping (SLAM) faces significant challenges due to high computational costs, low accuracy, and instability, which are particularly problematic because SLAM systems often operate in real-time environments where timely and precise state estimation is crucial. High computational costs can lead to delays, low accuracy can result in incorrect mapping and localization, and instability can make the entire system unreliable, especially in dynamic or complex environments. As the state-space dimension increases, the filtering error of the standard cubature Kalman filter (CKF) grows, leading to difficulties in multiplicative noise propagation and instability in state estimation results. To address these issues, this paper proposes an extended-dimensional embedded CKF based on truncated singular-value decomposition (TSVD-AECKF). Firstly, singular-value decomposition (SVD) is employed instead of the Cholesky decomposition in the standard CKF to mitigate the non-positive definiteness of the state covariance matrix. Considering the effect of small singular values on the stability of state estimation, a method is provided to truncate singular values by determining the truncation threshold using the Akaike information criterion (AIC). Furthermore, the system noise is embedded into the state variables, and an embedding volume criterion is used to improve the conventional CKF while extending the dimensionality. Finally, the proposed algorithm was validated and analyzed through both simulations and real-world experiments. The results indicate that the proposed method effectively mitigates the increase in localization error as the state-space dimension grows, enhancing time efficiency by 55.54%, and improving accuracy by 35.13% compared to the standard CKF algorithm, thereby enhancing the robustness and stability of mapping.