Short-range MEMS-based (Micro Electronical Mechanical System) LiDAR provides precise point cloud datasets for rock fragment surfaces. However, there is more vibrational noise in MEMS-based LiDAR signals, which cannot guarantee that the reconstructed point cloud data are not distorted with a high compression ratio. Many studies have illustrated that wavelet-based clustered compressive sensing can improve reconstruction precision. The k-means clustering algorithm can be conveniently employed to obtain clusters; however, estimating a meaningful k value (i.e., the number of clusters) is challenging. An excessive quantity of clusters is not necessary for dense point clouds, as this leads to elevated consumption of memory and CPU resources. For sparser point clouds, fewer clusters lead to more distortions, while excessive clusters lead to more voids in reconstructed point clouds. This study proposes a local clustering method to determine a number of clusters closer to the actual number based on GMM (Gaussian Mixture Model) observation distances and density peaks. Experimental results illustrate that the estimated number of clusters is closer to the actual number in four datasets from the KEEL public repository. In point cloud compression and recovery experiments, our proposed approach compresses and recovers the Bunny and Armadillo datasets in the Stanford 3D repository; the experimental results illustrate that our proposed approach improves reconstructed point clouds’ geometry and curvature similarity. Furthermore, the geometric similarity increases to 0.9 above in our complete rock fragment surface datasets after selecting a better wavelet basis for each dimension of MEMS-based LiDAR signals. In both experiments, the sparsity of signals was 0.8 and the sampling ratio was 0.4. Finally, a rock outcrop point cloud data experiment is utilized to verify that the proposed approach is applicable for large-scale research objects. All of our experiments illustrate that the proposed adaptive clustered compressive sensing approach can better reconstruct MEMS-based LiDAR point clouds with a lower sampling ratio.

With the increasing availability of multimodal remote sensing (RS) data, semantic segmentation that leverages complementary information from true orthophotos (TOP) and digital surface models (DSM) has become essential for urban analysis. Diffusion-based segmentation provides an effective iterative refinement mechanism for modeling complex multimodal distributions; however, conventional pixel-wise supervision emphasizes local accuracy while overlooking global distribution alignment, often leading to inconsistent predictions and blurred object boundaries. Although maximum mean discrepancy (MMD) measures global statistical differences between predicted and ground-truth distributions, its effectiveness in high-dimensional class-probability spaces is limited by directional cancellation effects that reduce sensitivity to complex distribution shifts. To address this issue, we propose a projection-kernel regularized diffusion-based multimodal RS segmentation framework that enforces global statistical alignment through distribution-level regularization rather than modifying the intrinsic diffusion process. The proposed regularization performs multi-directional projections of high-dimensional class-probability vectors onto one-dimensional subspaces and derives a closed-form kernel integration to avoid numerical sampling across projection directions, enabling efficient and stable global distribution matching. In addition, a Cross-Attention Dual-Encoder Fusion (CADEF) module is introduced to alleviate geometry–texture misalignment, and a Hierarchical EMA-Gated Recursive Denoising (HERD) mechanism is designed to stabilize multiscale feature refinement. Experiments on the ISPRS Vaihingen and Potsdam benchmarks demonstrate that the proposed regularization consistently improves segmentation accuracy over state-of-the-art CNN-, Transformer-, and diffusion-based baselines, yielding enhanced global consistency and sharper boundary delineation. Code is available at: https://github.com/tonyy127/PKDiff