Organizations: Remote Sensing Applications, TUM School of Engineering and Design, Technical University of Munich, Munich, Germany · Department of Geoscience & Remote Sensing, Delft University of Technology, Delft, The Netherlands
4D point clouds acquired by permanent laser scanning (PLS) enable accurate high-frequency monitoring of surface change in dynamic topographic environments. However, existing methods remain limited in organizing detected surface activities into meaningful process types. We propose DeepTopoClustering (DTC), an unsupervised framework for deriving a hierarchical process taxonomy from object-based surface activities, so-called 4D objects-by-change (4D-OBCs). We transform each 4D-OBC into a GeoMorphogram, a distributional sequence representing the temporal evolution of topographic change within a spatially bounded surface activity. A convolutional autoencoder learns latent embeddings from GeoMorphograms, which are jointly optimized using a hierarchical deep clustering objective to organize surface activities into a hierarchy. We evaluate the learned hierarchy using expert annotations on two 4D datasets of sandy beach sites and their combination. DTC with GeoMorphograms achieves the highest agreement with expert judgment at the taxonomy level comprising eight major process types (F1=0.78, match accuracy =0.92), outperforming dimensionality reduction and conventional flat clustering. The learned taxonomy separates major erosion- and deposition-dominated activities and distinguishes finer subtypes based on change magnitude, duration, compactness, and temporal evolution. DTC thus provides a scalable and interpretable route from 4D change detection to a data-driven, expert-supported surface process taxonomy, advancing automated knowledge derivation for understanding surface dynamics in topographic monitoring.
Figures & tables
Figure 1: Overall research framework for deriving surface process taxonomy from 4D point clouds, including representing extracted 4D surface activities as GeoMorphograms, organizing them into learnable hierarchical clusters, and validating the learned taxonomy on 4D test datasets with expert annotations.
Figure 2: Permanent laser scanning point cloud of the study areas in Noordwijk and Kijkduin sandy beach. The terrestrial laser scans are colorized using high-resolution aerial imagery in 2021 (Noordwijk) and in 2016 (Kijkduin). The aerial imagery and administrative areas are provided by the Public Service On the Map ( PDOK ) in the Netherlands.
Figure 3: Examples of 4D objects-by-change (4D-OBCs) and their corresponding GeoMorphograms. Subplots (a) and (c) show erosion- and deposition-dominated 4D-OBCs, respectively. For each object, the upper map shows the spatial extent with core points colored by their peak change magnitude and the seed point marked in red. The lower plot shows the change time series of all core points within the object, colored by their peak change magnitude; the red line indicates the seed time series and the gray dotted line marks the peak change epoch. Subplots (b) and (d) show the corresponding GeoMorphograms for the erosion 4D-OBC (a) and the deposition 4D-OBC (c), respectively. Color intensities show the distribution of change values at each epoch, and the activity duration is marked using a red dashed vertical line.
Figure 4: Labeling interface used to collect expert annotations. Each task presents a pair of 4D objects-by-change (4D-OBCs) through their spatial and temporal representation. Experts assess whether the two 4D-OBCs represent the same or different types of surface activity and provide a confidence score. The labeling interface figure is shown as guidance, as provided in the tutorial for expert annotators.
Figure 5: Evaluation metrics computed on pairwise annotations across different numbers of clusters k on the test set. The dashed line marks the selected level, k=8 , where the highest overall F1 score is achieved by our approach.
Figure 6: Learned hierarchical tree from the BeachOBC dataset. Each node image represents the decoded GeoMorphogram prototype from the corresponding cluster center, and each edge indicates the parent–child relation between nodes. Text labels indicate the dominant visual differences between sibling branches and are used to support the interpretation of the splitting sequence. The derived expert-supported types (at k=8 ) are highlighted by colorful boxes, and the branches are named based on the distinguishing properties along the tree.
Figure 7: Surface process taxonomy derived from the BeachOBC dataset, consisting of combined 4D-OBCs detected from the Kijkduin and Noordwijk datasets. The circular tree shows the selected hierarchical structure at k=8 , the outer panels show representative GeoMorphograms for each leaf node, and the surrounding feature rings summarize cluster-wise physical properties.
Figure 8: Temporal frequency of different surface process clusters at Kijkduin. Frequency is computed as the number of active 4D-OBCs per day for each selected cluster.
Figure 9: Temporal frequency of different surface process clusters at Noordwijk. Frequency is computed as the number of active 4D-OBCs per day for each selected cluster.
Figure 10: T-SNE visualization of the learned GeoMorphogram embeddings after pretraining (left) and clustering (right).
Figure 11: Performance comparison of integrating different handcrafted feature sets on the BeachOBC dataset. GM denotes the GeoMorphogram input (orange). Different conditioning settings (blue) are: (1) basic features, including area and total change volume; (2) geometric features, including area, principal axes of the point distribution estimated by PCA, PCA relative orientation, cross-shore location, initial mean elevation, and total change volume; (3) temporal features, including duration and cyclically encoded start time with sine/cosine transformation; and (4) all of the features of 1–3.
Figure 12: Evaluation metrics computed on pairwise annotations across different numbers of clusters k on the validation set. The dashed line marks the selected level, k=8 , where the highest overall F1 score is achieved by our approach.
Figure 13: Learned hierarchical tree from the Kijkduin dataset. Each node image represents the decoded GeoMorphogram prototype from the corresponding cluster center, and each edge indicates the parent–child relation between nodes.
Figure 14: Learned hierarchical tree from the Noordwijk dataset. Each node image represents the decoded GeoMorphogram prototype from the corresponding cluster center, and each edge indicates the parent–child relation between nodes.
We introduce a framework for learning latent representations of 4D objects which are descriptive, faithfully capturing object geometry and appearance; compressive, aiding in downstream efficiency; and accessible, requiring minimal input, i.e., an unstructured dynamic point cloud, to construct. Specifically, Velox trains an encoder to compress spatiotemporal color point clouds into a set of dynamic shape tokens. These tokens are supervised using two complementary decoders: a 4D surface decoder, which models the time-varying surface distribution capturing the geometry; and a Gaussian decoder, which maps the tokens to 3D Gaussians, helping learn appearance. To demonstrate the utility of our representation, we evaluate it across three downstream tasks -- video-to-4D generation, 3D tracking, and cloth simulation via image-to-4D generation -- and observe strong performances in all settings.
Real-time process monitoring requires methods that extract actionable information from high-dimensional time-series data. In this work, we present a new approach for process monitoring that combines tools of topological data analysis (TDA) and machine learning. In the proposed approach, we represent multivariate time-series data as manifolds and use topological descriptors to summarize the structure of such data; we then use a neural ordinary differential equation to learn the dynamic evolution of the topological structure of the system. Using real data from an industrial process, we show that this trajectory-based event detection approach is effective at detecting diverse types of events. We contrast this approach against reconstruction-based approaches such as principal component analysis and autoencoders and against a trajectory-based approach that uses Koopman autoencoders.
Angan Mukherjee, Tyler A. Soderstrom, Michael J. Kurtz +1
Department of Chemical & Biological Engineering, University of Wisconsin-Madison, 1415 Engineering Drive, Madison, WI 53706, USA · ExxonMobil Technology and Engineering, 22777 Springwoods Village Pkwy, Spring, TX 77389, USA
Advanced manufacturing technologies allow for the production of intricate parts featuring high shape complexity and spatially-varying material composition. Data fusion of point clouds with chromatic attributes provides 4D point clouds, a compact and informative representation that encodes both shape and material information. In this paper, we present a registration-free framework for Simultaneous Monitoring of shApe and Color (SMAC) via 4D point clouds. The proposed framework leverages Laplace-Beltrami operator spectral properties to capture and monitor geometric features and the relationship between shape and surface color. A combined monitoring scheme is proposed to effectively detect shape deformations and color anomalies, along with a spatially-aware post-signal diagnostic procedure to determine the source of change and localize color anomalies. Importantly, neither component relies on registration or mesh reconstruction, eliminating error-prone and computationally expensive preprocessing steps. A Monte Carlo simulation study and a case study on functionally graded materials demonstrate that SMAC achieves effective detection performance, particularly for subtle defects, while providing diagnostic capabilities to identify the source and location of anomalies.