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DeepTopoClustering: Unsupervised Derivation of Surface Process Taxonomy from 4D Point Clouds for Topographic Monitoring

Jiapan Wang, Daan Hulskemper, Mathilde Letard, Roderik Lindenbergh, Katharina Anders

arXiv:2610.09860v1cs.CVcs.LG

TL;DR

Long-term 4D monitoring detects surface activities, but existing methods remain limited in organizing them into meaningful process types. DeepTopoClustering represents 4D-OBCs as GeoMorphograms and learns a hierarchical clustering tree; against expert judgments, the resulting taxonomy identifies eight primary types with an F1 score of 0.78 and an accuracy of 0.92.

  • Problem

    Existing approaches have limited ability to organize detected surface activities into meaningful process types, while surface activities vary substantially in extent, duration, geometry, magnitude, and dynamics.

    Source: §1 · pp. 1–2

  • Method

    DeepTopoClustering represents each 4D-OBC as a GeoMorphogram and jointly learns latent embeddings and a hierarchical clustering tree for coarse-to-fine grouping.

    Source: §1 · p. 2

  • Results

    At the highest expert-agreement level, the taxonomy identifies eight primary surface-process types, with an F1 score of 0.78 and an accuracy of 0.92.

    Source: §6 · p. 19

  • Takeaways & Limitations

    The experiments demonstrate a data-driven, expert-supported surface-process taxonomy from two sandy-beach datasets and their combination.

    Source: §6 · p. 19

    GeoMorphograms reduce explicit spatial information, and transferability beyond sandy beach environments remains untested.

    Source: §5.5 · p. 19

Abstract

from arXiv · show

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 ($F_1=0.78$, 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.

1. Introduction

Long-term 4D monitoring detects many surface activities, but organizing them into process types remains difficult because labels and the number of types are unknown and activities vary widely. The paper introduces GeoMorphograms and DeepTopoClustering to derive a hierarchical taxonomy from individual activities, with expert evaluation of the learned clusters.

1. Introduction

  • A surface-process taxonomy can support comparison across space and time, but deriving one is difficult without labeled data or a known number of types, especially as activities vary in extent, duration, geometry, magnitude, and dynamics.Such a taxonomy can also help identify dominant and rare types and provide a basis for posthoc analysis of process interactions and environmental drivers.Source: §1 · p. 2
  • Existing clustering workflows rely on handcrafted features and domain knowledge, often for one geographic setting, limiting flexibility when relevant process properties are not known in advance.The paper motivates learning representations directly from detected 4D-OBCs and organizing them hierarchically without predefined labels or a known number of types.Source: §1 · p. 2
  • DeepTopoClustering combines object-based 4D change analysis, representation learning, and hierarchical deep clustering to derive an interpretable taxonomy from surface activities.The framework learns latent embeddings and a coarse-to-fine clustering tree from GeoMorphograms.Source: §1 · pp. 2–3
  • GeoMorphograms represent each 4D-OBC as a distributional sequence of topographic change over time, designed to accommodate irregular geometry, varying duration, and noise.Each sequence describes change within the spatial extent of its surface activity.Source: §1 · pp. 2–3
  • The paper presents the first data-driven sandy-beach surface-process taxonomy derived from 4D point clouds and an expert strategy for assessing clusters and selecting their number without ground-truth labels.The evaluation quantifies agreement between learned clusters and human interpretation.Source: §1 · pp. 2–3

2. Related work

Prior work has advanced 4D change detection and clustering, but characterization remains constrained by fixed-resolution inputs, handcrafted representations, or predefined cluster counts. The paper situates hierarchical deep clustering as a route to organizing variable surface activities without assuming their category structure in advance.

2. Related work

  • High-frequency 4D monitoring extends topographic analysis from static 3D surfaces to time series, yet interpreting detected changes as underlying processes remains limited.Existing work has developed data acquisition and alignment, then change detection and quantification, with process-level interpretation as the less-developed transition.Source: §2 · p. 3

Change detection and quantification

  • M3C2 estimates spatially averaged distances between bitemporal point clouds along local surface normals, while 4D-OBCs delineate connected surface activities with similar temporal behavior across space and time.These methods support change detection and activity extraction, but do not directly identify the process types represented by those activities.Source: §2 · p. 3

From change analysis to characterization

  • Clustering full point-cloud time series can reveal recurring change patterns, but point-wise or grid-wise analyses remain tied to fixed spatial resolutions rather than variable surface activities.Examples span sandy beaches, past-glacial valleys, vegetation, and landslides.Source: §2 · pp. 3–4
  • Handcrafted descriptors and resampled time series help compare 4D-OBCs, but location dependence, noise, data gaps, resampling loss, and reliance on prior assumptions limit systematic taxonomy derivation.The cited work includes temporal and geometric descriptors, seed time series, and multivariate statistical time series.Source: §2 · p. 4

Deep clustering for unsupervised class derivation

  • Deep clustering learns latent embeddings and cluster assignments without labeled input; representative approaches include alternating feature clustering with pseudo-label updates and iterative refinement with soft assignments.These methods have been applied to image and 3D data, including change analysis.Source: §2 · p. 4
  • Existing deep-clustering approaches for change analysis mostly use flat clustering and require a predefined cluster count, while process categories may be better represented hierarchically, from shared broad types to finer properties.Flexible or hierarchical methods exist, but no existing framework integrates object-centric 4D change analysis, representation learning, and hierarchical deep clustering for generic interpretable surface-process types.Source: §2 · pp. 4–5

3. Data and methods

The section describes how 4D objects-by-change are transformed into GeoMorphograms and clustered into a hierarchical taxonomy of surface activities, then evaluated against expert annotations. It compares clustering methods and input representations across three datasets and selects the eight-cluster level based on validation F1 and alignment with expert judgments.

3.1. Data and preprocessing

  • The study uses 2,021 Kijkduin and 4,654 Noordwijk 4D-OBCs, plus their 6,675-object BeachOBC combination, with month-stratified 80-20 training and unseen splits.The source datasets comprise hourly permanent laser scans of sandy beaches, monitored for approximately six months at Kijkduin and three years at Noordwijk.Source: §3.1 · p. 5

3.2. GeoMorphogram: a distributional sequence representation of a surface activity

  • GeoMorphograms encode each activity as hourly sequences of normalized change-magnitude distributions, preserving temporal evolution and within-activity variability for comparison across different spatial scales.The representation uses 42 change bins over [−0.5 m, 0.5 m] and a maximum duration of 1,024 hours; shorter activities are zero-padded and longer ones downsampled.Source: §3.2 · pp. 5, 7, 8

3.3. DeepTopoClustering for hierarchical grouping

  • DTC jointly learns GeoMorphogram embeddings and a binary clustering tree that separates broad activity patterns at shallow levels and finer differences at deeper levels.Decoded node centers provide representative GeoMorphogram prototypes for interpreting cluster patterns.Source: §3.3 · pp. 9–10

3.4. Evaluation

  • Experts labeled whether sampled 4D-OBC pairs represented the same activity type; 467 filtered pairs were divided equally into validation and test sets for tuning and evaluation.The labels were determined by weighted majority voting across experts, and the hierarchy was assessed at different split levels to identify granularity matching expert distinctions.Source: §3.4 · p. 11

3.5. Deriving a surface process taxonomy

  • The reported process types are the clusters at the hierarchy level with the highest agreement with expert annotations, characterized using change magnitude, orientation, cross-shore location, and activity duration.This selects an expert-supported number of clusters without manually choosing a preferred level of detail.Source: §3.5 · pp. 11–12

3.6. Competing methods

  • PCA + k-means, AE + k-means, AE + agglomerative clustering, and DEC provide baselines for comparing dimensionality reduction, separately optimized embeddings and clustering, and flat deep clustering with DTC.DEC jointly optimizes representation learning and clustering but requires a predefined number of target clusters.Source: §3.6 · p. 12
  • GeoMorphograms are compared with mean 4D-OBC time series to evaluate input representation alongside latent embedding learning and hierarchical clustering.The mean time series are described as comparable to inputs used in prior work.Source: §3.6 · p. 12
  • k = 8 is selected from the DTC hierarchy using the highest validation F1 score; metrics are evaluated across cluster counts on test-set expert pairwise annotations.Table 2 covers BeachOBC, Kijkduin, and Noordwijk, with precision, recall, F1, and match accuracy; Figure 5 marks k = 8, where the approach achieves its highest overall F1.Source: Figure 5 · p. 13, Table 2 · p. 13

4. Results

DTC with GeoMorphograms performs best against expert annotations at eight clusters. The learned hierarchy separates erosion- and deposition-dominated activity, distinguishes finer process types, and shows their occurrence over time.

4.1. Quantitative performance

  • The highest validation and test F1 scores occur with DTC at k = 8; smaller k over-aggregates expert-distinct activities, while larger k may over-split similar ones.The authors select k = 8 as the expert-supported target for comparison with flat-clustering baselines.Source: §4.1 · p. 13
  • DTC with GeoMorphograms achieves the highest F1 score, precision, and match accuracy across all three datasets; on BeachOBC, F1 is 0.78 and accuracy is 0.92.It also reaches F1 scores of 0.87 on Kijkduin and 0.83 on Noordwijk.Source: §4.1 · p. 13
  • For DTC, GeoMorphograms raise F1 from 0.60 to 0.78 on BeachOBC, 0.57 to 0.87 on Kijkduin, and 0.75 to 0.83 on Noordwijk.Across methods, GeoMorphogram inputs generally yield higher F1 than mean time series, and the best performance combines GeoMorphograms with hierarchical DTC.Source: §4.1 · p. 13

4.2. Learned hierarchy tree

  • Figure 6’s decoded GeoMorphogram prototypes and parent–child edges show the splitting sequence, with sibling differences labeling branches and expert-supported types boxed at k = 8.Branch labels describe properties such as change direction, magnitude, timing, duration, compactness, and temporal coherence.Source: Figure 6 · p. 14, §4.2 · p. 14
  • The hierarchy first separates negative-change erosion from positive-change deposition, then splits each branch by temporal pattern and finer properties.Deeper distinctions include duration, coherence, and distribution compactness; gradual and sudden deposition differ in continuous versus abrupt positive change.Source: §4.2 · pp. 14–16

4.3. Surface process taxonomy

  • At k = 8, the selected hierarchy defines expert-supported sandy-beach process types; feature rings show distinct combinations of physical, geometric, domain, and temporal properties.Neighboring branches share more similar feature profiles than more distant branches, alongside representative GeoMorphograms for each leaf.Source: Figure 7 · p. 15, §4.3 · p. 16

4.4. Temporal occurrence of different process types

  • At Kijkduin, long-term gradual erosion and coherent gradual deposition both become more frequent from February to March, coinciding with observed bar migration and erosion.The Noordwijk plots show a similar increase in February 2021, with weaker increases in 2020 and 2022; frequencies count active 4D-OBCs per day.Source: §4.4 · p. 16, Figure 8 · p. 16

5. Discussion

The discussion finds that GeoMorphograms and joint hierarchical clustering preserve distinctions useful for organizing surface activities, while the resulting taxonomy remains an expert-supported interpretation rather than a definitive classification. It describes practical uses and limitations of this hierarchy for sandy-beach monitoring.

5.1. GeoMorphograms and hierarchical clustering

  • GeoMorphograms preserve spatially distributed change within 4D-OBCs, producing more balanced precision and recall and higher F1 scores with DTC than time-series representations.The discussion attributes this to preservation of change magnitude, sign, temporal coherence, and evolution, which mean time series may suppress.Source: §5.1 · pp. 16–17
  • Finer latent distinctions emerge after joint hierarchical clustering optimization, beyond the erosion–deposition separation present after autoencoder pretraining.The discussion presents reconstruction learning as a meaningful initialization and hierarchical optimization as refining the space toward subtler patterns.Source: §5.1 · p. 17, Figure 10 · p. 17

5.2. E

  • Handcrafted feature conditioning gives limited and inconsistent improvement; combining all feature groups yields the highest mean F1 score, precision, and accuracy.Individual basic, geometric, or temporal feature groups can reduce recall, accuracy, or F1; simple concatenation does not essentially improve DTC.Source: §5.2 · pp. 17–18, Figure 11 · p. 17

5.3. Interpretation of the learned taxonomy

  • The hierarchy separates broad erosion- and deposition-dominated activities, then distinguishes deeper variations in duration, magnitude, coherence, compactness, and temporal evolution.The hierarchy is label-agnostic, but expert support is still required to derive major process types; k = 8 has the highest agreement with expert annotations.Source: §5.3 · p. 18
  • Decoded prototypes and successive tree splits support interpretation at multiple levels, while the taxonomy reduces thousands of 4D-OBCs to a limited set of process types.The occurrence summaries preserve the type and timing of surface processes.Source: §5.3 · p. 18, §5.4 · p. 18

5.4. Applicability in the coastal domain

  • Similar site occurrence patterns and performance scores suggest potential transferability across sandy beaches; branch occupancy may also support future environmental analysis and activity prediction.The proposed prediction use depends on whether simpler time-series algorithms can adequately predict future activities.Source: §5.4 · pp. 18–19

5.5. Limitations and future work

  • GeoMorphograms reduce explicit spatial information: sediment-transport directions, internal spatial structure, and interactions between neighboring activities are not directly modeled.Suggested future directions include spatial GeoMorphograms, graph-based interactions, or spatial attention mechanisms.Source: §5.5 · p. 19
  • Experiments cover sandy beaches, and expert pairwise annotations remain subjective rather than providing absolute ground truth for the selected taxonomy level.Transfer to other geomorphic settings remains untested.Source: §5.5 · p. 19

6. Conclusion

The conclusion presents DTC as a way to derive an expert-supported, data-driven hierarchy of surface process types from 4D point clouds without predefined labels or a fixed target-cluster count. At eight primary types, agreement with expert judgments is F1 = 0.78 and accuracy = 0.92.

6. Conclusion

  • DTC integrates GeoMorphograms, representation learning, and hierarchical deep clustering to derive a taxonomy without predefined labels or a fixed number of target clusters.The learned hierarchy captures major erosion–deposition distinctions and finer variations in duration, magnitude, coherence, compactness, and temporal evolution.Source: §6 · p. 19
  • At eight primary process types, expert-annotation agreement reaches F1 = 0.78 and accuracy = 0.92.The evaluation includes two sandy-beach 4D datasets and their combination.Source: §6 · p. 19
  • The conclusion describes DTC as a scalable, interpretable way to organize surface activities while allowing taxonomy detail to adapt to interpretation and application needs.It calls for extending the framework to more geomorphic environments and richer spatial representations.Source: §6 · p. 19

Appendix

The appendix figure evaluates pairwise-annotation metrics across cluster counts on a validation set. It marks k = 8 as the selected level, where the approach achieves its highest overall F1 score.

Appendix

  • The figure reports evaluation metrics from pairwise annotations across different cluster counts on the validation set.Source: Figure 12 · p. 20
  • A dashed line marks the selected clustering level, k = 8.Source: Figure 12 · p. 20
  • At k = 8, the approach achieves its highest overall F1 score.Source: Figure 12 · p. 20

Data and code availability

The availability statement identifies repositories for the underlying PLS data and derived 4D-OBCs, and says the code will be published after paper acceptance.

Data and code availability

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