PaperlayerView exact revision on arXiv

Source-linked AI summary

Determining Vertical Displacement of Agricultural Areas Using UAV-Photogrammetry and a Heteroscedastic Deep Learning Model

Wojciech Gruszczyński, Edyta Puniach, Paweł Ćwiąkała, Wojciech Matwij

arXiv:2609.39756v1cs.CV

TL;DR

Sparse, road-directed monitoring profiles and vegetation changes complicate agricultural ground-displacement assessment from UAV point clouds. The paper uses one heteroscedastic U-Net to predict elevation corrections and their uncertainty, then compares displacement estimates with ground-filter methods. The U-Net ranked at the top in most cases, with accuracy judged sufficient for subsidence-risk assessment but not for comprehensively measuring displacement extent.

  • Problem

    Sparse, often poorly placed geodetic profiles and vegetation changes between surveys complicate assessment of mining-related ground displacement across agricultural surfaces.

    Source: §1 · p. 2

  • Method

    A single U-Net predicts elevation corrections and their uncertainty, extending the approach to vertical-displacement estimation and comparison with ground-filter algorithms.

    Source: §1 · p. 3

  • Results

    The U-Net ranked at the top of the TOPSIS-based evaluation in most cases, while ATIN generally led the tested ground filters and CSF proved ineffective on the tested datasets.

    Source: §5 · p. 26

  • Takeaways & Limitations

    The U-Net and leading ground filters provide accuracy sufficient for assessing subsidence risk in agricultural areas, but not for comprehensively assessing mining-induced displacement extent.

    Source: §4 · p. 25, §5 · p. 26

    Evaluation focused on a Jaworzno test region and two specified time intervals, including a summer survey with peak vegetation and autumn surveys with little vegetation influence.

    Source: §2.4.4 · p. 16

Abstract

from arXiv · show

This article introduces an algorithm that uses a U-Net architecture to determine vertical ground surface displacements from unmanned aerial vehicle (UAV)-photogrammetry point clouds, offering an alternative to traditional ground filtering methods. Unlike con-ventional ground filters that rely on point cloud classification, the proposed approach em-ploys heteroscedastic regression. The U-Net model predicts the conditional expected val-ues of the elevation corrections, aiming to reduce the impact of vegetation on determined ground surface elevations. Concurrently, it estimates the logarithm of the elevation cor-rection variance, allowing for direct quantification of the uncertainty associated with each elevation correction value. The algorithm was evaluated using three metrics: the root mean square error (RMSE) of vertical displacements, the percentage of nodes with deter-mined displacement values, and the percentage of outliers among those values. Perfor-mance was assessed using the technique for order of preference by similarity to ideal so-lution (TOPSIS) method and compared against several ground-filter-based algorithms across four datasets, each including at least two time intervals. In most cases, the U-Net-based approach demonstrated a slight performance advantage over traditional ground filtering techniques. For example, for the U-Net-based algorithm, for one of the test da-tasets, the RMSE of the determined subsidences was 6.1 cm, the percentage of nodes with determined subsidences was 80.5%, and the percentage of outliers was 0.2%. For the same case, the algorithm based on the next best model (SMRF) allowed an RMSE of 7.7 cm to be obtained; for 77.3% of nodes, the subsidences were determined; and the percentage of outliers was 0.3%.

1. Introduction

The paper addresses how vegetation and sparse, road-determined survey profiles complicate monitoring mining-related ground displacement. It proposes a single U-Net that predicts elevation corrections and their uncertainty, and extends this approach to displacement estimation against conventional filters.

1. Introduction

  • Road-determined profiles leave relatively few, often poorly placed observations, so surface displacement models and associated risk assessments may deviate from reality despite precise measurements.The paper seeks an approach to monitoring ground-surface displacement across agricultural areas.Source: §1 · p. 2
  • UAV photogrammetry offers flexible, relatively low-cost, high-resolution observations for small areas, but displacement accuracy depends strongly on surface coverage, particularly vegetation.Vegetation can increase random elevation errors and make point clouds reflect vegetation rather than the ground.Source: §1 · p. 2
  • Vegetation and agricultural microrelief can change between surveys, so simply subtracting two point-cloud elevations may distort ground displacement estimates.The paper notes that reliable analysis is feasible where vegetation effects are both minimal and comparable across datasets.Source: §1 · p. 2
  • A prior two-network heteroscedastic approach reduced vegetation influence but faced limited training data, error dependence between networks, added computation, and occasional negative variance estimates.Machine-learning point-cloud segmentation has also been reported to face micro-topographic errors and reduced cross-dataset generalization from overfitting.Source: §1 · p. 3
  • The study uses one U-Net to predict elevation corrections and uncertainty, with preprocessing, loss-function, and training-data changes, and evaluates vertical displacement against ATIN, SMRF, and CSF.This extends prior work from corrected terrain elevations to vertical displacements.Source: §1 · p. 3

2. Materials and Methods

The methods section describes point-cloud processing, the datasets, and the comparison methodology used to assess vertical-displacement algorithms.

2. Materials and Methods

  • The methods cover the proposed point-cloud processing algorithm, ground-filter parameter ranges and processing, and datasets for U-Net training and comparative evaluation.The section is organized around algorithm, filter-comparison, and dataset methods.Source: §2 · p. 4

2.1. U-Net-Based Algorithm

The U-Net workflow corrects point-cloud elevations and estimates correction uncertainty, retaining lower-uncertainty cells to derive vertical displacement from corrected elevations across measurement series.

2.1. U-Net-Based Algorithm

  • For each node, U-Net predicts elevation corrections and their uncertainty over a surrounding region; corrected elevations are differenced between measurement series to estimate displacement.Only cells below the uncertainty threshold are retained, and cells with absolute corrections above 5 m are discarded.Source: §2.1 · p. 4, §2.1.4 · p. 9

2.1.1. Input Data Formulation

  • The input point cloud is gridded into 5 cm × 5 cm cells using each cell’s lowest point, outliers are removed, and Gaussian-blurred elevation differences form network inputs.The blurred surface uses a 205 × 205 cm filter with a 50 cm standard deviation.Source: §2.1.1 · pp. 5–6

2.1.2. Target Correction Values

  • Cleaned ALS ground and building returns are shifted against GNSS RTK elevations, screened against GNSS and UAV-DSM comparisons, and differenced from uniform UAV elevations to form correction targets.ALS sections with discrepancies exceeding 20 cm were excluded; absolute correction values above 5 m were excluded from training.Source: §2.1.2 · pp. 6–7

2.1.3. Neural Network and Its Training

  • The U-Net has two output channels for correction estimates and uncertainty, and its heteroscedastic loss estimates the conditional mean and log variance under a normal conditional-error assumption.The second channel models log variance rather than variance, avoiding negative variance outputs.Source: §2.1.3 · pp. 7–8
  • Training uses randomly cropped patches with random rotations, while systematically cropped validation examples support repeatable checks and early stopping.Training stopped after 328 epochs when the loss reached its minimum value.Source: §2.1.3 · pp. 8–9

2.1.4. Vertical Displacement Determination

  • Each node’s corrected elevation is the median of retained corrected cells in a centered 1 m × 1 m area, and displacement is the difference between series-level corrected node elevations.The median reduces the influence of outliers and high-frequency displacement associated with agricultural activity.Source: §2.1.4 · p. 9
  • Nodes are excluded when at least half the cells lack elevation data in either series; displacements are evaluated on a 10 m × 10 m grid using uncertainty thresholds of 15, 20, or 25 cm.The missing-data rule excludes areas requiring extensive interpolation.Source: §2.1.4 · p. 9

2.2. Vertical Displacement Determination Using Ground Filtering Algorithms

The comparison applies ATIN, CSF, and SMRF ground filters, plus an unfiltered baseline, to determine subsidence on a common grid. Filter parameters are selected to balance spatial coverage and errors.

2.2. Vertical Displacement Determination Using Ground Filtering Algorithms

  • ATIN, CSF, and SMRF subsidence estimates use differences between median elevations in 1 m × 1 m cells classified as ground, on the same 10 m × 10 m grid as U-Net.An unfiltered estimate, treating all points as ground, provides a comparison baseline.Source: §2.2 · pp. 9–10
  • Filter parameters were expanded and tuned to maximize the area with displacement estimates while minimizing errors, especially outliers; each parameter set was applied to both series.The authors selected paired series such that one was collected under negligible vegetation influence.Source: §2.2 · p. 10
  • The tested ATIN configurations varied max angle and max distance, CSF varied rigidity, and SMRF used specified grid, window, slope, elevation-threshold, and scale settings.Smaller SMRF grid resolution increased processing time with negligible accuracy impact, so densification was abandoned.Source: §2.2 · p. 10

2.3. Assessment and Ranking of Results

The section evaluates vertical-displacement results with three complementary metrics and ranks algorithm configurations using TOPSIS. It treats accuracy, coverage, and outliers together to avoid rankings based on only one measure.

2.3. Assessment and Ranking of Results

  • The assessment combines RMSE, the percentage of nodes with determined displacements, and the percentage of outliers, favoring lower RMSE and outliers but higher coverage.The authors state that using only one indicator could bias performance comparisons.Source: §2.3 · pp. 10–11
  • Displacements with absolute errors greater than 45 cm are treated as outliers, and RMSE excludes nodes with gross errors.RMSE uses the errors for determined displacements and their count.Source: §2.3 · p. 11
  • TOPSIS ranks variants by their distances from best and worst alternatives, with equal impact for all three metrics after L2 normalization.The no-filtering solution is included in normalization and ranking; only each method’s highest-TIndex configuration is reported in final tables.Source: §2.3 · p. 11

2.4. Datasets

The study evaluates UAV-photogrammetry datasets from four southern Polish agricultural sites, using selected regions for training, validation, and testing. Jaworzno includes mining-related ground displacement; the other analyzed areas are described as unaffected during their study periods.

2.4. Datasets

  • All four sites are in southern Poland with generally simple rural topography; selected regions were assigned to training, validation, or testing, and only Jaworzno had mining-induced displacement.Buildings and forests excluded parts of the study sites; the first three sites’ analyzed regions had no vertical ground displacements.Source: §2.4 · pp. 11–12

2.4.1. Jerzmanowice

  • Jerzmanowice comprises 12 UAV-photogrammetry series over approximately 220 ha, with training and validation regions and no reference subsidence.Its validation intervals include summer and autumn vegetation growth, particularly in corn-covered fields.Source: §2.4.1 · pp. 12–13

2.4.2. Karniowice

  • Karniowice comprises 10 UAV-photogrammetry series over approximately 200 ha, with training and validation regions and no reference subsidence.Vegetation growth during evaluated summer and autumn intervals was significant in parts of the validation area, especially corn and cereal fields.Source: §2.4.2 · pp. 13–14

2.4.3. Lędziny

  • Lędziny comprises four UAV-photogrammetry series over approximately 170 ha, but testing used only an approximately 40 ha field-and-meadow region unaffected by mining.The reference subsidence there was set to zero; vegetation effects varied across the tested region.Source: §2.4.3 · pp. 14–15

2.4.4. Jaworzno

  • Jaworzno comprises three UAV-photogrammetry series over approximately 80 ha and includes mining-related displacement; its reference subsidence model has an estimated RMSE of approximately 10–15 cm.The evaluated fragment contains meadows rather than grain fields because GNSS RTK reference measurements could negatively affect crop yields.Source: §2.4.4 · pp. 15–16

3. Results

Across validation and test regions, U-Net generally ranked best for subsidence determination, with ATIN also competitive and CSF often weak. Error distributions and map comparisons show how vegetation, correction thresholds, and uncertainty shaped the results.

3. Results

  • Training regions were excluded from assessment to avoid favoring U-Net; test regions were within the USCB and were not used for validation-based model selection.The authors describe the test regions as representative of surface topography and vegetation coverage.Source: §3 · p. 16, §3.2 · p. 19

3.1. Results for Validation Datasets

  • CSF had little effect on subsidence errors in validation and test examples, producing results similar to unfiltered point clouds.In one test case, CSF ranked below the unfiltered approach.Source: §3.1 · p. 16, §3.2 · p. 19
  • U-Net achieved the best validation ranking in three cases and ATIN in one, with their TIndex differences generally small.SMRF performed reasonably well except for Karniowice in 2022.03.–2022.06.; CSF results were comparable to unfiltered point clouds.Source: §3.1 · p. 16, Table 2 · p. 17
  • For Jerzmanowice, ulim = 15 cm gave U-Net its highest TIndex, while ulim = 20 cm enabled estimates in dense vegetation but with noticeably higher uncertainty.The comparison is shown in Figure 5e–f.Source: §3.1 · p. 17, Figure 5 · p. 18
  • For Jerzmanowice in 2022.03.–2022.06., U-Net had lower RMSE and a more compact error distribution than ATIN, whose mean error was closer to zero.Figure 6 shows probability-density estimates; its descriptive statistics use errors with absolute values below 0.45 m.Source: Figure 6 · p. 19, §3.1 · p. 19

3.2. Results for Test Datasets

  • U-Net ranked highest in four test cases and was nearly tied with ATIN in Jaworzno (TIndex difference 0.0001); SMRF outperformed ATIN in two Lędziny cases.ATIN generally ranked high, while CSF ranked low across test series and once performed worse than no filtering.Source: §3.2 · p. 19, Table 3 · p. 20
  • In Lędziny, U-Net corrected elevations in the region's north; higher correction uncertainty indicated a greater likelihood of larger errors, not that larger errors had occurred.ATIN and SMRF results were relatively similar, and high-uncertainty areas also occurred where those methods produced relatively high errors.Source: §3.2 · p. 20, Figure 7 · p. 21
  • In Jaworzno, the U-Net map showed a southeast-oriented low-subsidence anomaly and basin-flank asymmetry; areas without estimates were mainly forest and pre-harvest fields.Displacements outside −2.2 m to 0.2 m were marked as outliers, using a 20 cm margin relative to reference values.Source: §3.2 · p. 22, Figure 9 · p. 23

4. Discussion

The U-Net approach outperformed the compared ground filters in most tested cases, but its evidence is specific to relatively simple agricultural terrain. Its displacement maps may need outlier filtering before downstream modeling, and more complex terrain would require further testing and likely expanded training and validation data.

4. Discussion

  • In most cases, the U-Net algorithm outperformed compared ground filters, likely reflecting tested sites’ low slopes, limited surface complexity, and relatively dense vegetation.The datasets came from or resembled agricultural areas in the USCB.Source: §4 · p. 24
  • Extending the U-Net algorithm to more complex terrain would require additional testing and likely expanded training and validation datasets.Its main parameter, ulim, sets the maximum allowable uncertainty in elevation corrections; the model estimates corrections dynamically rather than classifying points.Source: §4 · p. 24
  • The U-Net displacement maps contain a small percentage of outliers, many with salt-and-pepper patterns, and require filtering before interpolation, subsidence modeling, or basin-development analysis.The authors identify moving-window methods with MAD, IQR, or RANSAC as possible filters.Source: §4 · p. 24
  • At Jaworzno in 2019.07.–2021.11., moving-window IQR filtering with 150 m x 150 m windows and 10 m steps yielded RMSE = 10.3 cm, 83.2% nodes with determined displacements, and 0.4% gross errors.The filtering removed many outliers without removing genuine non-standard displacement patterns and had negligible impact on quality indicators.Source: §4 · p. 24
  • Among ground-filter algorithms, ATIN generally performed best and SMRF slightly worse, but their accuracy was insufficient to determine the full extent of mining influence on farmland.Assessing that extent would require additional modeling or supplementary observations such as PSInSAR.Source: §4 · p. 25
  • CSF produced unsatisfactory results in the tested scenarios and was almost entirely ineffective on agricultural-field vegetation, despite classifying buildings and trees effectively.The authors suggest vegetation intensity, rather than terrain morphology, likely contributed to the poor results.Source: §4 · p. 25
  • The findings apply to low-slope agricultural areas and should not be directly extrapolated to mountainous or low-vegetation environments.The authors note ATIN has also been effective in other conditions.Source: §4 · p. 25
  • Accuracy assessment used a no-displacement assumption at three sites and interpolation from unmarked-point reference measurements at the fourth; marked-point methods are poorly representative of intensively cultivated fields.The authors identify similar no-displacement areas as the most reliable assessment option for intensive crops, while noting it applies only to comparable terrain.Source: §4 · pp. 25–26

5. Conclusions

The heteroscedastic U-Net was highly effective for displacement determination in agricultural areas of the USCB and similar regions, ranking at the top in most TOPSIS evaluations. Its accuracy supports subsidence-risk assessment, but not comprehensive determination of mining-induced displacement extent.

5. Conclusions

  • The heteroscedastic U-Net showed high effectiveness in agricultural areas of the USCB and similar regions, ranking at the top of the TOPSIS evaluation in most cases.Its accuracy was sufficient to assess subsidence risk, but not to comprehensively determine the full extent of mining-induced displacements.Source: §5 · p. 26
  • Among tested ground filters, ATIN performed best, SMRF was slightly worse, and CSF was ineffective on the tested datasets.CSF misclassified medium and low vegetation in fields and meadows, although it correctly classified buildings and trees.Source: §5 · p. 26

Related papers

Loading 2609.39756v1…