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

arXiv:2609.39756 · cs.CV · Submitted 2026-09-30 · Read on arXiv

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Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: I'm Tom, and with me are Jane, Lu, senior AI researcher at Tsinghua, Meng, lead engineer at a mysterious AI startup and Lalam, the in-house Large Language Model.

Jane: Today's paper: "Determining Vertical Displacement of Agricultural Areas Using UAV-Photogrammetry and a Heteroscedastic Deep Learning Model".

Tom: The developed algorithm, based on heteroscedastic regression using a U-Net network, demonstrates high effectiveness in determining vertical ground surface displacements in agricultural areas and regions with similar characteristics.

Jane: First, who's behind it and why it matters.

Title and authors: Tom: So, what does the paper actually claim they achieved with this U-Net architecture and heteroscedastic regression? Jane, can you simplify the core findings for our listeners?

Jane: Basically, the U-Net model is doing two things at once: it predicts how much each point's elevation needs to be corrected and it also calculates how uncertain that correction is. This lets them decide which data points are trustworthy for determining the actual ground surface movement.

Lu: The key finding seems to be that this method works well even when vegetation is present, because the model learns to separate the ground signal from the vegetation influence more effectively than older filtering methods.

Meng: So, instead of just throwing away points near trees or buildings based on simple slope rules, this AI system learns a more nuanced way to treat those areas based on prediction uncertainty.

Lalam: It’s about building a smarter system for risk assessment, making the data density and accuracy sufficient for reliably assessing subsidence risks in agricultural settings.

The paper's summary: Tom: I noticed the paper points out that they compared this U-Net approach against traditional ground filters, and Adaptive TIN ended up performing best for determining subsidence. What did they suggest as improvements over those established methods?

Jane: They highlighted that their proposed algorithm offers a slight performance edge when trying to determine subsidence specifically within agricultural areas compared to the conventional filters they tested.

Lu: The core improvement is using heteroscedastic regression, which allows the model to quantify uncertainty alongside its prediction, giving us a measure of reliability that other methods lack.

Meng: That quantification of uncertainty is crucial for practical application; it means we don't just get a number without knowing how much to trust it when making decisions about ground stability.

Lalam: The focus on uncertainty allows for a more informed decision-making process regarding subsidence risks, which has broader implications for land management and infrastructure planning.

The paper's improvements: Tom: We’ve seen how they use the U-Net and heteroscedastic regression to handle elevation corrections and uncertainty quantification. Jane, how should we wrap up the main implications of this work for our audience?

Jane: The main implication is that we can get a more reliable assessment of subsidence related risks in agricultural areas by using this advanced AI approach instead of just relying on older filtering techniques.

Lu: I think the potential for using this kind of model to analyze how subtle ground deformations affect large-scale agricultural productivity is fascinating, opening up new avenues for modeling complex environmental interactions.

Meng: I’m thinking about the practical deployment; if the accuracy and data density they achieved are good enough, it means this technology could become a real tool for monitoring land stability where we need it most.

Lalam: This work contributes to a deeper understanding of how remote sensing data can be used to monitor subtle changes in the ground surface across vast agricultural landscapes, which is very important for long-term environmental planning.

Conclusion: Tom: So, we've been digging into this paper on determining vertical displacement in agricultural areas using UAV photogrammetry and a heteroscedastic deep learning model, and now it's time for the wrap-up. Jane, can you give us the final summary of what this research actually accomplished?

Jane: Absolutely. The core takeaway is that by combining a U-Net network with heteroscedastic regression, they developed an approach that can predict elevation corrections while also quantifying the uncertainty behind those predictions, which gives us a much more dependable measurement of ground movement.

Lu: I think what's really impressive here is how the model handles the input data preparation—it uses grid cells and specific blurring techniques to isolate the relevant signals from vegetation influence, which is a creative way to approach this problem.

Meng: From an engineering standpoint, I’m really interested in how they handle the data retention based on those uncertainty thresholds; that selective filtering process sounds like it could make the system much more efficient for real-time monitoring applications.

Lalam: This level of technical refinement opens up exciting possibilities for cultural preservation and sustainable agriculture, as it offers a way to monitor subtle environmental changes across large tracts of land with high precision.

Tom: I agree, Lalam, the potential for improving how we manage our food systems is huge. Jane, what's the big picture implication here? Where does this research actually fit into the larger field of remote sensing?

Jane: This work suggests that moving beyond simple filtering methods to sophisticated AI models like this one allows us to extract much finer details from point cloud data, which is vital for understanding subtle ground subsidence risks in dynamic agricultural settings.

Lu: We’ve seen papers before on multimodal reasoning, but applying this specific uncertainty quantification technique directly to geophysical displacement modeling shows how powerful these deep learning structures can be when tailored correctly.

Meng: I'm just thinking about the scalability; if this methodology proves robust across different terrain types, it could eventually be adapted for monitoring infrastructure stability everywhere, not just farming fields.

Lalam: The ability to quantify uncertainty in physical measurements has a profound impact on how we build trust in data-driven insights, which is a vital cultural shift for how we approach environmental monitoring globally.

Tom: Fantastic points from everyone. So, to recap, this paper on "Determining Vertical Displacement of Agricultural Areas Using UAV Photogrammetry and a Heteroscedastic Deep Learning Model" shows a robust way to use U-Net networks and uncertainty quantification to reliably map ground surface changes in farming regions.

Jane: Exactly; it provides a reliable alternative to traditional methods by making the data selection process smarter based on predicted error levels.

Lu: It’s exciting because it proves that structuring the loss function to estimate both the average value and its variance is a very effective way to train models for physical sciences.

Meng: The practical impact lies in making monitoring systems more intelligent, requiring less manual data filtering and giving operators clearer indicators of when a measurement is trustworthy.

Lalam: It really shows how advanced AI can help us manage our physical world with greater accuracy and a deeper understanding of the risks involved across different land uses.

Tom: And that's all we have time for today on this paper, but keep an eye on these developments as they show us how to better measure the ground beneath our feet. Next up, we’re looking at how Large Language Models are tackling complex reasoning tasks in biology.

Wojciech Gruszczyński, Edyta Puniach, Paweł Ćwiąkała, Wojciech Matwij

AGH University of Krakow

cs.CV

Submitted: 2026-09-30

Updated: 2026-09-30

Journal ref: 2025, Remote Sensing, 17(18), 3259

DOI: 10.3390/rs17183259

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 64/100

The gist: The developed algorithm, based on heteroscedastic regression using a U-Net network, demonstrates high effectiveness in determining vertical ground surface displacements in agricultural areas and

Key concepts

U-Net Network
A type of deep learning model used here to correct point cloud elevations. It has four encoder and decoder layers with 64 filters in the first layer, using 3x3 convolutions and 2x2 maximum pooling. Its purpose is to learn complex patterns in elevation data to predict how the ground surface should look.
Heteroscedastic Regression
A statistical technique used within the U-Net loss function to model both the average prediction and its associated uncertainty. This allows the model to understand that some areas are more predictable than others, which is crucial for accurately quantifying risk in ground displacement predictions.
Vertical Displacement Determination
The final step where vertical movement is calculated. After filtering data based on correction uncertainty, the corrected elevation of a node is found by taking the median of surrounding cells within a 1m x 1m square. The actual displacement is then calculated as the difference between this corrected elevation and a reference measurement.
Adaptive TIN
A technique mentioned as achieving best performance in determining subsidence over agricultural areas. It suggests an adaptive method for creating Triangulated Irregular Networks (TINs) that adjusts to the specific characteristics of agricultural landscapes, leading to superior subsidence detection.

Terminology

Summary

The developed algorithm, based on heteroscedastic regression using a U-Net network, demonstrates high effectiveness in determining vertical ground surface displacements in agricultural areas and regions with similar characteristics. The proposed approach offers an alternative to traditional ground filtering methods by employing heteroscedastic regression to predict elevation corrections and quantify their uncertainty, providing reliable assessment of subsidence-related risks.

The gist

The U-Net model predicts elevation corrections and quantifies their uncertainty, enabling subsidence determination with minimal influence of vegetation, and Adaptive TIN achieved the best performance in determining subsidence over agricultural areas.

How it works

The core methodology involves utilizing a U-Net neural network to correct point cloud elevations to better reflect the actual ground surface while simultaneously predicting the uncertainty associated with these corrections. This approach allows only those segments of the corrected point clouds that correspond to ground surface elevations with relatively low uncertainty to be retained, and this difference between these corrected elevations is interpreted as the vertical displacement of the ground surface.

The input data formulation begins by dividing the area covered by a point cloud into 5 cm × 5 cm grid cells, assigning each cell the elevation of the lowest point within its boundaries to create a uniform density point cloud stored in variable 'uni'. Subsequently, outlier observations are removed using an algorithm inspired by SMRF, employing functions like 'inpaint' and 'morphological open' to interpolate missing or outlier values. Following this, the 'uni' variable undergoes Gaussian blurring with specific parameters (205 × 205 cm filter size and 50 cm standard deviation) to produce 'hgauss', from which the difference between 'uni' and 'hgauss' is computed as 'hdgauss'. Patches extracted from 'hdgauss' are then used as inputs for the neural network during both training and prediction.

Target Correction Values

The elevation data required for training is derived from point clouds obtained through ALS, which are cleaned of potential classification and systematic errors by comparing them with GNSS RTK surveys. To eliminate systematic discrepancies, the ALS point cloud is shifted by the median discrepancy between ALS and GNSS RTK elevations for each flight strip. Furthermore, to ensure accuracy, ALS elevations are validated against a Digital Surface Model (DSM) derived from UAV-photogrammetry conducted during periods of negligible vegetation influence. The differences between the uniform UAV-photogrammetry point cloud and the cleaned ALS elevations represent the corrections (to elevation), which serve as targets for training. If these absolute correction values exceed 5 m, the corresponding grid cells are excluded from training.

Neural Network and Its Training

To model elevation corrections, a U-Net network with an input size of 204 × 204 and one channel was used, featuring a depth of four encoder and decoder layers, with 64 filters in the first encoder. The network utilized 3 × 3 convolutions and 2 × 2 maximum pooling, resulting in over 31 million parameters (learnables) and 60 layers. To account for heteroscedasticity, a loss function derived from the likelihood is employed. This loss function is formulated as:

E = ∑ ∑ ∑ (1/2 ln σ(r,c)(x l) + 1/2 (y(r,c,1)(x l) − T(r,c) l) squared exp(y(r,c,2)(x l))) C c=1 R r=1 L l=1.

This loss function is designed to jointly estimate the conditional average value in the first output channel 'y(r,c,1)(x l)' and the natural logarithm of the conditional variance in the second output channel 'y(r,c,2)(x l)'. During prediction, the uncertainty u(r,c) l is determined by: u(r,c) l = √exp(y(r,c,2)(x l)).

Vertical Displacement Determination

Vertical displacements are determined at selected nodes based on the results generated by the U-Net model. For each node where vertical displacement is to be estimated, corrections and uncertainties are computed for all cells within 'uni' that fall within the network’s output region. Corrected elevations are computed only for cells where the uncertainty of corrections is below a predefined threshold (ulim), and absolute correction values exceeding 5 m are discarded. The corrected elevation of each node is computed as the median of all corrected cell elevations within a 1 m × 1 m square, which mitigates the influence of high-frequency vertical ground surface displacements caused by agricultural activities. The final vertical displacement of a node is determined as the difference between the corrected node elevations from two measurement series. Nodes are excluded if in one or both series, "50% or more of the cells within the 1 m × 1 m square in the uni variable lack elevation data.

Improvements for AI systems

As a fastidious and diligent researcher, I have analyzed the provided scientific paper, Determining Vertical Displacement of Agricultural Areas Using UAV-Photogrammetry and a Heteroscedastic Deep Learning Model.

The core innovation lies in using a U-Net architecture with heteroscedastic regression to simultaneously predict elevation corrections and the uncertainty (logarithm of variance) of those corrections, specifically designed to mitigate the impact of vegetation on ground surface elevation estimation.

Here are the specific improvements that can be made to AI systems based on this research, and what these improved systems can achieve:

  1. The U-Net Model for Elevation Correction and Uncertainty Estimation

  2. Heteroscedastic Regression Loss Function (Equation 7)

  3. Selective Data Retention Based on Uncertainty Thresholds (ulim)

  4. Performance Ranking Metric (TOPSIS methodology)

Specific Improvements and Capabilities:

Abstract

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%.

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