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arxiv: 2606.24786 · v2 · pith:B6BYLVJMnew · submitted 2026-06-23 · 💻 cs.CV

Counting Trees from Satellite Imagery with Noisy Supervision

Dimitri Gominski , Maurice Mugabowindekwe , Qiue Xu , Xiaowei Tong , Martin Brandt , Hieu Le , Rasmus Fensholt , Dimitris Samaras
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Loic Landrieu
This is my paper

Pith reviewed 2026-06-26 05:33 UTC · model grok-4.3

classification 💻 cs.CV
keywords tree countingsatellite imageryunbalanced optimal transportnoisy supervisiondensity matchingremote sensingenvironmental monitoringLiDAR annotations
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The pith

Unbalanced optimal transport with residual-based self-correction enables tree counting from satellite imagery despite noisy LiDAR labels.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper seeks to establish that tree counting at satellite resolutions can be cast as a spatial density matching task solved by unbalanced optimal transport. This formulation handles both isolated trees with precise locations and dense forests where boundaries are ambiguous, while a self-correction step uses transport residuals to improve noisy supervision derived from airborne LiDAR during training. A sympathetic reader would care because manual annotation of individual trees at this scale is prohibitively expensive, yet large-area forest monitoring requires reliable counts. The authors test the claim on a new benchmark covering three continents and over 216 million annotations, where the method beats detection, regression, and other transport baselines.

Core claim

The authors claim that formulating tree counting as a spatial density matching problem supervised through Unbalanced Optimal Transport, together with a self-correction mechanism that leverages transport residuals to progressively refine noisy supervision, produces accurate counts from satellite imagery even when individual tree definitions are ill-posed and labels come from imperfect LiDAR sources.

What carries the argument

Unbalanced Optimal Transport formulation for spatial density matching, with transport residuals supplying reliability-aware signals to refine noisy labels during training.

If this is right

  • Large-scale tree counts become feasible over 25,890 square kilometers spanning multiple continents and satellite sensors without requiring fully verified labels.
  • One framework simultaneously supports precise localization of isolated trees and robust density estimation inside dense forests.
  • The cost of manual annotation drops because noisy but scalable LiDAR-derived labels can be used directly.
  • Environmental monitoring gains a practical route to repeated, wide-area inventories of tree populations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same residual-driven correction might extend to counting other objects whose instances blur together at the imaging scale.
  • Testing the approach on labels from even cheaper or lower-quality sources would reveal how far the self-correction can compensate.
  • Integration with temporal sequences of satellite images could turn the density estimates into change detection for forest loss or growth.

Load-bearing premise

The self-correction mechanism can progressively refine noisy supervision during training without introducing new errors or biases.

What would settle it

On the TinyTrees benchmark the method fails to outperform detection-based, regression-based, and transport-based baselines in counting accuracy across the tested regions and sensors.

Figures

Figures reproduced from arXiv: 2606.24786 by Dimitri Gominski, Dimitris Samaras, Hieu Le, Loic Landrieu, Martin Brandt, Maurice Mugabowindekwe, Qiue Xu, Rasmus Fensholt, Xiaowei Tong.

Figure 1
Figure 1. Figure 1: Counting Trees From Space. We introduce TREEMATCH, a model to estimate the number of trees in a VHR satellite image (a). Training relies on two supervision sources: strong labels consisting of manually annotated tree centers (b), and weak labels automatically derived from airborne laser scanning (c). The model predicts a per-pixel tree density map (d), enabling precise localization of isolated trees while … view at source ↗
Figure 2
Figure 2. Figure 2: TREEMATCH. Given a VHR satellite image, the network ϕ predicts a continuous tree density map. Training uses two supervision sources: strong labels (manual point annotations) and weak labels (automatically derived tree-cover masks). Strong labels supervise both a global count loss and a UOT-based alignment loss. For weak labels, we first solve a UOT problem (without backpropagation) to compute marginal resi… view at source ↗
Figure 3
Figure 3. Figure 3: Marginal Residuals. A satellite image (a) is annotated with weak labels (b) and processed by the model to produce a density prediction (c). The resulting marginal residuals (d) highlight dis￾agreements between annotation and prediction, revealing potential missed trees (in red) and spurious annotations (in blue). yi = 1 indicates the annotated center of a tree crown at pixel i. This representation defines … view at source ↗
Figure 4
Figure 4. Figure 4: Qualitative results across regions and sensors. Each row corresponds to a different dataset: China (Gaofen2), Rwanda (PlanetScope), and France (SPOT6). In the France split, ground￾truth annotations are only available on 15m radius inventory plots. From left to right: input RGB image (a), strong manual annotations (b), TREEMATCH’s predictions (c), DM-Count (c), density regression baseline (d), and CenterNet… view at source ↗
read the original abstract

Counting individual trees is a fundamental task for environmental monitoring, yet remains largely unexplored with satellite imagery. At these resolutions, isolated trees may still be identifiable, but crown boundaries become ambiguous in dense forests, making the notion of an individual tree inherently ill-defined. Moreover, large-scale manual annotations of individual trees are prohibitively expensive. While scalable supervision can be derived from airborne LiDAR, the resulting annotations are noisy and difficult to exploit effectively. We address these challenges by formulating tree counting as a spatial density matching problem supervised through Unbalanced Optimal Transport. This formulation naturally accommodates both precise localization of isolate trees and robust density estimation in dense forests. We further introduce a self-correction mechanism that leverages transport residuals to progressively refine noisy supervision during training. We evaluate our approach on TinyTrees, a new benchmark spanning three continents and three satellite sensors, comprising over 216 million tree annotations (including 639k manually verified instances) across $25\,890$ km$^2$. Our method consistently outperforms detection-based, regression-based, and transport-based distribution-matching baselines, demonstrating the effectiveness of unbalanced transport and reliability-aware supervision for large-scale tree counting from satellite imagery. Code, data and models are available at https://github.com/dgominski/treematch.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper formulates tree counting from satellite imagery as a spatial density matching problem solved via unbalanced optimal transport, introduces a self-correction step that iteratively refines noisy LiDAR-derived density maps using transport residuals, and reports consistent outperformance over detection-based, regression-based, and transport-based baselines on the new TinyTrees benchmark (216M annotations, 639k manually verified, 25,890 km² across three continents and sensors).

Significance. If the central claims hold, the work would enable scalable tree counting at continental scales by exploiting noisy but cheap LiDAR supervision where manual annotation is infeasible; the public release of code, data, and models is a clear strength that supports reproducibility and follow-on research.

major comments (2)
  1. [self-correction mechanism] The headline outperformance claim rests on the self-correction mechanism (described after the unbalanced OT formulation). No quantitative validation is supplied that transport residuals predominantly capture annotation noise rather than model underfitting in dense canopies or sensor-specific artifacts; a direct comparison of residual magnitude against the 639k verified manual counts would be required to substantiate that the loop improves rather than entrenches supervision errors.
  2. [evaluation on TinyTrees] The abstract states that the method 'consistently outperforms' the three classes of baselines, yet the provided experimental summary contains no error analysis, ablation of the reliability-aware weighting, or per-sensor/per-density breakdown that would confirm the gains are attributable to unbalanced transport plus self-correction rather than implementation details of the baselines.
minor comments (1)
  1. [method] Notation for the unbalanced transport cost and the residual update rule should be introduced with explicit equations rather than prose descriptions to aid reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful comments and the opportunity to clarify and strengthen our manuscript. We address each major comment below and outline the revisions we will make.

read point-by-point responses

  1. Referee: [self-correction mechanism] The headline outperformance claim rests on the self-correction mechanism (described after the unbalanced OT formulation). No quantitative validation is supplied that transport residuals predominantly capture annotation noise rather than model underfitting in dense canopies or sensor-specific artifacts; a direct comparison of residual magnitude against the 639k verified manual counts would be required to substantiate that the loop improves rather than entrenches supervision errors.

    Authors: We agree that additional validation would strengthen the presentation of the self-correction mechanism. In the revised manuscript, we will provide a quantitative analysis comparing the magnitude of transport residuals on the 639k manually verified annotations versus the noisy LiDAR-derived ones. This will demonstrate that residuals are larger in regions with known annotation discrepancies, supporting that they capture noise rather than systematic underfitting. We will also include breakdowns by canopy density and sensor to address potential artifacts. revision: yes

  2. Referee: [evaluation on TinyTrees] The abstract states that the method 'consistently outperforms' the three classes of baselines, yet the provided experimental summary contains no error analysis, ablation of the reliability-aware weighting, or per-sensor/per-density breakdown that would confirm the gains are attributable to unbalanced transport plus self-correction rather than implementation details of the baselines.

    Authors: We acknowledge the need for more detailed evaluation to attribute the gains specifically to our contributions. The full manuscript includes some ablations, but we will expand the experimental section with error bars, an ablation study isolating the reliability-aware weighting, and per-sensor and per-density performance breakdowns. These additions will confirm the improvements stem from the unbalanced OT and self-correction components. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper formulates tree counting as a spatial density matching problem using unbalanced optimal transport, with an iterative self-correction step that refines noisy LiDAR-derived labels via transport residuals. This derivation follows standard OT principles applied to the given supervision and is evaluated on an external benchmark (TinyTrees) containing independent manual verifications across continents and sensors. No equations reduce the output to the input by construction, no fitted parameters are renamed as predictions, and no load-bearing self-citations or uniqueness theorems from the authors are invoked. The central claims rest on empirical outperformance against baselines rather than tautological redefinitions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, specific free parameters or additional axioms are not detailed; the approach relies on standard optimal transport assumptions adapted to the task.

axioms (1)
  • domain assumption Unbalanced optimal transport is suitable for matching densities with noisy supervision in this domain
    Central to the formulation in the abstract.

pith-pipeline@v0.9.1-grok · 5781 in / 1153 out tokens · 31802 ms · 2026-06-26T05:33:26.767992+00:00 · methodology

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    Siyu Liu, Martin Brandt, Thomas Nord-Larsen, Jerome Chave, Florian Reiner, Nico Lang, Xiaoye Tong, Philippe Ciais, Christian Igel, Adrian Pascual, Juan Guerra-Hernandez, Sizhuo Li, Maurice Mugabowindekwe, Sassan Saatchi, Yuemin Yue, Zhengchao Chen, and Rasmus Fensholt. The overlooked contribution of trees outside forests to tree cover and woody biomass ac...

    2023