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REVIEW 4 major objections 6 minor 20 references

An Object-Based Deep Learning Approach for Building Height Estimation from Single SAR Images

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Building heights can be estimated from a single SAR image plus building footprints, with about one-storey error on European-style cities.

desk verdict A useful new multi-city dataset and an honest OOD evaluation, but the height-inversion equation is inconsistent with the claimed ground-range processing and needs resolution before the numbers can be trusted. read the letter →

arxiv 2507.08096 v1 pith:56L6PJWB submitted 2025-07-10 cs.CV cs.AI

Babak Memar , Luigi Russo , Silvia Liberata Ullo , Paolo Gamba This is my paper · ORCID
classification cs.CVcs.AI
keywords buildingheightestimationsingleSARimageCOSMO-SkyMedobject-basedregressionboundingboxout-of-distributiongeneralizationurbanremotesensingdeeplearning
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that building heights can be estimated from a single very-high-resolution synthetic aperture radar (SAR) image, provided the building footprints are known. The proposed object-based network turns each footprint into an aligned bounding box and learns to predict the larger box that the building's height creates in radar geometry, with the length difference between the two boxes divided by the cosine of the incidence angle giving the height. Under leave-one-city-out tests on eight COSMO-SkyMed cities, the method reports mean absolute errors of about 2.20 m in Munich, 2.24 m in Los Angeles, and 2.26 m in Milan, roughly one building story. It also reports much larger errors, above 10 m, on Asian high-rise cities and on buildings taller than 40 m, so the claim is conditional on low- and mid-rise urban morphologies. If accepted, the result would make single-pass, single-sensor height mapping practical in cities that already have footprint databases.

What carries the argument

The load-bearing identity is the SAR bounding-box relation $h = (L_{\mathrm{BBB}} - L_{\mathrm{FBB}})/\cos\theta$, where the FBB is the smallest rectangle enclosing the footprint, rotated to match the orbit inclination, and the BBB is the corresponding box that includes the height-induced displacement in the range direction. The network's job is to regress the BBB from the SAR image and footprint-derived features, using only the box dimensions as extra features rather than the center coordinates to reduce overfitting. Operating directly in ground-range coordinates rather than reprojecting into the radar slant-range plane, the method uses the acquisition incidence angle to convert the measured displacement into a height estimate.

What would settle it

Take a held-out city with LiDAR ground-truth heights and feed the network footprint polygons that are deliberately shifted by one ground-range pixel (2.5 m) while keeping the SAR image unchanged. The height formula $h = (L_{\mathrm{BBB}}-L_{\mathrm{FBB}})/\cos\theta$ predicts a systematic bias near $2.5/\cos\theta$ m, so a much smaller or inconsistent bias would mean the bounding-box geometry is not the mechanism driving the estimates.

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Extended reading notes

Core claim

The central claim is that a footprint-guided object-based regressor can extract building heights from a single VHR SAR image with accuracy comparable to one storey for European-style urban fabrics. The network processes a SAR patch together with the binary footprint mask, computes a footprint-aligned bounding box (FBB) rotated according to the orbit inclination, and regresses a building bounding box (BBB) whose range-direction length exceeds the FBB length by $L$; the height is $h = L / \cos\theta$. Trained with a mean squared error loss on 160,000 patches from seven cities and tested one city at a time, it achieves a leave-one-city-out MAE of 2.20 m in Munich, 2.24 m in Los Angeles, and 2.26 m in Milan, while rising above 10 m for Shanghai and Shenzhen, and an overall in-distribution MAE of 4.95 m. The same experiments show systematic failure on buildings above 40 m and on cities dominated by tall, narrow-footprint structures, which the paper attributes to tall-building scarcity in the training data and to slant-range ambiguity. The paper's conclusion is therefore conditional: single-VHR-SAR height estimation generalizes across continents mainly for the low- and mid-rise building stock that dominates the training distribution.

Load-bearing premise

The method assumes that an accurate footprint polygon is available for every building at prediction time; if footprints are missing, misaligned, or stale, the footprint-aligned box that the height formula is anchored to is wrong.

Editorial extensions

If this is right

  • If the central claim holds, a city with up-to-date footprints needs only one VHR SAR acquisition, not multi-date or multi-sensor stacks, to produce a building height map at roughly one-storey accuracy in low- to mid-rise areas.
  • The same trained model can be applied to an unseen European-style city without local training data, with expected MAE in the 2–3 m range for buildings under 40 m.
  • For cities with many buildings above 40 m or with dense high-rise cores, expected errors are much larger, above 10 m MAE in the reported tests, so height products from this method should be flagged as low-confidence there.
  • The 53,079 paired SAR and reference patches assembled for the eight cities become a reusable benchmark for future single-image SAR height estimation methods.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Our inference: adding synthetic tall buildings or incidence-angle augmentation to the training set is a direct test of the paper's tall-building data-scarcity explanation; if Asian-city MAE drops sharply, that explanation is confirmed.
  • Our inference: running the same network on VHR images from other sensors with the height formula unchanged would show whether the learned features are geometric or radiometrically sensor-specific.
  • Our inference: in cities without footprint databases, the method would need an automated footprint extractor upstream, and footprint boundary errors would then enter the height estimate directly through the $L_{\mathrm{FBB}}$ term.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The manuscript proposes an object-based method for estimating building heights from a single very high resolution (VHR) COSMO-SkyMed SAR image. Given a building footprint polygon and the corresponding SAR patch, a ResNet-101 regressor augmented with footprint-derived geometric features predicts bounding-box information, from which the height is recovered through the incidence-angle relation in Eq. (2). The method is evaluated with leave-one-city-out experiments over eight cities on three continents, reporting test MAEs of about 2.2-2.3 m for several European and North American cities and 8-11 m for dense or high-rise Asian cities, together with an additional 70/30 in-distribution experiment. The paper claims that this constitutes state-of-the-art out-of-distribution performance for single-image SAR height estimation.

Significance. If the reported results hold, the paper would represent a useful advance: story-level accuracy from single-date VHR SAR on unseen cities of similar morphology is a nontrivial and practically relevant result, and the assembled multi-city dataset (about 53,000 patches and 3.3 million buildings) is a valuable benchmarking resource. The leave-one-city-out protocol is an appropriate and demanding test of generalization. However, the central geometric derivation needs to be corrected or clarified before the numerical results can be interpreted, and the comparisons against prior work are not direct. The paper does not provide code, and the SAR data are restricted by an ASI research agreement, so independent replication is not immediately possible.

major comments (4)
  1. [Section 3, Eq. (2) and Section 3.1] Eq. (2), h = L/cos(theta), is inconsistent with the paper's explicit statement that the method operates in the ground-range domain. In a geocoded ground-range SAR image, the layover offset between the footprint and the building top is L = h * tan(theta), so the correct inversion would be h = L/tan(theta), not h = L/cos(theta). For the Munich image, with theta = 20.04 degrees (Table 1), the two formulas differ by about a factor of 2.6 for the same offset L. The paper must state unambiguously whether L is measured in slant range or ground range; if it is measured in ground range, Eq. (2) is wrong, and if it is measured in slant range, the claims in Section 3.1 about avoiding the slant-range plane are contradicted. Please provide a derivation and, if Eq. (2) is used as written, explain how the network can produce the reported accuracies despite the factor-of-2.6 discrepancy.
  2. [Sections 2.4 and 3.2] The description of what the network actually regresses is internally inconsistent. Section 2.4 states that the model regresses a single height value per building and uses an MSE loss on height, while Section 3.2 states that the output of the fully connected layer is used to estimate bounding boxes from which the height is then computed. This distinction is material: if the loss is on height, Eq. (2) is not part of the training objective and the bounding-box interpretation is only a post-hoc explanation; if the loss is on box offsets, the generation of ground-truth bounding-box labels from footprint and height must be specified exactly, including which geometric formula is used to create those labels. Please clarify the training loss and the label-generation procedure.
  3. [Table 5 and Related Work] The comparisons in Table 5 do not support the abstract's claim of outperforming state-of-the-art methods in similar out-of-distribution scenarios. The cited methods use different sensors and data sources (Sentinel-1/2 time series, ICESat-2/GEDI LiDAR, GaoFen-7 multi-view photogrammetry) and different evaluation protocols. In particular, there is no direct comparison with Sun et al. [14], which is the direct predecessor and the baseline against which the two claimed innovations (ground-range processing and removal of center coordinates) are defined. Please add a direct comparison with [14] on the same COSMO-SkyMed data and the same leave-one-city-out protocol, or substantially soften the state-of-the-art claim.
  4. [Table 3] All reported results come from a single leave-one-city-out run with no error bars, no multiple seeds, and no significance tests. Small differences between cities, such as Munich 2.20 m, Los Angeles 2.24 m, and Milan 2.26 m, are likely within seed-to-seed or bootstrap variability. Please add repeated runs (at least a few seeds) or bootstrap confidence intervals for the headline MAE and RMSE values, especially for the claim of state-of-the-art accuracy.
minor comments (6)
  1. [Throughout] The manuscript contains numerous typographical and grammatical errors that should be corrected, including 'ibjecxt' in Section 4, 'compatisons' in the text before Table 5, 'specificaly' in Section 2.3, 'rigourous' and 'othere' in Section 2.2, and 'amd' in the Shenzhen comparison paragraph.
  2. [Figure 7] The caption says 'Scatter plots of absolute errors per city relative to reference heights,' but the surrounding text refers to 'orange regions' and 'yellow and red zones,' which suggests a spatial map or image. Please make the figure type and caption consistent.
  3. [Section 3.1] The 'inclination angle' is defined as the angle between the orbital plane and the equator, but its role in rotating the footprint-aligned bounding box is not derived or explained. Please clarify how this angle relates to the SAR acquisition geometry (incidence angle and heading) and how the FBB rotation is computed.
  4. [Introduction] The Introduction states that center coordinates contribute marginally to height prediction, but no ablation or experiment is presented to support this claim. Please either add an ablation study or remove the causal claim and present the choice as a design decision.
  5. [Table 3] The h >= 40 m columns are based on very small samples in several cities, for example 80 buildings in Munich and 72 in Milan (Table 2), making the reported MAE and RMSE values for tall buildings unstable. Please report the number of buildings in each height category for each city and consider suppressing or clearly caveating these tall-building metrics.
  6. [Header] The manuscript header contains placeholder submission metadata ('Received:', 'Revised:', 'Accepted:', 'Published:', 'Citation: ... Remote Sens. 2025, 1, 0') that should be removed or completed before publication. The keyword list also repeats 'SAR'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the height estimates are supervised regressions against external reference data and are evaluated on held-out cities.

full rationale

The derivation chain is not circular. The network is trained with an MSE loss against reference heights (Section 2.4) taken from independent databases (EUBUCCO, NYC Open Data, LA GeoHub, and the China dataset of Egger et al.), and the footprint-aligned bounding box is constructed from footprint geometry and the incidence angle (Section 3.1), not from the reference heights. Evaluation uses leave-one-city-out cross-validation (Section 4), so the Munich MAE of 2.20 m is produced by a model that did not train on Munich data. Equation (2) is a fixed conversion from a predicted bounding-box offset to height; it is not fitted to the test data, and the offset is not defined in terms of the target height. The method does depend on footprint polygons at inference, but that is an explicit data requirement rather than a circular input. The only related concern is that the paper's claim to operate in the ground-range domain is in tension with Eq. (2), which matches slant-range layover geometry; that is a geometric/correctness issue, not a circularity, and therefore does not change the circularity score.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claim rests on a physical geometry model and on external footprint and reference-height data. No height constants are fitted to test data, but several preprocessing and sampling choices (patch size, per-city sample cap, 40 m threshold) are hand-set and affect the reported error metrics.

free parameters (3)
  • Patch size and overlap = 256 x 256 px, 20% overlap
    Chosen for tiling; not fitted, but affects what each building patch contains and thus the learnt features.
  • Per-city training sample cap = 20,000 random buildings per city
    Introduced to limit computational cost; changes class balance and may affect OOD tall-building performance.
  • Height split threshold = 40 m
    Used to group error metrics; arbitrary and affects the tall-building MAE/RMSE numbers reported.
assumptions (5)
  • domain assumption Building height can be estimated from the range-direction difference between the building bounding box (BBB) and the footprint bounding box (FBB) via h = L / cos theta.
    Invoked in Eq. (2); assumes side-looking SAR geometry, flat terrain, no severe layover or shadowing.
  • domain assumption Accurate building footprint polygons are available at inference for every building.
    Section 3 states the basic element is the building footprint; the FBB is derived from it, so the method cannot run from SAR alone.
  • domain assumption Reference building heights and footprints are accurate and temporally aligned with the SAR acquisitions.
    Table 2 lists reference data from EUBUCCO, NYC Open Data, etc.; errors in these propagate to training labels and evaluation.
  • domain assumption Consistent acquisition geometry (descending orbit, HH polarization) across cities makes cross-city transfer meaningful.
    Table 1; the method assumes a fixed side-looking geometry and incidence angle corrections are sufficient.
  • domain assumption A ResNet-101 can learn the mapping from SAR intensity plus footprint mask to bounding box displacement.
    Section 3.2; no proof, standard DL capacity assumption.

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Cite this review

Pith. "Pith review of An Object-Based Deep Learning Approach for Building Height Estimation from Single SAR Images." pith.science (2026). https://pith.science/paper/56L6PJWB

@misc{pith2026250708096,
  author       = {Pith},
  title        = {Pith review of: An Object-Based Deep Learning Approach for Building Height Estimation from Single SAR Images},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/56L6PJWB}},
  note         = {Machine review of arXiv:2507.08096}
}
read the original abstract

Accurate estimation of building heights using very high resolution (VHR) synthetic aperture radar (SAR) imagery is crucial for various urban applications. This paper introduces a Deep Learning (DL)-based methodology for automated building height estimation from single VHR COSMO-SkyMed images: an object-based regression approach based on bounding box detection followed by height estimation. This model was trained and evaluated on a unique multi-continental dataset comprising eight geographically diverse cities across Europe, North and South America, and Asia, employing a cross-validation strategy to explicitly assess out-of-distribution (OOD) generalization. The results demonstrate highly promising performance, particularly on European cities where the model achieves a Mean Absolute Error (MAE) of approximately one building story (2.20 m in Munich), significantly outperforming recent state-of-the-art methods in similar OOD scenarios. Despite the increased variability observed when generalizing to cities in other continents, particularly in Asia with its distinct urban typologies and prevalence of high-rise structures, this study underscores the significant potential of DL for robust cross-city and cross-continental transfer learning in building height estimation from single VHR SAR data.

Figures

Figures reproduced from arXiv: 2507.08096 by the authors.

Figure 1
Figure 1. Study area consisting of 8 cities: Los Angeles, New York, Buenos Aires, Munich, Milan, Rome, Shanghai, and Shenzhen is highlighted in red across 3 different continents. The study was conducted across eight cities located on three continents: Milan, Rome, and Munich in Europe; Shenzhen and Shanghai in Asia; and Los Angeles, New York, and Buenos Aires in the Americas. The geographical distribution of these areas is il… view at source ↗
Figure 2
Figure 2. Building height density distributions for the eight cities considered in this study. As shown in the figure, the distributions exhibit a typical long-tail pattern, characteristic of urban environments, where lower buildings are predominant, while taller structures are less frequent. a total of 53,079 paired SAR and reference patches across all urban environments [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Graphical representation of a building in the UTM and SAR image coordinate systems. achieve this, in each initial patch created during the pre-processing stage, as described in Section 2.3, all building footprints are identified and the corresponding SAR patch is extracted. Given that the initial patches include an overlap of 20%, some buildings may appear two to four times in different patches. To ensure a clean an… view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Extracting FBB with consideration of the inclination angle: (a) building footprint in New York City, (b) FBB before and (c) after angle correction, and the corresponding (d) optical and (e) SAR images with superimposed FBB and BBB (yellow and red boxes, overlap in oran…
Figure 5
Figure 5. Figure 5: Overview of the proposed workflow for the object-based building height estimation. The model utilizes ResNet101 as the backbone in combination with the extracted features from 2D coordinates of the building. After generating the extra features using the footprint of th…
Figure 6
Figure 6. Figure 6: Comparison of building height estimation results for different cities. Each row displays an image patch for a specific city (from top to bottom: Buenos Aires, Los Angeles, Milan, Munich, New York, Rome, Shanghai, and Shenzhen), showing (from left to right): the CSK inp…
Figure 7
Figure 7. Figure 7: Scatter plots of absolute errors per city relative to reference heights. Each point represents the error of a single building [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]

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