Predicting Anthropometric Body Composition Variables Using 3D Optical Imaging and Machine Learning

Gyaneshwar Agrahari; Jackson Knox; Jacob Kapita; Kiran Bist; Monika Pandey; Nadejda Drenska; Peter Wolenski; Sophia Ramirez; Steven Heymsfield; Zachary James

REVIEW 4 major objections 10 minor 40 references

Predicting Anthropometric Body Composition Variables Using 3D Optical Imaging and Machine Learning

T0 review · 4 major / 10 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper claims that 3D optical body scans plus machine learning can predict appendicular lean mass and bone mineral density with about 8% RMSE, and that a semi-supervised p-Laplacian model holds BMD error near 10% using only 10% of…

desk verdict A credible supervised benchmark for 3D-optical body composition, but the semi-supervised p-Laplacian claim is untestable as reported—no same-label-rate supervised baseline. read the letter →

arxiv 2506.14815 v1 pith:QN77NXMZ submitted 2025-06-08 cs.LG

Gyaneshwar Agrahari , Kiran Bist , Monika Pandey , Jacob Kapita , Zachary James , Jackson Knox , Steven Heymsfield , Sophia Ramirez

show 2 more authors

Peter Wolenski Nadejda Drenska

This is my paper

classification cs.LG MSC 68T0568R1035J92

keywords semi-supervisedlearningp-Laplacianregression3Dopticalimagingappendicularleanmassbodyfatpercentagebonemineraldensitysupportvectorgraph-basedlabelpropagation

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 three body-composition measurements normally obtained from DXA scans, namely appendicular lean mass (ALM), body fat percentage (BFP), and bone mineral density (BMD), can be estimated from 44 biomarkers extracted from 3D optical body images. It reports that supervised support vector regression predicts ALM and BMD with about 8% root-mean-square error, and least-squares SVR predicts BFP with about 11% error, using 80% of the data for training. The central advance is the first regression application of a semi-supervised p-Laplacian model, which reaches about 13% error for ALM, 10% for BMD, and 20% for BFP when only 10% of patients are labeled. If these numbers hold, clinicians and researchers could reduce dependence on costly, time-consuming DXA scans, especially in data-constrained settings.

What carries the argument

The central object is the game-theoretic p-Laplacian regression model, solved by the tug-of-war dynamic programming principle. Patients are vertices of a k-nearest-neighbor graph, edge weights decay with the Euclidean distance between z-score-normalized biomarker vectors, and the predicted value at each unlabeled vertex solves $L_p u = 0$ subject to labeled values on the training vertices; the parameter $p$ interpolates between a weighted random-walk average ($p=2$) and a min-max tug-of-war as $p \to \infty$. This graph-based label propagation carries the argument: when biomarker similarity implies target similarity, the labeled patients' values flow through the graph to unlabeled patients, which is what allows the model to work with a 10% training set.

What would settle it

Permute the training labels among patients on the same k-NN graph and re-run the 10% training p-Laplacian; if RMSE stays near 10% for BMD, the graph similarity is not carrying the prediction. A second check is to hold out an entire scanner type or age group and see whether the 10% training errors grow beyond the reported values.

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Extended reading notes

Core claim

The central claim is that p-Laplacian regression on a patient similarity graph can propagate body-composition labels from a small labeled set to the rest of the population, and that this propagation is accurate enough to be clinically useful. In the paper's own terms, the authors show that a graph whose nodes are patients and whose edges encode similarity of 3D-derived biomarkers supports the hypothesis that similar patients have similar ALM, BFP, and BMD values. With 10% of the data labeled, the model predicts ALM within about 13% RMSE, BMD within about 10% RMSE, and BFP within about 20% RMSE; with 80% labeled, supervised SVR and LSSVR do better on all three targets. The paper concludes that DXA could potentially be replaced when estimating ALM and BMD, pending further validation on larger datasets.

Load-bearing premise

The method assumes that patients with similar 3D body measurements have nearly the same ALM, BFP, and BMD values, so that labels can flow across the similarity graph; if that smoothness fails, the 10% training results have no basis.

Editorial extensions

If this is right

If the results replicate on larger cohorts, 3D optical imaging plus supervised SVR/LSSVR could replace DXA for routine ALM and BMD estimation, cutting cost and scan time.
The p-Laplacian model's roughly 10% BMD error at 10% labeled data suggests that body-composition prediction can proceed with only a small curated labeled set, easing data-privacy and annotation bottlenecks.
BFP remains the hardest target across every model, indicating that the current 44-biomarker set carries weaker signal for adipose distribution than for muscle and bone.
The reported convergence of p-Laplacian RMSE as $p$ grows justifies treating large-$p$ behavior as a stable regime for this regression method.
Training sex-stratified models generally improves accuracy for ALM and BFP, so population stratification is a built-in component of the method.

Reading between the lines

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

A straightforward external test would be to run the same pipeline on a cohort scanned with a different 3D device, since the paper used three internal scanner types, to see whether the similarity graph transfers across hardware.
Because the graph weights all 44 biomarkers equally, weighting edges by target-specific correlations, which the paper itself floats as future work, would likely lift BFP accuracy given its top-ten correlations of only 0.4 to 0.6.
The relative RMSE metric means that a 10% error on BMD is a small absolute error on a variable whose mean is near 1.03 g/cm²; clinicians would need absolute comparisons against DXA repeatability before judging replacement.
If the smoothness hypothesis is the true driver, deliberately violating it, for example requiring the model to extrapolate to an age or body-mass range absent from the labeled set, should produce a measurable accuracy cliff.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague,

Here's the short take on arXiv:2506.14815. The supervised benchmark is credible; the semi-supervised headline is not yet supported. The paper applies p-Laplacian regression, from Calder and Drenska, to predict ALM, BFP, and BMD from 3D optical biomarkers, and it's the first time that model is used for regression in this domain. That's a real application-level novelty, and the authors are honest that the method comes from prior work and is implemented in the public GraphLearning package.

What works: the supervised results are plausible and consistent with prior body-composition studies—SVR and LSSVR land around 8% RMSE for ALM and BMD, 11% for BFP at an 80/20 split. The per-sex analysis and correlation tables are useful. The paper is also candid about BFP's weak biomarker correlations and about the need for larger datasets before clinical conclusions.

The main soft spot, and it's load-bearing: the p-Laplacian numbers at 10% training are never compared against a supervised model trained on the same 10%. Since the paper's motivation is that supervised methods are data-hungry, you need that same-label-rate comparison. With ALM biomarkers correlating above 0.9, a ridge or linear SVR on the same ~52 labeled subjects might match the p-Laplacian's ~13%—or beat it. The stress-test note is right about this; it's not a minor missing ablation, it's the comparison that would justify the central claim.

Two smaller problems: the top-10 biomarker selection for p-Laplacian-2 uses the full dataset, which leaks test information; and Tables 7-12 report the minimum RMSE over p and k for each training percentage, suggesting hyperparameters were selected on the test folds. Both need fixing with inner validation and within-fold feature selection.

The "DEXA could be potentially replaced" sentence in Section 9 is overreach at 8% RMSE; the Discussion's own caveat about larger datasets is the right level of caution.

Bottom line: this deserves peer review, but it needs a revision that adds low-label supervised baselines and cleans up the validation protocol. A serious referee could turn this into a solid benchmark paper. If I were in this area I'd want to see the fixed version before citing it.

Referee Report

4 major / 10 minor

Summary. This paper compares supervised machine-learning algorithms and a semi-supervised p-Laplacian regression model for predicting ALM, BFP, and BMD from 44 anthropometric biomarkers extracted from 3D optical images. After cleaning, 515 records are split into combined, male, and female subsets. All supervised models (linear/polynomial regularized regressions, SVR, LSSVR, random forest, XGBoost, MLP) are evaluated with five-fold cross-validation at an 80/20 training/test split. The p-Laplacian model is evaluated at training proportions of 80%, 50%, 33%, 25%, 20%, 10%, and 5%, using either all 44 biomarkers or the top-10 correlated biomarkers. The paper reports best RMSEs around 6-8% for ALM and BMD and about 11% for BFP with SVR/LSSVR at 80% training, and about 10-13% for ALM, 9-10% for BMD, and 14-25% for BFP with the p-Laplacian at 10% training, depending on the dataset. It concludes that the p-Laplacian model is promising in data-constrained healthcare settings.

Significance. If the reported accuracies hold, the paper would provide a useful benchmark for replacing DXA-based body-composition measurement with 3D imaging plus machine learning, which is practically relevant because DXA is costly and time-consuming. The empirical coverage is broad: seven model families, three targets, three population partitions, and seven training proportions for the semi-supervised method. The paper also makes the graph-smoothness hypothesis explicit and reports errors separately for male, female, and combined data, which is helpful. However, the central data-constrained claim is not yet supported: the p-Laplacian results at 5-50% training are never compared with any supervised model at the same label budget, and the selection of both biomarkers and hyperparameters appears to use test-fold information. The paper does not ship code or an external validation set, so reproducibility rests on the textual description and the GraphLearning package. The supervised benchmark results themselves are plausible and internally consistent.

major comments (4)

[Section 6; Section 8.5; Tables 7-15] The headline claim that the p-Laplacian model is 'promising in a data-constrained environment' is not tested against any supervised method at the same label rate. All supervised models are fixed at an 80-20 split (Section 6, Tables 13-15), while the p-Laplacian is evaluated at 80%, 50%, 33%, 25%, 20%, 10%, and 5% training (Tables 7-12). The p-Laplacian's 10%-training RMSEs (e.g., 13.21% for ALM and 9.65% for BMD on the combined data) are therefore never compared with, say, a linear SVR or ridge model trained on the same roughly 52 labeled subjects. Because the ALM biomarkers have correlations above 0.9 (Table 4), a simple linear model might match or beat those numbers at the same label budget. Please add supervised baselines at the same training percentages, using identical fold splits and hyperparameter-selection protocols, and report the mean and standard deviation over the 10 runs.
[Section 4.3; Section 8.5; Tables 4-6, 10-12] The top-10 biomarker subsets for p-Laplacian-2 are selected using correlations computed on the full dataset (Section 4.3), before the cross-validation splits are made. This means test-fold information enters the graph construction for the results in Tables 10-12, making the p-Laplacian-2 RMSEs optimistically biased. The biomarker selection must be performed inside each training fold, or the authors should demonstrate that the results are insensitive to this choice by recomputing Tables 10-12 with training-fold-only selection.
[Section 8.5; Tables 7-12] The hyperparameter protocol for the p-Laplacian results is unclear, and the presentation suggests test-set selection. The text states that the models were run 'for different combinations of p and k for a fixed Training %' and Figure 6 plots the 'lowest RMSE' for each training percentage; Tables 7-12 report the 'optimal' p and k with the corresponding RMSE. If p and k are chosen by minimizing RMSE on the test folds, all reported semi-supervised errors are optimistic. Please specify a nested validation scheme (e.g., an inner hold-out or a separate validation split) and report the RMSE at fixed, pre-specified parameters as well as the selected-parameter RMSE.
[Section 5; Section 7.1] It is not stated whether the StandardScaler/z-score normalization is fitted on the training fold only or on the entire dataset before splitting. If the scaler is fitted on all data, label information from the test patients is used in preprocessing for every model, including the p-Laplacian graph. Please state explicitly that all preprocessing statistics are computed from training folds only, and if that is not currently the case, rerun the experiments with a proper per-fold scaling pipeline.

minor comments (10)

[Section 8.5] The description of the modified K-fold scheme is ambiguous because K=5 is used both for the standard 80/20 split and for the modified one-fold-training scheme, which would give 20% training rather than 80%; please clarify which protocol produced each column in Tables 7-12.
[Section 7.1] Immediately after Eq. (2), the text calls eta a 'nondecreasing function' after defining it as a nonnegative decreasing function and choosing eta(t)=exp(-t^2); correct this contradiction.
[Section 8.1; Figures 11-13] The cross-references to the figures are inconsistent; for example, 'Figure 12d' is cited, but the figure is a nine-subplot grid with no 'd' label described. Please renumber or describe the subplots precisely.
[Tables 13 and 15] The 'Regression' rows in Tables 13 and 15 list parameter names without specifying which regression variant (traditional, Ridge, or Bayesian) was used for each dataset; please complete these rows.
[Table 15 caption] The caption reads 'Optimal Parameters and corresponding parameters'; it should read 'Optimal Parameters and corresponding RMSEs'.
[Abstract; Section 9] Please use 'DXA' consistently instead of alternating with 'DEXA'.
[Section 8.4] The MLP description is incomplete; please report the number of hidden layers and units, the learning rate, and any regularization so that the neural-network results are reproducible.
[Abstract] The claim that 'This paper is the first to demonstrate the application of a p-Laplacian model for regression' is too strong, since reference [10] already develops p-Laplacian regression; rephrase as the first application to body-composition prediction from 3D optical biomarkers.
[Section 9] The statement that DXA 'could be potentially replaced in the future to estimate ALM and BMD' goes beyond the evidence, because the reported RMSEs are not compared with DXA measurement error or with clinical decision thresholds; please soften the conclusion and add these caveats.
[Sections 8.2 and 8.5] There are typos in the text, including 'kernrel' in 'linear kernrel' (Section 8.2) and 'p-Lapacian' in the Section 8.5 heading; these should be corrected.

Circularity Check

1 steps flagged · score 6.0 of 10

Headline p-Laplacian errors are minima over hyperparameters selected on the same test folds; otherwise the paper is an empirical benchmark with no definitional circularity.

fitted input called prediction [Section 8.5, Figure 6, Tables 7-12; abstract headline numbers]
"For optimization, we implemented p-Laplacian-1 and p-Laplacian-2 for different combinations of p and k for a fixed Training %. ... Figure 6 demonstrates how the lowest RMSE p-Laplacian-1 and p-Laplacian-2 yielded changes with Training %."

The abstract's headline errors (~13% ALM, ~10% BMD, ~20% BFP at 10% training) are the 'lowest RMSE' entries in Tables 7-12, reached after sweeping p and k at each Training %. The same K-fold test folds both select the optimal p,k and produce the reported RMSE, and no inner validation split is described. Consequently the reported accuracy is by construction the minimum over the searched grid; the low-label 'prediction' is a test-set-fitted best case, statistically forced rather than an unbiased estimate. The p-Laplacian predictions are still real held-out estimates, but the headline performance figures are partly constructed by the selection procedure.

full rationale

The paper's derivation chain is mostly an empirical benchmark: ALM/BFP/BMD predictions are held-out estimates, and the graph-smoothness hypothesis in Section 7.1 is an assumption tested by the data, not a definition of the target. The self-citations ([9], [10], [11], [12]) provide the model, software, and low-label-rate theorems; these are real external results and are used to explain trends, not to establish the accuracy numbers, so they are not load-bearing circularity. The one construction issue is in Section 8.5: the low-label RMSEs in the abstract and Tables 7-12 are the 'lowest RMSE' over a p,k grid evaluated on the same K-fold test folds that selected them. Since no inner validation loop is described, these headline numbers are minima by construction and are optimistically selected; this makes the central data-constrained claim partially self-fulfilling. Separately, p-Laplacian-2's top-10 features are chosen from full-data target correlations (Section 4.3), a leakage that is secondary because the headline figures are essentially p-Laplacian-1. The missing 10%-label supervised baseline is a comparison gap, not a circularity.

Assumptions & free parameters 8 free parameters · 6 assumptions · 0 invented entities

The paper's models rest on a large set of hyperparameters fitted to the same data used for evaluation, plus an inherited p-Laplacian framework from the authors' own prior work. The most serious entry is the top-10 biomarker selection done on the full dataset, which contaminates the p-Laplacian-2 cross-validation. No new physical or mathematical entities are introduced.

free parameters (8)

p (p-Laplacian exponent) = 2 to 10 depending on target, dataset, and training% (Tables 7-12)
Tuned per experiment to minimize RMSE; controls balance between graph averaging and min/max tug-of-war terms.
k (k-NN graph neighbors) = 10 to 60 across tables
Tuned jointly with p; determines graph sparsity and label propagation range.
epsilon (edge weight bandwidth in Eq. 2) = not reported
Free scale parameter in the Gaussian edge weight eta(d/epsilon); no value or search range given.
SVR hyperparameters C and epsilon = e.g., ALM Male C=50, eps=0.7 (Table 13)
Selected from heatmaps over C and epsilon to minimize test RMSE.
LSSVR hyperparameters C and gamma = e.g., BFP Combined C=250, gamma=0.001 (Table 14)
Selected from heatmaps; RBF kernel parameters.
RF and XGBoost n_estimators and max_depth = n up to 50, d up to 25 for RF; n up to 35, d=5 for XGB
Tuned per model to minimize RMSE.
NN epochs and batch size = epochs 50-400, batch size 16
Selected based on RMSE versus epochs curves.
Top-10 biomarker subset for p-Laplacian-2 = different 10 features per target per sex (Tables 4-6)
Feature selection computed on the full dataset before splitting, leaking test information; a modeling choice that affects all p-Laplacian-2 results.

assumptions (6)

standard math Game-theoretic p-Laplacian with DPP (Eq. 4) solves Lp u = 0 on the k-NN graph
Borrowed from Calder-Drenska [10]; the paper assumes the solver and its convergence properties are correct.
standard math Low-label-rate consistency results for p-Laplacian semi-supervised learning ([12])
Used to explain why accuracy declines at low training%; relies on previously published theory.
domain assumption Graph smoothness: patients with similar 44-dimensional biomarker vectors have similar target values
Stated in Section 7.1 as the primary hypothesis; the entire label propagation depends on it.
domain assumption DXA target measurements are accurate ground truth
ALM, BFP, BMD from DXA are treated as error-free labels, although DXA itself has measurement variability.
domain assumption Listwise deletion of missing rows leaves an unbiased sample
330 of 847 patients dropped; the retained 515 skew young (median age 17), so generalization to adults may be limited.
ad hoc to paper Choice of eta(t)=exp(-t^2) and k-NN graph construction
Follows [9]; other kernels or graph constructions are not tested, yet the semi-supervised results depend on this choice.

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Cite this review

Pith. "Pith review of Predicting Anthropometric Body Composition Variables Using 3D Optical Imaging and Machine Learning." pith.science (2026). https://pith.science/paper/QN77NXMZ

@misc{pith2026250614815,
  author       = {Pith},
  title        = {Pith review of: Predicting Anthropometric Body Composition Variables Using 3D Optical Imaging and Machine Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QN77NXMZ}},
  note         = {Machine review of arXiv:2506.14815}
}

abstract

Accurate prediction of anthropometric body composition variables, such as Appendicular Lean Mass (ALM), Body Fat Percentage (BFP), and Bone Mineral Density (BMD), is essential for early diagnosis of several chronic diseases. Currently, researchers rely on Dual-Energy X-ray Absorptiometry (DXA) scans to measure these metrics; however, DXA scans are costly and time-consuming. This work proposes an alternative to DXA scans by applying statistical and machine learning models on biomarkers (height, volume, left calf circumference, etc) obtained from 3D optical images. The dataset consists of 847 patients and was sourced from Pennington Biomedical Research Center. Extracting patients' data in healthcare faces many technical challenges and legal restrictions. However, most supervised machine learning algorithms are inherently data-intensive, requiring a large amount of training data. To overcome these limitations, we implemented a semi-supervised model, the $p$-Laplacian regression model. This paper is the first to demonstrate the application of a $p$-Laplacian model for regression. Our $p$-Laplacian model yielded errors of $\sim13\%$ for ALM, $\sim10\%$ for BMD, and $\sim20\%$ for BFP when the training data accounted for 10 percent of all data. Among the supervised algorithms we implemented, Support Vector Regression (SVR) performed the best for ALM and BMD, yielding errors of $\sim 8\%$ for both, while Least Squares SVR performed the best for BFP with $\sim 11\%$ error when trained on 80 percent of the data. Our findings position the $p$-Laplacian model as a promising tool for healthcare applications, particularly in a data-constrained environment.

Figures

Figures reproduced from arXiv: 2506.14815 by the authors.

**Figure 3.** Heatmap of RMSEs (in %) for RF with parameters n and d As we see in [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗

**Figure 4.** Heatmap of RMSEs (in %) for XGBoost with parameters n and d minimal variation once n and d exceed a certain threshold. We tested the model for the values of n and d between 5 and 35. The model’s run time is exceptionally high for larger values of the parameters. The model performs the best for BMD by yielding errors between 8 and 9 percent for each dataset. The RMSE for BMD for Male, Female and Combined are 8.22 %… view at source ↗

Figures from the paper (7 more)

**Figure 6.** Figure 6: RMSEs (in %) vs Training % of pLaplacian-1 and p-Laplacian-2 across the target variables and datasets [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]

**Figure 7.** Figure 7: Optimal p vs Training % of pLaplacian-1 and p-Laplacian-2 across target variables and datasets Section 3. We used six different supervised algorithms namely-Linear/Polynomial Regression, SVR, LSSVR, Random Forest, XGBoost and Neural Network. The second objective is …

**Figure 8.** Figure 8: Optimal k vs Training % of pLaplacian-1 and p-Laplacian-2 across target variables and datasets [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]

**Figure 9.** Figure 9: Asymptotic behavior of p-Laplacian-1 as p → ∞ for k = 10, 30 ,and 50 cantly higher accuracy for ALM and BMD compared to BFP. The BFP predictions for Female were on average better than those for Male and Combined . One of the reasons behind models’ poor performance on …

**Figure 11.** Figure 11: Distribution of RMSEs in predicting ALM by Polynomial Regression Models across [PITH_FULL_IMAGE:figures/full_fig_p021_11.png]

**Figure 12.** Figure 12: Distribution of RMSEs in predicting BFP by Polynomial Regression Models across [PITH_FULL_IMAGE:figures/full_fig_p021_12.png]

**Figure 13.** Figure 13: Distribution of RMSEs in predicting BMD by Polynomial Regression Models across [PITH_FULL_IMAGE:figures/full_fig_p022_13.png]

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