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REVIEW 3 major objections 6 minor 39 references

Scalable and Realistic Virtual Try-on Application for Foundation Makeup with Kubelka-Munk Theory

T0 review · 3 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A first-order Taylor expansion of the Kubelka-Munk blend equation, evaluated directly in XYZ color space, reproduces full spectral integration for foundation-on-skin rendering while cutting blend time from 0.925 s to 0.17 s per face.

desk verdict The Taylor approximation is real and validated; the coverage-to-scattering mapping is a hand-picked guess that carries the realism claim. read the letter →

arxiv 2507.07333 v1 pith:TXOHZTG3 submitted 2025-07-09 cs.CV

Hui Pang , Sunil Hadap , Violetta Shevchenko , Rahul Suresh , Amin Banitalebi-Dehkordi This is my paper
classification cs.CV
keywords virtualtry-onfoundationmakeupKubelka-MunktheoryTaylorexpansionreflectanceestimationintrinsicimagedecompositioncolorblendinge-commercescalability
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 tries to show that virtual try-on for foundation makeup can be both realistic and scalable: realistic because synthesis is driven by Kubelka-Munk light-transport theory rather than alpha blending, and scalable because the only inputs needed are the product images and coverage labels already found on e-commerce pages. The central move is to approximate the KM blend equation with a first-order Taylor expansion in XYZ space, so that the expensive per-wavelength spectral integration is replaced by a direct combination of skin and foundation color channels. If the approximation holds, foundation blending drops from 0.925 s to 0.17 s per face with near-identical output, and the end-to-end system beats alpha blending on real after-makeup photos. The paper's realism claim ultimately rests on a hand-set mapping from coverage level to opacity.

What carries the argument

The load-bearing object is the two-layer Kubelka-Munk reflectance formula for a finite foundation layer over opaque skin, $R = R_m + T_m^2 R_s/(1 - R_m R_s)$, which sums the infinite series of internal reflections between foundation and skin. The paper expands the second term $f(R_m,R_s)=T_m^2 R_s/(1-R_m R_s)$ in a first-order Taylor series around midpoints $r_m,r_s$ chosen per spectral segment. With the two partial derivatives $f_{R_m}=t R_s^2/(1-R_m R_s)^2$ and $f_{R_s}=t/(1-R_m R_s)^2$, replacing the spectral integral by moments of the color-matching functions turns blending into a linear combination of the skin and foundation XYZ values plus a constant; the result is then reconstructed from $X,Y,Z$. A piecewise-linear reflectance model with breakpoints at 400, 500, 600, and 700 nm supplies the spectra from sRGB alone, and the coverage-derived scattering coefficient fixes the layer transmittance $T_m$.

What would settle it

Measure the reflectance of thin layers of commercial foundations at controlled thickness on known skin-tone substrates; if the inferred scattering coefficient for a given coverage label varies across shades or brands beyond noise, the fixed 30/20/10 mapping is false. The Taylor approximation itself can be checked by sampling skin and foundation reflectances from a wide color gamut and comparing the XYZ output against full spectral integration; any color pair with $\Delta$ E CIE2000 well above 1 would falsify the no-noticeable-loss claim.

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Extended reading notes

Core claim

The paper's central claim is that Eq. (7), the Kubelka-Munk blend of a finite foundation layer over skin, can be replaced by a first-order Taylor expansion evaluated directly in XYZ color space with no perceptible loss: the term $f(R_m,R_s) = T_m^2 R_s/(1 - R_m R_s)$ is expanded as $f(R_m,R_s) \approx f_{R_m}(r_m,r_s) R_m + f_{R_s}(r_m,r_s) R_s + \text{const}$, so the per-wavelength integration over the visible spectrum can be skipped. Combined with a piecewise-linear sRGB-to-reflectance conversion and a coverage-based scattering coefficient, this makes the whole pipeline depend only on product images and coverage labels from e-commerce pages. In the paper's experiments the approximation matches full spectral integration with SSIM 0.99, $\Delta$ E CIE2000 0.22, and LPIPS 8.5e-5, cuts KM blending time from 0.925 s to 0.17 s per face, and produces LPIPS 0.226 against real after-makeup photos versus 0.236 for $\alpha$ blending.

Load-bearing premise

The load-bearing premise is that a foundation's coverage label fixes its opacity: full, medium, and low coverage are assumed to reflect 30%, 20%, and 10% of the fully opaque reflectance at a fixed thickness; real products might not follow that mapping.

Editorial extensions

If this is right

  • Foundation VTO becomes practical on phones: per-face KM blending drops from 0.925 s to 0.17 s on a laptop-class CPU, with preprocessing also reduced from 11.17 s to 6.85 s.
  • New products can be added without lab measurements: any foundation with an sRGB product image and a coverage label can be blended using the pipeline.
  • The Taylor approximation is visually indistinguishable from full KM spectral integration in the reported metrics (SSIM 0.99, Delta E CIE2000 0.22, LPIPS 8.5e-5), so the faster path does not sacrifice color realism.
  • On real after-makeup photos, the method scores LPIPS 0.226, beating plain alpha blending (0.236) and alpha blending on decomposed albedo (0.231), and it avoids the per-product alpha hand-tuning.
  • The intrinsic decomposition plus semantic mask lets the system preserve facial features such as eyebrows and eyelashes, which makeup-transfer models tend to alter.

Reading between the lines

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

  • A likely consequence is that the same Taylor-in-XYZ trick transfers to any two-layer KM compositing problem, such as lipstick, concealer, or sunscreen rendering, wherever the blend term is smooth in the two reflectances; the bottleneck would shift from integration to reflectance estimation.
  • Because the approximation matches full integration to SSIM 0.99, any remaining realism gap versus real photos probably comes from the sRGB-to-spectrum reflectance model and the coverage-to-S mapping, not from the Taylor step; improving those inputs should be the next lever.
  • The fixed 30/20/10 coverage fractions suggest a calibration experiment: measure real foundation layers on known substrates and fit the scattering coefficient per product; if it varies within a coverage class by shade, adding shade-dependent opacity would improve realism beyond the current single scalar.
  • The comparison against alpha blending at LPIPS 0.226 versus 0.236 is close enough that the practical advantage may be less about raw fidelity and more about removing per-product tuning and preserving features; a larger before/after dataset would sharpen the claim.
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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

3 major / 6 minor

Summary. The paper proposes an end-to-end virtual try-on framework for foundation makeup. The pipeline performs face semantic segmentation, intrinsic image decomposition into albedo, shading, and specular highlight, and then blends foundation color with skin albedo using Kubelka-Munk (KM) theory. The authors introduce a piecewise-linear reflectance estimation from sRGB values, a coverage-to-scattering-coefficient mapping, and a first-order Taylor expansion that approximates the KM blending in XYZ space to avoid per-wavelength spectral integration. They validate the approximation against full spectral integration (SSIM 0.99, Delta E 0.22, LPIPS 8.5e-5) and compare the end-to-end result against alpha blending on a small set of real before/after makeup images.

Significance. If the coverage-to-scattering calibration is sound, this is a practically useful contribution: the Taylor approximation is internally validated against full spectral integration, runs roughly 5x faster than vanilla KM blending, and the overall pipeline is plausible for e-commerce virtual try-on. The paper correctly identifies and attacks a real scalability barrier of KM-based makeup rendering. The main significance is limited by two load-bearing weaknesses: the hand-set 30/20/10% reflectance mapping in Sec. 4.3 is unvalidated, and the real-image comparison in Table 4 rests on only 10 images with no statistical test. The approximation result itself is credible and well supported by the reported metrics.

major comments (3)
  1. [Sec. 4.3, Eqs. (3)-(7)] The coverage-to-scattering mapping is the central load-bearing assumption of the realism claim. The sentence 'for fixed D=0.25, we set the reflectance R of full coverage foundation to be 30% of R∞, 20% for medium coverage and 10% for low coverage' is an empirical assertion with no measurement, citation, or sensitivity study. Since S determines Rm and Tm through Eqs. (4)-(5), and Rm and Tm fully control the blended reflectance in Eq. (7), any error in these fractions changes both color and opacity of the synthesized result. Consequently, the Table 4 comparison to alpha blending evaluates this particular calibration as much as it evaluates KM theory; a different calibration could erase or reverse the reported LPIPS margin. The additional free parameter D=0.25 (with no unit or justification) has the same problem. Please provide either a calibration against measured foundation-on-skin data, a sensitivity analysis over the R/R∞ fractions and D, or a clearly stated limitation that the method requires per-product calibration before it can be claimed to work 'solely depending on the product information available on e-commerce sites.'
  2. [Sec. 5.2, Table 4] The claim that the framework 'outperforms other techniques' on real after-makeup images is supported only by mean LPIPS over 10 images (0.226 vs. 0.236 and 0.231), with no error bars, confidence intervals, per-subject results, or paired statistical test. The margin is small, and the paper itself acknowledges that lighting direction and intensity may differ between before and after images. With n=10, this evidence is insufficient to establish a robust advantage over alpha blending. Please report the per-subject LPIPS values and a paired test (e.g., Wilcoxon signed-rank), and ideally add a colorimetric metric on color-checker-normalized skin regions.
  3. [Sec. 4.4, Eq. (15)] The derivation of the Taylor approximation is internally consistent, and the validation in Table 3 is strong. However, the approximation is validated only against the same KM model with the same inputs; it does not validate the realism of the KM inputs themselves. Thus the Table 3 numbers (SSIM 0.99, Delta E 0.22) confirm that the approximation preserves the KM output, but the end-to-end realism claim still inherits the unvalidated coverage mapping and D value from Sec. 4.3. This should be stated explicitly in the conclusion and abstract, or the missing calibration must be supplied.
minor comments (6)
  1. [Sec. 3.2] The phrase 'reflectance and transmittance of the foundation foundation' contains a duplicated word and should read 'foundation layer.'
  2. [Table 1] The column header 'Ment2015' is a typo for 'Meng2015' (reference [24], Meng et al.).
  3. [Sec. 4.4] The text says 'we only need to integrate over the values for wavelength from 500 to 600' for the X channel, but Eq. (15) is written for the Z channel and the X-channel derivation is not shown. Please present the X-channel piecewise integration explicitly.
  4. [Sec. 4.2, Fig. 6] The figure caption refers to 'black lines' and a 'green dotted line,' but the printed figure may not distinguish these clearly; please use distinct markers and annotate the three-piece approximation, including the flat 600-700 nm segment.
  5. [Abstract and Sec. 1] The phrase 'solely depending on the product information available on e-commerce sites' is too strong given that Sec. 4.3 introduces a hand-set coverage-to-S mapping and a fixed D. If those parameters are not calibrated, please soften the claim to 'depending on product information plus an assumed coverage-opacity relationship.'
  6. [Sec. 5.2] The statement that the method achieves a better LPIPS score '100% of the time' is not a meaningful statistic by itself; please report the number of paired comparisons and the distribution of per-image differences.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the KM Taylor approximation is derived from the model and validated against full spectral integration; the coverage-to-scattering mapping is an unvalidated assumption, not a fitted input or a renamed prediction.

full rationale

The central derivations are self-contained. Sec. 4.4 derives the Taylor expansion of Eq. (7) and checks it against vanilla integration over the full visible spectrum (Tab. 2-3: SSIM 0.99, Delta E 0.22, LPIPS 8.5e-5); this is an independent numerical benchmark, not the paper's own fitted values. The reflectance estimation (Sec. 4.2) inverts a piecewise-linear spectral model against XYZ targets and is compared to a public skin-reflectance dataset [5]; it is not equivalent to its inputs by construction. The only potentially load-bearing hand-set quantity is the coverage-to-scattering mapping in Sec. 4.3: 'for fixed D=0.25, we set the reflectance R of full coverage foundation to be 30% of R∞, 20% for medium coverage and 10% for low coverage.' This is an unvalidated assumption, with no measurement or sensitivity study reported, and it does affect the realism comparison in Tab. 4. However, the paper does not fit these fractions to the 10 real after-makeup images, nor does it rename them as a prediction; the external LPIPS comparison is a system-level evaluation of a pipeline containing this assumed parameter. Under the stated rules, an unvalidated assumption is a correctness risk, not circularity, unless it is shown to be equivalent to the target result by construction. No self-citation is load-bearing: the sole author-affiliated reference [27] is related work cited for intrinsic-image disentangling, not for the KM derivation. Therefore the paper's derivation chain does not reduce to its inputs.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new physical entities. The central claim rests on two hand-set free parameters (coverage fractions and thickness) and on four background assumptions inherited from KM theory, sRGB-to-spectrum conversion, and intrinsic image decomposition. The coverage mapping is the most fragile component because it is a pure input with no external validation.

free parameters (2)
  • Coverage reflectance fraction = Full=0.30, Medium=0.20, Low=0.10 (of R∞)
    Hand-set in Sec. 4.3 to map coverage level to finite-layer reflectance at fixed thickness; no measurement or sensitivity analysis provided, yet it directly determines the scattering coefficient S and hence the blended color.
  • Foundation layer thickness D = 0.25 (arbitrary units)
    Fixed by hand in Sec. 4.3; combined with the coverage fraction it determines the scattering coefficient S. No physical basis is given for this value.
assumptions (4)
  • domain assumption Kubelka-Munk two-layer reflectance/transmittance formulas (Eqs. 3-7) are valid for a foundation layer on skin.
    Adopted from Kubelka (1954) and Kortüm (1969); assumes homogeneous, diffuse illumination, which real skin and makeup only approximately satisfy.
  • domain assumption The foundation product image represents an opaque layer with reflectance R∞.
    Used in Sec. 4.3 to estimate the K/S ratio from sRGB; reasonable for product swatches but not verified in the paper.
  • ad hoc to paper Skin and foundation reflectance is well approximated by a 3-piece linear spectrum with a flat 600-700 nm segment.
    Introduced in Sec. 4.2 and motivated by observed flatness of foundation and skin spectra, but no error analysis is given for arbitrary skin tones or foundation shades.
  • domain assumption Shading and specular highlight are grayscale in the intrinsic image decomposition.
    Used in Eq. (2); a common simplification that can lose color information, partially compensated by LaMa inpainting for highlight areas.

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Cite this review

Pith. "Pith review of Scalable and Realistic Virtual Try-on Application for Foundation Makeup with Kubelka-Munk Theory." pith.science (2026). https://pith.science/paper/TXOHZTG3

@misc{pith2026250707333,
  author       = {Pith},
  title        = {Pith review of: Scalable and Realistic Virtual Try-on Application for Foundation Makeup with Kubelka-Munk Theory},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TXOHZTG3}},
  note         = {Machine review of arXiv:2507.07333}
}
read the original abstract

Augmented reality is revolutionizing beauty industry with virtual try-on (VTO) applications, which empowers users to try a wide variety of products using their phones without the hassle of physically putting on real products. A critical technical challenge in foundation VTO applications is the accurate synthesis of foundation-skin tone color blending while maintaining the scalability of the method across diverse product ranges. In this work, we propose a novel method to approximate well-established Kubelka-Munk (KM) theory for faster image synthesis while preserving foundation-skin tone color blending realism. Additionally, we build a scalable end-to-end framework for realistic foundation makeup VTO solely depending on the product information available on e-commerce sites. We validate our method using real-world makeup images, demonstrating that our framework outperforms other techniques.

Figures

Figures reproduced from arXiv: 2507.07333 by the authors.

Figure 1
Figure 1. End-to-end framework of foundation virtual try-on ap [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Examples of face image intrinsic decomposition: First row is original face image; second row is albedo layer; third row is shading [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. An illustration of the reflectance and transmittance of the [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figures from the paper (6 more)
Figure 3
Figure 3. Figure 3: Workflow of conventional implementation of KM model. [PITH_FULL_IMAGE:figures/full_fig_p004_3.png]
Figure 5
Figure 5. Figure 5: The CIE XYZ standard observer color matching functions [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 6
Figure 6. Figure 6: The black lines are the reflectance examples of bright, [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]
Figure 7
Figure 7. Figure 7: Visualization of skin reflectance comparison. Our method achieves similar performance with significantly less latency (See Tab. [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 8
Figure 8. Figure 8: Real-world examples of comparison between our results with alpha blending using alpha=0.3, BeautyREC[ [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 10
Figure 10. Figure 10: (a) Original images; (b) Synthesized images with high [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]

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