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REVIEW 3 major objections 4 minor 41 references

Shadow Removal via Shadow Image Decomposition

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A shadow removal method decomposes each image into a relit layer and a soft matte, cutting shadow-area error on ISTD from 13.3 to 7.9 RMSE.

desk verdict A plausible shadow-removal method built on a classic linear illumination model and matting decomposition, but the headline 40% RMSE improvement rests on a color-corrected test set whose baseline numbers appear to come from the original, unadjusted ground truth. read the letter →

arxiv 1908.08628 v1 pith:5NPRC6YI submitted 2019-08-23 cs.CV

Hieu Le , Dimitris Samaras This is my paper · ORCID
classification cs.CV
keywords shadowremovalimagedecompositionilluminationmodelmattingdeeplearningISTDdatasetdataaugmentationlinearrelighting
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

The paper proposes a shadow-removal method that avoids making a network predict shadow-free pixels directly. Instead, it decomposes a shadow image into a relit image and a soft matte, combining them through a classic compositing equation. The relit image is produced by a per-channel linear transformation of the shadow image, whose parameters are predicted by one network while a second network predicts the matte. On the ISTD benchmark the authors report reducing shadow-area RMSE from 13.3 to 7.9, a 40% drop over the prior state of the art, and further to 7.4 when trained on synthetically re-shadowed data. The significance, if correct, is that physically grounded decomposition can match or beat end-to-end generative approaches while avoiding typical generative artifacts.

What carries the argument

The load-bearing identity is the decomposition $I_{\text{shadow-free}} = I_{\text{shadow}} \cdot \alpha + I_{\text{relit}} \cdot (1-\alpha)$, with $I_{\text{relit}} = w \cdot I_{\text{shadow}} + b$. The shadow parameters $(w, b)$ are three-channel scale and offset values that model how shadows darken and color-shift pixels; SP-Net regresses them from the input image and mask. The matte $\alpha$ blends shadow and relit pixels per location, with $\alpha$ near 1 outside the shadow and near 0 in its umbra, and it is predicted by M-Net. This split lets network outputs be low-dimensional (six parameters plus a matte) instead of full images, which the paper argues avoids blur and artifacts.

What would settle it

Re-run the baseline methods (Gong et al. and Wang et al.) on the color-corrected ISTD test ground truth used in this paper and recompute shadow-area RMSE; if either baseline reaches 7.9 or lower, the state-of-the-art claim is not supported.

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Extended reading notes

Core claim

The central claim is that a shadow image can be decomposed as $I_{\text{shadow-free}} = I_{\text{shadow}} \cdot \alpha + I_{\text{relit}} \cdot (1-\alpha)$, where $I_{\text{relit}} = w \cdot I_{\text{shadow}} + b$ and $\alpha$ is a per-pixel matte. The vectors $w$ and $b$ are assumed constant across the umbra for each RGB channel, capturing the linear relation between lit and shadowed intensities under direct plus ambient illumination. The paper trains SP-Net to regress $w$ and $b$ from the shadow image and mask, and M-Net to predict $\alpha$ from the image, relit image, and mask. With this two-network system the paper reports state-of-the-art RMSE of 7.9 on the shadow area of the ISTD test set, compared with 13.3 for the previous best, and 7.4 after augmenting training data with synthetic shadows generated by varying the recovered parameters.

Load-bearing premise

The comparison assumes that the published RMSE values of earlier methods were computed on the same color-corrected ground truth as the paper's numbers, but the paper does not show that the baselines were rerun on the corrected images.

Editorial extensions

If this is right

  • If the decomposition is correct, shadow removal no longer requires a network to hallucinate full shadow-free images; predicting six illumination parameters and a matte suffices.
  • Because the relit image is computed analytically from the parameters, the output resolution is limited only by the input, not by the network's output resolution.
  • The same decomposition gives a shadow-editing tool: modifying $w$ and $b$ and recombining through Eq. 8 generates new shadow images of controllable strength, which the paper uses to augment training.
  • The matte layer absorbs errors in the predicted parameters, because M-Net learns to down-weight pixels that SP-Net over- or under-relights.
  • On the ISTD benchmark, the full system lowers shadow-area RMSE from 13.3 to 7.9, and to 7.4 with the augmented training set.

Reading between the lines

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

  • The reported margin depends on the color-corrected ground truth being fair to all methods; if the published baseline numbers were computed on the original ground truth, the comparison is not apples-to-apples and the 40% figure would shrink. The paper does not show that baselines were rerun on the corrected images.
  • The constant $(w, b)$ assumption should break on shadows that cross multiple materials with different spectral responses, since a single per-channel affine map cannot relight both; testing on such scenes would reveal the model's boundary.
  • The same decomposition could be applied to other spatially varying illumination effects, such as specular highlights or vignetting, as long as a linear relighting model and a matte can be defined.
  • The augmentation scheme suggests a controllable data-generation recipe for shadow removal, but the synthetic shadows share the same linear-model biases as the training data, so gains might not transfer to shadows that violate the model.
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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 / 4 minor

Summary. The paper proposes a shadow-removal framework built on a physical illumination model in which the shadow-free image is a channel-wise affine function of the shadow image, combined with a per-pixel shadow matte. Two deep networks, SP-Net and M-Net, are trained to predict the affine shadow parameters (w, b) and the matte layer α, and the output is formed by Eq. 5. The authors evaluate on the ISTD dataset, reporting RMSE 7.9 on the shadow area versus 13.3 for Gong et al., and further report 7.4 after augmenting the training set with synthetic shadow images generated by the model itself. The main claim is state-of-the-art shadow removal on ISTD.

Significance. If the comparison is made valid, the paper is a useful contribution: it combines a physically motivated low-dimensional illumination model with learned parameter and matte estimators, leading to a compact and interpretable decomposition (Eqs. 4–6). The augmentation idea in Sec. 5.3 is also interesting because it permits targeted synthesis of shadow variations without an external renderer. The paper clearly states its assumptions, including the color-correction protocol, and it provides an explicit failure-case discussion. The central architectural idea is sound and the reported internal ablations (SP-Net alone vs. SP+M-Net) support the value of the matte network. However, the headline quantitative claim is currently tied to a non-standard adjusted test set, and the paper does not provide the re-evaluations needed to make the numbers comparable.

major comments (3)
  1. [§5.2, Table 1] The claim that 'All numbers are computed on the adjusted testing images so that they are directly comparable' is not supported by the evidence in the paper. The values reported for Gong et al. (13.3) and Wang et al. (13.4) are identical to the numbers in the original publications, which evaluated on the unadjusted ISTD ground truth, and the paper does not report any re-run of these baselines on the corrected ground truth. In fact, Table 1 shows the Input Image row with Non-Shadow RMSE 2.6, which is exactly the value the correction is designed to produce on the non-shadow area, while Wang et al. is listed as 7.7 on the same column; a method that leaves the non-shadow area unchanged would score near 2.6 on the corrected ground truth, so the listed baseline number cannot have been computed on the corrected testing images. The headline 40% reduction from 13.3 to 7.9 is therefore not established unless every baseline is re-evaluated on the same corrected ground truth. I request that the authors either run all baseline methods on the corrected test set and report those numbers, or remove the direct comparison and restate the contribution as an evaluation under a modified protocol.
  2. [§5.1] The color-correction step changes the ground-truth images by a per-channel linear regression that maps the non-shadow area of the shadow-free image onto the shadow image. This is a legitimate response to the known color-inconsistency problem of ISTD, but it changes the evaluation metric itself, so RMSE values against the corrected ground truth are not comparable to RMSE values against the original ground truth. The paper should report results under both protocols (original and corrected) or, at minimum, provide the original-GT numbers for the proposed method so readers can assess the effect of the correction. Without this, the magnitude of the claimed improvement cannot be separated from the effect of modifying the ground truth.
  3. [§5.3, Table 2] The augmentation experiment is interesting, but the 7.4 result is only reported on the corrected test set. Since the synthetic images are generated using the same decomposition model that is being trained (Eqs. 8–9), it is possible that the augmented training set biases the model toward the specific form of the model's assumptions. The paper should report the augmented-model results on the original ISTD ground truth as well, and ideally on a second shadow-removal benchmark, to show that the improvement is not an artifact of the matched evaluation protocol.
minor comments (4)
  1. [Acknowledgments] The text 'National Geographic/Microsoft AI for Earth program' contains a typo: 'Neographic' should be 'Geographic'.
  2. [Eq. 7] Equation 7 divides by I_shadow − I_relit, which can be zero or near-zero for pixels where the shadow has no effect; the paper should state how such pixels are handled in the numerical computation of the training target for M-Net.
  3. [§5.1, §5.3] Both the color-correction regression and the synthetic-shadow generation use linear-regression and inverse operations that can produce out-of-range pixel values; the paper should specify whether clipping or other range enforcement is applied and whether this affects the reported metrics.
  4. [Fig. 8] The qualitative comparison figure would be easier to read if the shadow region were outlined or enlarged, since the differences between methods are mostly visible at boundaries and in the penumbra.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the shadow-free image is produced from network-predicted illumination parameters and a matte, supervised by held-out ISTD ground truth; comparison-protocol concerns are not circularity.

full rationale

The derivation is self-contained. The shadow-free output is computed by Eq. 5 from a shadow image, network-predicted shadow parameters (w,b), and a network-predicted matte alpha, where the relit image is defined by Eq. 6. The linear illumination model in Eq. 4 is an openly stated physical assumption rather than a restatement of the target output, and the target shadow-free image is external supervisory data from the ISTD dataset. SP-Net is trained with regression targets computed from training pairs, and M-Net is trained with a reconstruction loss equivalent to supervised matte estimation; both are standard supervised-learning setups, not fitted quantities later renamed as predictions. The augmentation procedure in Sec. 5.3 synthesizes additional training images from estimated decompositions and is a data-generation step, not a claim that a prediction reduces to its input. Self-citations, such as the authors' prior A+D Net work, appear only in related-work context and are not load-bearing for the central derivation. The concern that baseline RMSE values in Table 1 may not have been recomputed on the authors' color-adjusted ground truth is a potential evaluation-fairness issue, but it is not a circularity: no fitted parameter or definitional equation is being presented as an independent prediction.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The method rests on a known linear shadow model and a known matting decomposition; it does not introduce new physical entities. The main load-bearing choices are the hand-selected augmentation factors and threshold, and the test-set color correction, which is an ad hoc adjustment to the evaluation protocol.

free parameters (3)
  • augmentation factor k = [0.8, 0.9, 1.1, 1.2]
    Used in Sec. 5.3 to generate synthetic shadow images from the decomposition; chosen by hand, not learned.
  • shadow mask threshold = 0.95
    Used in Sec. 5.2 to binarize the detected shadow mask for SP-Net-only evaluation; arbitrary threshold.
  • shadow mask erosion = 5 pixels
    Used in Sec. 4.1 to exclude penumbra when regressing ground truth shadow parameters; hand-chosen.
assumptions (4)
  • domain assumption The linear illumination relation Ishadow-free = w * Ishadow + b holds per color channel, and w,b are constant across the umbra.
    Sec. 3.1; inherited from Shor and Lischinski; assumes the environment light has the same color from all directions and the camera preserves the linear relation.
  • ad hoc to paper The test-set color inconsistency between shadow and shadow-free images can be removed by a per-channel linear regression on the non-shadow area.
    Sec. 5.1; the color correction changes the evaluation ground truth; if the linear correction is wrong, the reported errors are not meaningful.
  • domain assumption The shadow matte alpha can be represented by a U-Net output conditioned on the shadow image, relit image, and binary mask.
    Sec. 4.2; the network capacity and input set are assumed sufficient to capture penumbra blending.
  • domain assumption The shadow detection network (Zhu et al.) fine-tuned on ISTD provides sufficiently accurate masks at test time.
    Sec. 5.2; errors in the mask propagate to parameter estimation and matting.

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Pith. "Pith review of Shadow Removal via Shadow Image Decomposition." pith.science (2026). https://pith.science/paper/5NPRC6YI

@misc{pith2026190808628,
  author       = {Pith},
  title        = {Pith review of: Shadow Removal via Shadow Image Decomposition},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5NPRC6YI}},
  note         = {Machine review of arXiv:1908.08628}
}
read the original abstract

We propose a novel deep learning method for shadow removal. Inspired by physical models of shadow formation, we use a linear illumination transformation to model the shadow effects in the image that allows the shadow image to be expressed as a combination of the shadow-free image, the shadow parameters, and a matte layer. We use two deep networks, namely SP-Net and M-Net, to predict the shadow parameters and the shadow matte respectively. This system allows us to remove the shadow effects on the images. We train and test our framework on the most challenging shadow removal dataset (ISTD). Compared to the state-of-the-art method, our model achieves a 40% error reduction in terms of root mean square error (RMSE) for the shadow area, reducing RMSE from 13.3 to 7.9. Moreover, we create an augmented ISTD dataset based on an image decomposition system by modifying the shadow parameters to generate new synthetic shadow images. Training our model on this new augmented ISTD dataset further lowers the RMSE on the shadow area to 7.4.

Figures

Figures reproduced from arXiv: 1908.08628 by the authors.

Figure 1
Figure 1. Shadow Removal via Shadow Image Decom￾position. A shadow-free image Ishadow-free can be expressed in terms of a shadow image Ishadow, a relit image Irelit and a shadow matte α. The relit image is a linear transformation of the shadow image. The two unknown factors of this sys￾tem are the shadow parameters (w, b) and the shadow matte layer α. We use two deep networks to estimate these two unknown factors. These metho… view at source ↗
Figure 2
Figure 2. Shadow Removal Framework. The shadow parameter estimator network SP-Net takes as input the shadow image and the shadow mask to predict the shadow parameters (w, b). The relit image I relit is then computed via Eq. 6 using the estimated parameters from SP-Net. The relit image, together with the input shadow image and the shadow mask are then input into the shadow matte prediction network M-Net to get the shadow matte… view at source ↗
Figure 3
Figure 3. A comparison of the ground truth shadow mask and our shadow matte. From the left to right: The input image, the relit image computed from the parameters estimated via SP-Net, the ground truth shadow mask, the final results when we use the shadow mask, the shadow matte computed using our M-Net, and the final shadow-free image when we use the shadow matte to combine the input and relit image. The matting layer handles… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: An example of our color correction method. From left to right: input shadow image, provided shadow￾free ground truth image (GT) from ISTD dataset, and the GT image corrected by our method. Comparing to the input shadow image on the non-shadow area only, the root-mean￾s…
Figure 5
Figure 5. Figure 5: Comparison of shadow removal between our method and ST-CGAN [34]. ST-CGAN tends to produce blurry images, random artifacts, and incorrect colors of the lit pixels while our method handles all cases well. overall illumination changes compared to the model of Gong et al.…
Figure 7
Figure 7. Figure 7: Shadow editing via our decomposition model. We use Eq. 8 to generate synthetic shadow images. As we change the shadow parameters, the shadow effects change accordingly. We show two example images from the ISTD training set where in the middle column are the original im…
Figure 6
Figure 6. Figure 6: Failure cases of our method. In the first row, our method overly lights up the shadow area. In the second row, our method generates incorrect colors. As can be seen in the two bottom rows of Tab. 1, both de￾signs achieved slightly worse shadow removal results than our …
Figure 8
Figure 8. Figure 8: Comparison of shadow removal on ISTD dataset. Qualitative comparison between our method and previous state-of-the-art methods: Guo et al.[13], Yang et al.[38], Gong et al.[12], and Wang et al.[34]. “SP-Net” are the shadow removal results using the parameters computed f…

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