A hue-preserving tone mapping scheme based on constant-hue plane without gamut problem

Artit Visavakitcharoen; Hitoshi Kiya; Kouki Seo; Yuma Kinoshita

REVIEW 4 major objections 4 minor 27 references

A hue-preserving tone mapping scheme based on constant-hue plane without gamut problem

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

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Pith's one-line read Hue distortion in tone-mapped images can be largely removed by replacing each tone-mapped pixel's maximally saturated color with the original HDR pixel's, a post-processing step that works with any tone mapping operator.

desk verdict A clean, modest post-processing idea that mostly works but overclaims universality; deserves serious review with revisions. read the letter →

arxiv 1908.06557 v1 pith:M42CTO5M submitted 2019-08-19 eess.IV

Yuma Kinoshita , Kouki Seo , Artit Visavakitcharoen , Hitoshi Kiya This is my paper · ORCID

classification eess.IV

keywords tonemappinghuepreservationconstant-hueplanemaximallysaturatedcolordistortionclippingandroundingHDRimagingCIEDE2000

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 argues that hue errors in tone-mapped HDR-to-LDR images come mainly from rounding and clipping pixel values, not just from the tone curve. It proposes a post-processing step: after any tone mapping operator produces an LDR image, replace each pixel's maximally saturated color (the purest color on its constant-hue plane) with the maximally saturated color of the original HDR pixel. Because the new pixel stays on the same constant-hue plane as the HDR pixel, the hue distortion is reduced without introducing clipping errors, while the luminance from the underlying tone mapper is preserved. Experiments report lower CIEDE2000 hue differences and closer maximally saturated colors for six tone mappers, with nearly unchanged TMQI quality scores.

What carries the argument

The constant-hue plane in RGB space, anchored by white $w=(1,1,1)$, black $k=(0,0,0)$, and the maximally saturated color $c = (x - \min(x))/(\max(x)-\min(x))$. Every pixel is expressed as a linear combination $x = a_w w + a_k k + a_c c$, where the coefficients encode luminance and saturation; the compensation step in Eq. (15) splices the HDR pixel's hue into the tone-mapped pixel by replacing $c'$ with $c_H$ while keeping the tone mapper's coefficients intact.

What would settle it

Take HDR images with many pixels far outside the RGB gamut and many near-gray pixels (where max minus min is small), apply the proposed compensation, and measure CIEDE2000 hue error; if hue error does not drop for out-of-gamut pixels or increases for near-gray pixels, the geometric hue proxy fails.

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Extended reading notes

Core claim

For a tone-mapped LDR pixel $x'$, expressed on its constant-hue plane as $x' = a'_w w + a'_k k + a'_c c'$, the paper's central step is to replace $c'$ with $c_H$, the maximally saturated color of the original HDR pixel computed from Eq. (8). The compensated pixel $x'' = a'_w w + a'_k k + a'_c c_H$ lies on the same constant-hue plane as the HDR pixel, and because $c_H$ has components in $[0,1]$, $x''$ remains inside the RGB gamut, so no clipping occurs. This replacement gives the tone-mapped LDR image the same maximally saturated color values as the HDR image and reduces measured hue degradation for any tone mapping operator.

Load-bearing premise

The RGB constant-hue plane anchored by the maximally saturated color is assumed to align with perceived hue, so swapping the saturated color pulls the tone-mapped pixel toward the hue a human would see.

Editorial extensions

If this is right

The scheme is a plug-in post-filter, so any existing tone mapping operator can adopt it without redesigning the tone curve.
It directly addresses hue shifts caused by rounding quantization and clipping, which earlier color-correction formulas did not consider.
Measured CIEDE2000 hue difference and maximally saturated color difference decrease for all tested tone mappers.
The small TMQI quality loss from the compensation step can be recovered by a simple mean-luminance adjustment afterward.

Reading between the lines

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

If the constant-hue-plane proxy holds perceptually, the same replacement could improve gamut mapping and multi-exposure fusion, both of which struggle with hue fidelity.
Applying the substitution iteratively or in a perceptual color space could test whether the geometric hue proxy matches human color perception more closely.
The method's benefit likely depends on how far the original HDR pixel lies outside the RGB gamut; testing on extreme out-of-gamut HDR values would clarify its limits.

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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

Short version: this is a modest but legitimate idea, presented with cleaner math than the claims. The method — post-hoc swap the tone-mapped pixel's normalized color c' for the HDR pixel's maximally saturated color c_H on the constant-hue plane (Eq. 15) — is simple, gamut-safe, and independent of the underlying TMO. That is a real contribution, even though the constant-hue plane and maximally saturated colors are not new. What is new is applying them as a TMO-agnostic post-processing step and explicitly calling out clipping and rounding as hue-distortion sources. The CIEDE2000 numbers mostly support the claim, and Table 3 shows TMQI is roughly preserved. Credit where due: the compensation formula is clear, the gamut argument is sound, and the paper does not oversell the mechanics.

The soft spots are in the scope of the claims, not the mechanics. First, the paper says the proposed method outperforms conventional TMOs for "all TMOs" based on averages. Its own Table 2 contains counterexamples: for 'rosette', ΔH worsens under Fattal (0.8894 to 0.9286) and Shan (0.8983 to 0.9128). Those cells should force a softer conclusion like "usually reduces average hue difference" plus a disclosure of where it does not. Second, Δc is nearly circular: the method replaces c' with c_H, so a smaller Δc is built into the construction; the independent evidence has to come from CIEDE2000, and there it is decent but not universal. Third, Eq. (8) divides by max-min, so near-achromatic HDR pixels make c_H unstable or undefined; the paper never says what happens there. Fourth, there are no error bars or statistical tests, and the Mantiuk comparison uses only three images. No code or data is shipped.

This is not a fatal flaw. The core idea is plausible, cheap to implement, and probably useful in practice. But the "any TMO" claim is unsupported as written, and the near-gray case needs an explicit treatment. A serious referee should ask for restricted claims, per-image results, a small statistical analysis, and ideally code or data. I would take a look at the revised version.

Referee Report

4 major / 4 minor

Summary. The paper proposes a post-processing hue compensation scheme for tone-mapped images. After an arbitrary conventional tone mapping operator (TMO) produces a low dynamic range (LDR) image, each pixel is expressed in the RGB constant-hue plane as a weighted combination of white, black, and the pixel's maximally saturated color (Equations (8)-(10)). The compensation step (Equation (15)) replaces the tone-mapped pixel's maximally saturated color c' with the maximally saturated color c_H computed from the original high dynamic range (HDR) pixel, while keeping the coefficients unchanged. This places the compensated pixel on the same geometric constant-hue plane as the original HDR pixel and, because c_H is in [0,1]^3, avoids gamut clipping. The method is evaluated on 10 HDR images with six TMOs using three metrics: the geometric color difference Δc, the CIEDE2000 hue difference ΔH, and TMQI. The paper reports average improvements in Δc and ΔH, similar TMQI scores, and a favorable comparison with Mantiuk's color correction formula.

Significance. The proposed method is simple, parameter-free, applicable as a post-processing step to any TMO, and correctly avoids gamut clipping; these are genuine strengths, and the derivation of the compensation formula in Section 3.2 is straightforward and clearly presented. The per-image results in Tables 1 and 2 provide useful empirical information. However, the central claim that the method reduces hue degradation for all TMOs is not supported by the paper's own data, and the construction guarantees only a geometric hue match, not a perceptual one. With appropriate scoping of the claims and an explicit treatment of achromatic pixels, this could be a useful contribution; as written, the overstatement undermines the conclusion.

major comments (4)

[Table 2, Section 4.2] The claim in Section 4.2 that "the proposed method outperformed the conventional approach for all TMOs" is contradicted by the CIEDE2000 hue differences for image 'rosette': with Fattal's TMO, ΔH increases from 0.8894 to 0.9286, and with Shan's TMO, it increases from 0.8983 to 0.9128. These are not negligible differences and they concern exactly the pairwise comparison the abstract and conclusion rely on. The conclusion should be restricted to the observed average behavior over the test set, and these failure cases should be explicitly disclosed and, if possible, analyzed.
[Section 3.3, Equation (15)] Equation (15) ensures that the normalized RGB vector of the compensated pixel equals c_H, but this geometric equality in RGB space does not imply a reduction in CIEDE2000 hue difference ΔH, because ΔH is computed from nonlinear transformations to CIELAB and depends on the retained coefficients a'_w, a'_k and on the display luminance. The empirical average improvements in Table 2 are therefore not a proof of the statement that the method reduces hue degradation "for any TMO"; the two worsening cells in Table 2 confirm that the guarantee is false as stated. The paper should frame the hue-preservation claim as an empirical average improvement rather than a mathematical consequence of the construction.
[Section 4.2, definition of Δc] The Δc metric measures the Euclidean distance between the maximally saturated colors c1(i) and c2(i), which is exactly the quantity the proposed operation replaces (c' with c_H). Consequently, the large improvement in Table 1 is substantially by construction and should not be presented as independent evidence for hue preservation. The independent evidence must come from the CIEDE2000 hue difference ΔH and, secondarily, from TMQI; the paper should say so explicitly so that readers do not interpret Table 1 as validating the perceptual benefit.
[Section 2.2, Equation (8)] Equation (8) defines the maximally saturated color using division by max(x)-min(x), which is undefined when max(x)=min(x), i.e., for achromatic pixels. The paper does not specify how the proposed method handles such pixels, either in the original HDR image or in the tone-mapped LDR image. Natural images contain many gray and near-gray pixels, so this is a real gap in the procedure. A fallback should be defined (for example, leaving achromatic pixels unchanged) and the effect of that fallback on the reported metrics should be evaluated.

minor comments (4)

[Section 4.1] The text says "using four TMOs" but then enumerates six TMOs (Reinhard global, Reinhard local, Drago, Fattal, Shan, Gu). The count should be corrected.
[Section 4.3] The phrase "the our method" should be corrected to "our method" or "the proposed method."
[Sections 2.2 and 3.2] The paper uses the term "constant-hue plane" to describe a geometric construction in RGB space, but perceptual hue is measured by CIEDE2000. The paper should explicitly state that the RGB constant-hue plane is a geometric proxy for hue and that the perceptual evaluation is carried out separately with ΔH.
[Figure 8] The caption reports ΔH=2.5178 for (b) and ΔH=2.9721 for (c), while the only difference between (b) and (c) is a mean-luminance adjustment. Since global luminance scaling should not change hue, the reason for the ΔH change should be explained (e.g., the effect of rounding quantization on the compensated values).

Circularity Check

1 steps flagged · score 4.0 of 10

The Δc metric is self-defined by Eq. (15), but the central hue-preservation claim also rests on independent ΔH and TMQI evidence; circularity is partial.

self definitional [Sec. 3.2, Eq. (15); Sec. 4.2, metric Δc definition; Tables 1 and 4.]
"To correct the hue of x′, we replace x′ with x′′ as, x′′ =a′_w w +a′_k k +a′_c c_H. (15) ... The difference Δc(i) between c1(i) and c2(i) for each pixel is given by Δc(i) =‖c1(i)− c2(i)‖"

By construction, before the re-quantization step, the maximally saturated color of the compensated pixel x′′ is exactly the original HDR pixel's c_H: with a′_w = min(x′), a′_c = max(x′)−min(x′), and c_H having components in {0,1} at its extremes, (x′′ − min(x′′))/a′_c = c_H. The Δc metric then compares c(x′′) with c_H, so the reported Δc improvement is the algorithm's own optimization target, not an independent measurement. The paper even concedes the residual is only due to re-rounding: 'Δc for the proposed method does not become zero... because the rounding quantization has to be carried out again.' Thus Tables 1 and 4 partly demonstrate a definitional consequence of Eq. (15) rather than an empirical hue-preservation result; the CIEDE2000 ΔH and TMQI results are independent evidence.

full rationale

The proposed scheme is not globally circular. Eq. (15) replaces the tone-mapped color direction c′ with the original HDR direction c_H on the RGB constant-hue plane, and the reported CIEDE2000 hue differences and TMQI scores are external metrics that do not follow from the construction; those results provide independent, though imperfect, evidence. However, one of the three headline metrics, Δc, is the very quantity the algorithm forces toward zero: before re-quantization, the maximally saturated color computed from the compensated pixel equals c_H by construction because the min/max subtraction cancels the coefficients a′_w and a′_c. Therefore the Δc improvement in Tables 1 and 4 is largely self-defined rather than an empirical finding. The central hue-preservation claim still has independent grounding in ΔH and TMQI, so the circularity is partial rather than total, warranting a score of 4 rather than higher.

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

The proposed method introduces no free parameters and no invented physical or mathematical entities. It rests on geometric assumptions about the RGB constant-hue plane and on a qualitative claim that clipping and rounding are important distortion sources. The absence of fitted parameters is a strength, but the hue-plane-to-perception link remains an unverified premise.

assumptions (5)

domain assumption Perceived hue is represented by the maximally saturated color c from Eq. (8), so pixels sharing c have the same hue.
Used throughout Sections 2.2 and 3.2 to justify replacing c' with c_H; the paper does not derive this correspondence from perception or colorimetry.
standard math Every pixel in the RGB cube lies on a constant-hue plane spanned by white, black, and the maximally saturated color, with coefficients from Eq. (10).
This is a geometric property of max/min normalization and affine combinations, and it holds for valid RGB pixels.
domain assumption Hue distortion in tone mapping is caused by the tone curve, rounding quantization in Eq. (3), and clipping in Eq. (4), with clipping and rounding treated as major sources beyond the tone curve.
The paper motivates the method with this decomposition in Section 3.1 but does not quantify the relative magnitude of each source.
domain assumption The compensation remains valid when the HDR pixel x_H is not an interior point of white, black, and c_H, as acknowledged in Section 3.2.
HDR pixels can lie outside the RGB gamut, and the paper assumes the same constant-hue-plane coefficients still carry useful hue information.
domain assumption TMQI, CIEDE2000 hue difference, and Δc are accepted measures of perceptual quality and hue fidelity.
The evaluation in Section 4 relies on these metrics without validating that improvements in them correspond to perceptually meaningful gains.

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Cite this review

Pith. "Pith review of A hue-preserving tone mapping scheme based on constant-hue plane without gamut problem." pith.science (2026). https://pith.science/paper/M42CTO5M

@misc{pith2026190806557,
  author       = {Pith},
  title        = {Pith review of: A hue-preserving tone mapping scheme based on constant-hue plane without gamut problem},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/M42CTO5M}},
  note         = {Machine review of arXiv:1908.06557}
}

read the original abstract

We propose a novel hue-preserving tone mapping scheme. Various tone mapping operations have been studied so far, but there are very few works on color distortion caused in image tone mapping. First, LDR images produced from HDR ones by using conventional tone mapping operators (TMOs) are pointed out to have some distortion in hue values due to clipping and rounding quantization processing. Next,we propose a novel method which allows LDR images to have the same maximally saturated color values as those of HDR ones. Generated LDR images by the proposed method have smaller hue degradation than LDR ones generated by conventional TMOs. Moreover, the proposed method is applicable to any TMOs. In an experiment, the proposed method is demonstrated not only to produce images with small hue degradation but also to maintain well-mapped luminance, in terms of three objective metrics: TMQI, hue value in CIEDE2000, and the maximally saturated color on the constant-hue plane in the RGB color space.

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Reference graph

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

Photo- graphic tone reproduction for digital images,

E. Reinhard, M. Stark, P. Shirley, and J. Ferwerda, “Photo- graphic tone reproduction for digital images,” ACM Trans. (a) Conventional (TMQI=0.8825, ∆c=0.0221, ∆H=7.9052) (b) Proposed (TMQI=0.8436, ∆c=0.0029, ∆H=2.5178) (c) Proposed with mean lu- minance adjustment (TMQI=0.8827, ∆c=0.0029, ∆H=2.9721) Fig. 8 Eﬀects of mean luminance adjustment. (a)Tone- ma...

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F. Drago, K. Myszkowski, T. Annen, and N. Chiba, “Adap- tive Logarithmic Mapping For Displaying High Contrast Scenes,” Computer Graphics Forum, vol.22, no.3, pp.419– 426, 2003

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Gradient domain high dynamic range compression,

R. Fattal, D. Lischinski, and M. Werman, “Gradient domain high dynamic range compression,” ACM Trans. Graph., vol.21, no.3, pp.249–256, July 2002

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[4] [4]

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Q. Shan, J. Jia, and M.S. Brown, “Globally optimized lin- ear windowed tone mapping,” IEEE Transactions on Visu- alization and Computer Graphics, vol.16, no.4, pp.663–675, July 2010

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B. Gu, W. Li, M. Zhu, and M. Wang, “Local edge- preserving multiscale decomposition for high dynamic range image tone mapping,” IEEE Transactions on Image Pro- cessing, vol.22, no.1, pp.70–79, Jan 2013

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F. Durand and J. Dorsey, “Fast bilateral ﬁltering for the dis- play of high-dynamic-range images,” ACM Trans. Graph., vol.21, no.3, pp.257–266, July 2002

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A gamut-mapping framework for color-accurate reproduction of hdr images,

E. Sikudov, T. Pouli, A. Artusi, A.O. Akyz, F. Banterle, Z.M. Mazlumoglu, and E. Reinhard, “A gamut-mapping framework for color-accurate reproduction of hdr images,” IEEE Computer Graphics and Applications, vol.36, no.4, pp.78–90, July 2016

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A. Artusi, T. Richter, T. Ebrahimi, and R.K. Mantiuk, “High dynamic range imaging technology [lecture notes],” IEEE Signal Processing Magazine, vol.34, no.5, pp.165–172, Sep. 2017

work page 2017