AutoLumNet: Monotone Optimal Transport for Single-Shot Exposure Correction

Airin Akter Tania; Md Raihan Khan; Mohiuddin Ahmad

cs.CVAug 20, 2026

AutoLumNet: Monotone Optimal Transport for Single-Shot Exposure Correction

Authors: Airin Akter Tania, Md Raihan Khan, Mohiuddin Ahmad

Organizations: Department of Electrical and Electronic Engineering (EEE) Khulna University of Engineering & Technology (KUET), Bangladesh

Abstract

Single-shot exposure correction aims to map an arbitrarily degraded image---whether under-exposed, over-exposed, or a spatial mixture of both---to a well-exposed output from a single capture. We present AutoLumNet, a framework that decomposes this task into a global monotone tone curve and a bounded local residual, making the global component the locus of formal guarantees. The tone curve is parameterized as the normalized cumulative integral of a strictly positive density, ensuring strict monotonicity by construction rather than by penalty. We prove that this parameterization (i)~preserves the pairwise luminance ordering of all pixels and all spatial extrema unconditionally, and (ii)~is dense in the space of valid tone corrections, containing the one-dimensional optimal-transport map from the input to any target luminance distribution. A differentiable sorted-sample Wasserstein-2 objective drives the learned curve toward the OT optimum during training. Spatially varying effects that the global map provably cannot address---local shading, chrominance shifts, and clipped-region restoration---are handled by a bounded residual decoder with dual-branch convex fusion, for which we provide an explicit sufficient condition for local order preservation. Experiments on five benchmarks (MSEC, SICE, LCDP, LOL-v1, LOL-v2-real) show that AutoLumNet achieves state-of-the-art PSNR and SSIM across both under- and over-exposure regimes at 11.2,ms per frame, and generalizes zero-shot to pure low-light benchmarks without retraining. To our knowledge, AutoLumNet is the first exposure-correction method to unite structural monotonicity, optimal-transport optimality, and bounded local adaptivity within a single trainable architecture. Code is available at https://github.com/kraihan/Autolumnet.

Figures & tables

Fig. 1: Single-shot exposure correction with AutoLumNet. Top two rows: the same SICE scene captured under under-exposure (UE) and over-exposure (OE). Exposure-Slot [ 54 ] , the current multi-exposure SOTA, produces acceptable but imperfect results in both directions; AutoLumNet recovers colour and detail more faithfully. Bottom row: average PSNR on three standard benchmarks. AutoLumNet achieves the highest PSNR on all three datasets among the compared multi-exposure methods, while being the only method whose global tone correction carries formal monotonicity and optimal-transport guarantees (Sec. III ).

Symbol	Meaning
$I,\,\hat{I},\,I^{\star}$	Input, predicted, ground-truth image
$Y,\,\hat{Y},\,Y^{\star}$	Corresponding luminance channels
$C$	Chrominance channels of $I$
$\Omega$	Pixel domain $\{1,\dots,H\}\times\{1,\dots,W\}$
$p,q$	Pixel indices
$\varphi_{p}$	Pixelwise degradation map

TABLE I: Summary of notation used throughout Section III .

Fig. 2: Architecture of AutoLumNet. (a) A shared Resnet encoder $\mathcal{E}$ feeds two paths. The global path (top) realizes principles P1 and P2 : the input is split into luminance–chrominance, the input luminance law $\mu$ is aligned to a well-exposed target law $\nu$ by the one-dimensional optimal-transport map $T^{\star}{=}F_{\nu}^{-1}\!\circ F_{\mu}$ ( $\mathcal{L}_{\mathrm{align}}$ ), and a pooled descriptor $g{=}\mathrm{GAP}(F_{4})$ is mapped by an MLP to bin logits $v_{k}$ , passed through $\mathrm{softplus}$ with a positive floor to give strictly positive masses $m_{\theta}{=}\mathrm{softplus}(v_{k}){+}\varepsilon$ , normalized and cumulatively summed into the strictly increasing tone curve $T_{\theta}$ (boxed insets), applied to the input luminance $Y$ . The local path (bottom) realizes principle P3 : a dual-branch convex-fusion decoder $\mathcal{D}$ produces a bounded residual $r_{\theta}$ ( $|r_{\theta}|\!\leq\!\rho$ ) and a chroma residual $r_{c}$ . The luma estimate $\hat{Y}{=}\mathrm{clip}_{[0,1]}(T_{\theta}(Y){+}r_{\theta})$ is recomposed into RGB. Colored tags mark where each theoretical guarantee is enforced. (b) Progressive exposure correction across stages. (c1) Construction of the strictly increasing tone curve from positive bin masses (Lemma 1). (c2) Dual-branch convex fusion remains inside the convex hull of its two hypotheses (Lemma 3).

Fig. 3: Learned monotone tone curves $T_{\theta}$ . For three exposures of the same scene (top), the model produces image-adaptive, strictly increasing curves (bottom). The under-exposed (UE) curve lies above the identity (brightening), the correctly exposed curve is near-identity, and the over-exposed (OE) curve lies below (darkening). All three curves are monotone by construction (Lemma III.2 ), start at $(0,0)$ and end at $(1,1)$ , and the piecewise-linear staircase from $K{=}64$ bins is clearly visible. This validates the structural guarantee of Proposition III.3 : a single global curve per image preserves the spatial luminance ordering regardless of the exposure direction.

Fig. 4: Visual ablation study on SICE Scene 257. Removing the tone curve ( w/o $T_{\theta}$ ) leaves the image dark, confirming that the bounded residual ( $\rho{=}0.20$ ) alone cannot correct large global exposure shifts. Removing the decoder ( w/o Decoder ) yields a globally lifted but flat result with no local contrast. Removing the OT alignment loss ( w/o $\mathcal{L}_{\mathrm{align}}$ ) produces desaturated, tonally inaccurate output. Removing the perceptual loss ( w/o $\mathcal{L}_{\mathrm{perc}}$ ) causes severe colour bleeding and structural distortion, confirming its role as a critical regulariser. The full model recovers both global exposure and local detail, closely matching the GT. Zoomed insets highlight the book-cover text, which is legible only in the full model and the GT.

Fig. 5: Hyperparameter sensitivity. (a) Effect of the residual bound

\rho

: too small (

\rho{=}0.01

) restricts local correction and loses

3.95

dB; too large (

\rho{=}0.50

) permits artifacts and loses

1.70

dB; the optimum is

\rho{=}0.20

. (b) Effect of the number of tone-curve bins

K

: performance plateaus at

K{=}64

;

K{=}256

overfits (

-0.88

dB). (c) Backbone comparison: ResNet-34 with ImageNet pretraining outperforms both the lighter ResNet-18 (

-1.03

dB) and NAFNet without pretraining (

-0.66

dB), indicating that the framework benefits more from strong initialisation than from task-specific block design. PSNR (solid, left axis) and SSIM (dashed, right axis) are reported on the MSEC dataset.

Fig. 6: Qualitative comparison on SICE Scene 4 (outdoor landscape). Left block : under-exposed (UE) input. Right block : over-exposed (OE) input. Zoomed insets highlight the island trees on the horizon. UE-only methods applied to the OE input produce severe artifacts: SCI [ 46 ] yields a complete white-out, RetinexFormer [ 6 ] generates cloudy banding, and Zero-DCE++ [ 45 ] further amplifies the overexposure. Among multi-exposure methods, LCDPNet [ 49 ] introduces a green colour shift on UE, while ECLNet [ 51 ] and RECNet [ 52 ] over-saturate the sky. AutoLumNet closely matches the GT in both exposure directions, preserving natural colour and fine structural detail in the zoomed region.

Group A — Low-light enhancement
	MSEC Dataset							SICE Dataset							LCDP
	Under-exp.		Over-exp.		Average			Under-exp.		Over-exp.		Average			Average
Method	PSNR $\uparrow$	SSIM $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$
Zero-DCE++ [ 45 ]	13.82	.589	9.74	.514	11.37	.558	.312	11.93	.476	6.88	.409	9.41	.442	.362	18.42	.767
SCI [ 46 ]	9.97	.668	5.84	.519	7.49	.579	.312	17.86	.640	4.45	.363	12.49	.505	.424	11.87	.523
RetinexFormer [ 6 ]	15.42	.793	7.37	.387	11.31	.586	.342	17.19	.761	5.51	0.315	11.35	0.538	.405	12.61	.653

TABLE II: Quantitative comparison on the MSEC [ 16 ] , SICE [ 55 ] , and LCDP [ 49 ] datasets.

\uparrow

: higher is better;

\downarrow

: lower is better. Bold : best; underline : second best. Group A methods target low-light only; Group B methods handle both under- and over-exposure.

Fig. 7: Qualitative comparison on SICE Scene 40 (indoor, building seen through a window). The zoomed inset targets the building façade visible through the glass, testing fine-structure and colour fidelity. On the UE input, SCI [ 46 ] produces a flat yellow cast with no visible building detail; FECNet [ 48 ] introduces reddish colour distortion. On the OE input, RetinexFormer [ 6 ] produces strong golden artefacts through the window; Zero-DCE++ [ 45 ] over-brightens the already saturated glass. AutoLumNet recovers the building detail in both cases, with colour and contrast closely matching the GT. Best viewed zoomed in on screen.

Group A — Low-light enhancement
	MSEC			SICE			LCDP
Method	NIQE $\downarrow$	BRISQUE $\downarrow$	PI $\downarrow$	NIQE $\downarrow$	BRISQUE $\downarrow$	PI $\downarrow$	NIQE $\downarrow$	BRISQUE $\downarrow$	PI $\downarrow$
Zero-DCE++ [ 45 ]	6.663	24.152	13.745	8.384	33.503	17.560	10.992	43.271	21.140
SCI [ 46 ]	9.186	33.188	16.934	10.349	42.780	21.076	7.924	31.841	16.959
RetinexFormer [ 6 ]	7.850	14.090	11.120	11.612	25.708	12.048	6.370	16.396	10.013
Group B — Multi-exposure correction

TABLE III: No-reference perceptual quality comparison on the MSEC, SICE, and LCDP datasets. NIQE [ 56 ] measures naturalness, BRISQUE [ 57 ] measures spatial quality, and PI is the Perceptual Index [ 58 ] . All three metrics are lower is better . Bold : best; underline : second best.

Group A — Low-light only
Method	#P (M)	FLOPs (G)	Time (ms)	PSNR $\uparrow$
Zero-DCE++ [ 45 ]	0.01	0.17	1.3	11.37
SCI [ 46 ]	0.001	0.02	0.4	7.49
RetinexFormer [ 6 ]	1.61	17.02	43.7	—
Group B — Multi-exposure
MSEC [ 16 ]	7.04	9.64	46.8	20.08

TABLE IV: Model complexity comparison. FLOPs and inference time measured on

256{\times}256

input on a single NVIDIA P100 GPU. PSNR is the average on the MSEC dataset.

	LOL-v1		LOL-v2-real
Method	PSNR $\uparrow$	SSIM $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$
RetinexNet [ 2 ]	16.77	0.560	15.47	0.567
KinD++ [ 59 ]	21.30	0.822	14.68	0.640
Zero-DCE++ [ 45 ]	14.81	0.540	18.06	0.580
SCI [ 46 ]	14.78	0.525	17.36	0.614
SNR-Aware [ 60 ]	24.61	0.842	21.48	0.849

TABLE V: Comparison on the LOL low-light benchmarks. All methods evaluated using their officially released weights. AutoLumNet is trained on MSEC and tested without retraining on LOL, demonstrating zero-shot generalization from multi-exposure to low-light correction.

Variant	PSNR $\uparrow$	SSIM $\uparrow$	$\Delta$ PSNR
w/o $T_{\theta}$ (residual only)	21.21	0.865	$-$ 2.54
w/o Decoder (tone only)	20.36	0.877	$-$ 3.39
w/o $\mathcal{L}_{\mathrm{align}}$	19.84	0.886	$-$ 3.91
w/o $\mathcal{L}_{\mathrm{perc}}$	17.68	0.763	$-$ 6.07
Full model (Ours)	23.75	0.907	0

TABLE VI: Ablation study on the MSEC dataset. Each row removes one component from the full model.

\Delta

PSNR shows the drop from the full model.

Param	Value	PSNR $\uparrow$	SSIM $\uparrow$	$\Delta$ PSNR
$\rho$	0.01	19.80	0.829	$-$ 3.95
	0.10	22.66	0.894	$-$ 1.09
	0.20 $\;\star$	23.75	0.907	0
	0.30	23.02	0.899	$-$ 0.73
	0.50	22.05	0.890	$-$ 1.70
$K$	4	20.50	0.843	$-$ 3.25

TABLE VII: Hyperparameter sensitivity on the MSEC dataset.

\star

denotes the default setting used in all other experiments.

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