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Constrained Color Carrier: Characterization-Preserving Conditional Color Rendering in Multi-Illuminant Camera Profiles

Xilai Liang

arXiv:2609.18361v1eess.IV

TL;DR

DNG multi-illuminant profiles share interpolation slots between characterization and nonlinear rendering, so an added rendering slot also adds a characterization state. CCC keeps its pre-serialization matrices on the protected dual segments while using three HueSatMap bases and solving condition-specific payloads through a fixed serialized operator. On the evaluated profile, CCC stays below the prescribed preservation tolerance and reduces worst-condition target error relative to the Dual representation.

  • Problem

    DNG’s shared calibration interpolation means that adding a third HueSatMap payload also adds a characterization state, while the paper seeks additional nonlinear rendering capacity without moving the executed characterization beyond a prescribed deviation from the protected dual mapping.

    Source: §1 · pp. 2–3

  • Method

    CCC constructs three pre-serialization matrix states from the original dual matrix segments, solves condition-specific HueSatMap preimages through a fixed serialized downstream operator, and constrains host-effective characterization preservation.

    Source: §1 · p. 3, §2.4 · p. 9

  • Results

    0.003857 preservation error, below the 0.004 tolerance, and 0.03508 worst-condition target P95 for CCC versus 0.08208 for the Dual representation.

    Source: §6 · p. 20

  • Takeaways & Limitations

    The evaluated serialized artifacts reproduce the color-table payloads exactly and yield numerically identical offline execution to solver-side execution, showing CCC is representable in the evaluated profile format.

    Source: §5 · p. 20, §6 · p. 21

    The evaluation uses one protected camera profile and one recovered rendering family, tests preservation only across color temperature at zero tint, and does not establish a general perceptual threshold.

    Source: §5 · p. 20

Abstract

from arXiv · show

In Digital Negative (DNG) multi-illuminant profiles, characterization matrices and nonlinear rendering payloads share condition-dependent interpolation slots, so adding a slot for rendering capacity also introduces an additional characterization state. We introduce Constrained Color Carrier (CCC), which constructs the three pre-serialization ColorMatrix and ForwardMatrix states from the original dual matrix segments while allowing the same shared slots to carry three HueSatMap rendering bases. Condition-specific HueSatMap payloads are solved as numerical preimages of the target through a fixed serialized downstream rendering operator, and carrier selection enforces a preservation bound on the host-effective interpolated characterization. We evaluate CCC on the Sony ILCE-7RM5 Adobe Standard dual-illuminant profile using a white-balance-dependent Standard ColorCorrect target recovered from Phocus 4.0.1 for the Hasselblad X2D 100C. Using Euclidean Oklab error, CCC yields a worst-temperature 95th-percentile preservation error of 0.003857, below the prescribed tolerance of 0.004, and reduces the worst-condition 95th-percentile target error from 0.08208 for the Dual representation to 0.03508. The synthetic Ordinary Triple yields a preservation error of 0.014802 and exceeds the same tolerance. The serialized DNG Camera Profile (DCP) and Extensible Metadata Platform (XMP) artifacts reproduce the final color-table payloads exactly and yield zero numerical difference from solver-side offline execution, showing that the CCC solution is representable within the evaluated serialized profile format.

1 Introduction

Multi-illuminant profiles use shared interpolation slots for characterization and nonlinear rendering, so adding a rendering slot also adds a characterization state. CCC uses three rendering bases while keeping its pre-serialization matrices within the original dual matrix segments and constraining host-effective characterization preservation.

1 Introduction

  • A conventional third DNG calibration slot adds a characterization state alongside its third HueSatMap payload, coupling rendering capacity to the shared calibration geometry.Prior multi-illuminant methods also use additional calibration states to increase characterization capacity.Source: §1 · p. 2
  • CCC constructs three pre-serialization ColorMatrix and ForwardMatrix states from the original dual matrix segments while using three HueSatMap rendering bases.It solves condition-specific HueSatMap payloads as preimages through a fixed serialized downstream operator and separately constrains host-effective characterization preservation.Source: §1 · p. 3
  • The evaluation compares Dual, synthetic Ordinary Triple, Affine-only Triple, and CCC using a Sony ILCE-7RM5 Adobe Standard profile and a recovered white-balance-dependent target for the Hasselblad X2D 100C.The target is Standard ColorCorrect recovered from Phocus 4.0.1; serialized DNG artifacts are checked by payload readback and comparison with offline execution.Source: §1 · p. 3

2 Method

The method uses DNG’s shared calibration geometry to carry three HueSatMap rendering bases while constraining the characterization matrices and the host-effective interpolated mapping. It solves condition-specific rendering preimages through a fixed downstream operator, fits carrier and rendering parameters, and audits preservation over the discretized domain.

2.1 Shared Multi-Illuminant Profile Representation

  • A conventional three-slot profile pairs each characterization state with a rendering payload, so its third rendering payload also introduces a third characterization state.The method uses the same host-defined interpolation geometry for both branches.Source: §2.1 · p. 4

2.2 Constrained Carrier Construction

  • CCC constructs three pre-serialization ColorMatrix and ForwardMatrix states on the protected dual matrix families, while the three HueSatMap payloads provide distinct nonlinear rendering bases.The matrix-segment constraint alone does not determine the host-executed characterization, which is evaluated after serialization and runtime interpretation.Source: §2.2 · pp. 6–7

2.3 Host-Effective Characterization Preservation

  • Characterization preservation is evaluated using serialized matrix states and interpolation weights recomputed along the candidate profile’s recovered white-point trajectory.The interpolation weights depend on the white point recovered from the candidate characterization itself.Source: §2.3 · pp. 7–8

2.4 Conditional Rendering Compilation

  • For each condition, CCC solves an HSM payload as a numerical preimage of the desired rendering through the fixed serialized downstream operator.The condition-specific independent preimages are then approximated jointly by the three carrier bases.Source: §2.4 · p. 9

2.5 Numerical Solution

  • The solver updates carrier geometry in an outer search and obtains rendering-basis coordinates through conditional linear solves, with reweighting to favor lower worst-state rendering error.Accepted candidates undergo a complete discretized-domain preservation audit, with additional near-worst conditions inserted when needed.Source: §2.5 · pp. 9–11

3 Experiments

The experiments compare four profile representations using a protected Sony camera characterization and a recovered, white-balance-dependent Phocus rendering target. Evaluation separates characterization preservation from target-rendering fidelity across the specified conditions and sample sets.

3.1 Experimental Setup

  • The evaluation uses a recovered Phocus 4.0.1 Standard ColorCorrect target for the Hasselblad X2D 100C with the Sony ILCE-7RM5 Adobe Standard profile as the protected characterization.The Film Tone stage is excluded from the target and target-error evaluation.Source: §3.1 · p. 11
  • The evaluation covers 7,601 integer temperature states from 2400 to 10000 K, with zero query tint for characterization preservation and seven exposure offsets for target rendering.Each temperature–exposure state uses the same 1,458-color set.Source: §3.1 · pp. 11–12
  • A complete 7,601-temperature preservation audit is the final carrier test, with at most four solve–audit–exchange cycles; the recovered Phocus numerical assets are not redistributed.The implementation of the profile-construction and evaluation pipeline is publicly available.Source: §3.1 · p. 13

3.2 Evaluation

  • Four representations compare rendering-basis capacity, characterization geometry, and carrier selection, with Affine-only Triple and CCC preserving the original dual matrix segments.The Ordinary Triple uses a synthetic third calibration state fixed at 5000 K and zero tint.Source: §3.2 · pp. 13–14
  • Preservation and target-rendering fidelity are measured separately using Euclidean distances in Oklab; the preservation audit compares the complete base-rendering path, including serialized Adobe Look re-representation.The study’s 0.004 preservation tolerance is an engineering feasibility bound, not a perceptual visibility threshold.Source: §3.2 · p. 14

4 Results

CCC keeps the characterization within the prescribed preservation tolerance while improving target rendering over the Dual representation. Removing that constraint improves target fit but violates the preservation criterion; serialized payloads reproduce solver-side execution exactly.

4.1 Representation Comparison

  • CCC meets the 0.004 preservation criterion with Ebase = 0.003857 and lowers worst-condition target error to 0.03508, versus 0.08208 for Dual.The synthetic Ordinary Triple reaches 0.06344 worst-condition target error but has preservation error 0.014802; the Affine-only Triple also meets the criterion and improves both target-error metrics over Dual.Source: Figure 2 · p. 16, Table 2 · p. 17, §4.1 · p. 17

4.2 Error and Capacity Analysis

  • Removing the preservation constraint lowers Emean target from 0.01904 to 0.01716 and Emax target from 0.03508 to 0.03083, but raises Ebase to 0.011854, above ϵ = 0.004.Source: §4.2 · pp. 17–18
  • Across the 26-temperature diagnostic set, independent preimages and three-basis approximations have comparable target errors, with no common ordering of their maximum state-wise P95 across carrier settings.Under the target-only carrier, three bases have higher mean but lower maximum state-wise P95 than independent preimages; under CCC, their mean is higher and maximum only slightly higher.Source: §4.2 · p. 17, Figure 3 · p. 18

4.3 Serialization and Offline Execution Validation

  • Artifact-readback payloads produce zero numerical difference from solver-side offline execution.The final profile was serialized and read back before numerical validation.Source: §4.3 · p. 18, Table 4 · p. 19

5 Discussion

CCC and Affine-only Triple meet the preservation criterion, while Ordinary Triple exceeds it; CCC has the lowest target errors among the three-basis representations. The evaluation also exposes a fidelity–preservation trade-off and remains limited to one profile and target, with commercial-host agreement untested.

5 Discussion

  • Ordinary Triple exceeds the preservation criterion, while Affine-only Triple and CCC remain within tolerance; CCC has the lowest mean and worst-condition target errors among three-basis representations.Because Affine-only Triple also meets the criterion, the comparison does not establish a separate preservation advantage from host-effective carrier selection.Source: §5 · p. 19
  • Removing the preservation constraint reduces both full-domain target-error metrics but raises Ebase to 0.011854, above the ϵ = 0.004 criterion.The independent-preimage diagnostic is not a lower bound on the three-basis metric, and the experiment does not identify finite-basis approximation as the dominant source of residual target error.Source: §5 · pp. 19–20
  • Exact payload readback and numerically identical offline execution confirm serialization fidelity, but agreement with execution in a commercial Adobe host remains untested.The complete discretized-domain audit verifies preservation outside the finite optimization set for the reported carrier; the exchange update was not triggered in the final solution.Source: §5 · p. 20
  • The evaluation covers one protected camera profile and one recovered rendering family; transfer across cameras and targets remains untested.The target excludes the Film Tone stage, and the zero-tint preservation audit samples only a one-dimensional subset of the white-point domain.Source: §5 · p. 20

6 Conclusion

CCC adds conditional nonlinear rendering capacity while constructing pre-serialization characterization matrices from a protected dual-illuminant family. In the evaluated profile, it remains within the prescribed preservation tolerance, reduces worst-condition target error relative to Dual, and reproduces its payloads and offline execution exactly after serialization.

6 Conclusion

  • Ebase = 0.003857 is below ϵ = 0.004, while worst-condition target P95 falls from 0.08208 for Dual to 0.03508 for CCC.The synthetic Ordinary Triple violates the preservation criterion, whereas the dual-segment-constrained three-basis representations remain feasible.Source: §6 · pp. 20–21
  • CCC increases conditional nonlinear rendering capacity while constructing pre-serialization characterization matrices from a protected dual-illuminant family.The three shared interpolation slots carry HueSatMap rendering bases while the matrix states remain within the protected dual matrix families.Source: §6 · p. 21
  • Serialized payload readback is exact, and artifact-readback offline execution is numerically identical to solver-side execution.These results establish representability within the evaluated serialized profile format.Source: §6 · p. 21
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