CPrefix：用于结构化离散颜色映射的组合张量框架
CPrefix: A Combinatorial Tensor Framework for Structured Discrete Color Mappings
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中文总结 AI 辅助
该研究提出CPrefix组合张量框架，将离散多通道映射的组合组织与测量值分离，在ICC配置文件验证后可应用于多类结构化离散映射场景。
中文摘要 AI 辅助
离散多通道映射通常通过采样值表示，虽能提供准确评估，但对其底层结构的理解有限。我们提出CPrefix，一种用于离散映射的组合可观测表示，实现于统一张量框架中，支持表示、重构与结构分析。该框架基于多项式计数可观测值诱导的计数张量，其支撑集构成离散帕斯卡单纯形，并非对可观测空间的约束，而是用于重构映射的潜在组合表示。此表述将映射的组合组织与其测量值分离，揭示映射底层的可观测结构。该框架在ICC显示器和打印机配置文件上通过潜在重构与感知色域迁移进行验证，准确的重构表明颜色映射可获得忠实的可观测表示，而重构残差则能反映底层映射与所提表示的兼容性。尽管在颜色变换上得到验证，该框架独立于可观测值的物理解释，适用于彩色成像、光谱测量及其他离散系统产生的结构化多通道映射。
英文摘要
Discrete multi-channel mappings are typically represented through sampled values, providing accurate evaluations but limited insight into their underlying structure. We introduce CPrefix, a combinatorial observable representation for discrete mappings, realized within a unified tensor framework that enables representation, reconstruction, and structural analysis. The framework is based on a counting tensor induced by multinomial counting observables. Its support forms a discrete Pascal simplex, not as a constraint on the observable space, but as a latent combinatorial representation from which mappings are reconstructed. This formulation separates the combinatorial organization of a mapping from its measured values, exposing the observable structure underlying the mapping. The framework is validated on ICC display and printer profiles through latent reconstruction and perceptual gamut transport. Accurate reconstruction demonstrates that color mappings admit faithful observable representations, while reconstruction residuals provide insight into the compatibility of the underlying mapping with the proposed representation. Although demonstrated on color transformations, the framework is independent of the physical interpretation of the observables, making it applicable to structured multi-channel mappings arising from color imaging, spectral measurements and other discrete systems.
