Stain normalization reduces color variations caused by variations in staining protocols and imaging conditions, thereby enhancing computer-aided diagnostic system performance. Traditional methods derive mapping relationships from individual or limited reference images through pixel-wise transformation, offering style flexibility but suffering from inaccurate color mapping extraction. While existing deep-learning-based approaches achieve accurate dataset-wide color mapping through complex neural networks, they face challenges including computational inefficiency, artifact generation, and fixed normalization directions requiring model retraining for directional changes. To address these limitations, we propose StainPresetNet - a novel framework that combines structural preservation with dataset-level color mapping while maintaining computational efficiency. Our method implements pixel-wise normalization guided by preset reference images, enabling multi-directional adaptability without retraining. Evaluations on cytopathology and histopathology datasets demonstrate that StainPresetNet achieves superior color mapping accuracy compared to conventional methods, effectively improves classifier generalization in diagnostic tasks, and reduces computational overhead by 90\% versus existing deep learning approaches. The proposed preset-guided mechanism facilitates flexible adjustment of normalization directions through simple reference image replacement, overcoming the directional rigidity of current deep-learning-based solutions.
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.