Library-Interior Colour Analysis Based on Multimodal-LLM Records: Weighted Circular Clustering, Perceptual Modelling, and a Proposed Decision-Support Workflow

Architectural colour in public libraries significantly influences indoor atmospheric quality and occupant emotional well-being, yet palette selection in design practice remains predominantly reliant on subjective intuition, precedents, and vendor catalogues. This study develops a computational framework that links multimodal image colour extraction, circular clustering, human perceptual evaluation, and multi-criteria decision weighting into a structured analysis pipeline. Using a corpus of 500 curated library interior images across diverse geographic regions, a multimodal large language model extracted dominant architectural colour records and visual weights, which were deterministically converted to HSV space and clustered using weighted circular k-means. A semantic differential experiment involving fifty design students across five bipolar scales provided empirical perceptual ratings, evaluated through repeated nested ten-fold cross-validation across five machine learning algorithms. The analysis identified five recurrent colour paradigms, demonstrating that spatial hue distributions form distinct chromatic clusters across modern library architecture. Perceptual models revealed that average colour features reliably predict perceived warmth and quietness, whereas modernity and naturalness depend more heavily on non-chromatic spatial cues. By integrating these predictive models with analytic hierarchy process and Delphi expert weights, the framework establishes a transparent decision-support protocol for early schematic design. This allows architects and clients to quantitatively compare alternative colour schemes against functional zoning requirements, providing an objective, accountable foundation for evidence-based interior design.