Multi-Scale Structural Response in Calligraphic Layout Deviation Detection

Structural deviation detection in calligraphic layout is an important problem in intelligent calligraphy tutoring systems. Existing approaches typically rely on isolated geometric or pixel-level statistics and lack a unified representation across spatial levels and scales. To address this issue, this study formulated a layout analysis for hard-pen regular script written in Tianzigē grids as a structural deviation detection task. A continuous writing density field was first constructed from the binary stroke foreground, and a three-level spatial partition consisting of page level, row-column level, and single cell level regions was established. Multi-scale structural responses (MSRs) were then computed within these regions to characterize layout deviations in a unified manner. Under controlled parametric perturbations, an original dataset of 1200 pages was evaluated to assess detection performance. In repeated experiments, the joint MSR features achieved an AUC of 0.94 and an F1-score of 0.90, outperforming geometric, pixel-statistical, page-level structural, and traditional machine-learning baselines. The results indicate that multi-level MSRs provide complementary structural information for reliable layout deviation detection and offer a useful basis for hierarchical diagnostic feedback in intelligent calligraphy tutoring systems.