Geometric Scene Formalization in Vision-Based Educational Sensing via Multimodal Large Models

This paper studies geometric scene formalization in vision-based educational sensing environments, where textual conditions and geometric diagram images jointly constitute heterogeneous perceptual inputs. The goal is to convert multimodal sensed information into standardized formal representations for machine understandable educational analysis. Existing methods remain limited by unstable cross modal alignment, inadequate expression of geometric relational constraints, and insufficient verifiability of generated outputs. To overcome these challenges, a unified modeling framework is proposed based on multimodal large models with structure-aware prompting and verification feedback. A geometry-oriented structure prompt injection mechanism is first introduced to encode prior cues of geometric entities, relational patterns, and constraint dependencies, which enhances the intrinsic alignment among textual descriptions, visually sensed diagram regions, and formal symbolic representations. In addition, an external verification feedback strategy is employed to constrain and iteratively refine the initial outputs, thereby improving structural consistency, syntactic correctness, and target proposition accuracy. To support this task, a new vision-based multimodal geometry formalization dataset is further constructed for model training and evaluation. Extensive experiments show that the proposed method can more effectively accomplish the transformation from multimodal sensed educational inputs to executable formal expressions, while also demonstrating stronger robustness and reliability in complex visual conditions. These results indicate that the proposed framework offers a feasible solution for structured scene interpretation, automatic problem analysis, error diagnosis, and intelligent feedback in vision-based educational systems.