Bridging Vision, Language, and Mathematics: Pictographic Character Reconstruction with Bézier Curves

Zihao Wan, Pau Tong Lin Xu, Fuwen Luo, Ziyue Wang, Peng Li, Yang Liu

Keywords: Vision-Language Models, Bézier Curves, Program Synthesis, Character Reconstruction, Zero-Shot Generalization, Pictographic Scripts

TL;DR: This paper trains a Vision-Language Model to decompile pictographic characters into Bézier curve programs, demonstrating that this mathematical approach enables the model to learn a transferable geometric grammar for cross-script generalization.

Abstract: While Vision-language Models (VLMs) have demonstrated strong semantic capabilities, their ability to interpret the underlying geometric structure of visual information is less explored. Pictographic characters, which combine visual form with symbolic structure, provide an ideal test case for this capability. We formulate this visual recognition challenge in the mathematical domain, where each character is represented by an executable program of geometric primitives. This is framed as a program synthesis task, training a VLM to decompile raster images into programs composed of Bézier curves. Our model, acting as a ``visual decompiler'', demonstrates performance superior to strong zero-shot baselines, including GPT-4o. The most significant finding is that when trained solely on modern Chinese characters, the model is able to reconstruct ancient Oracle Bone Script in a zero-shot context. This generalization provides strong evidence that the model acquires an abstract and transferable geometric grammar, moving beyond pixel-level pattern recognition to a more structured form of visual understanding.

Submission Number: 160