OptiComics: A Mathematical Programming Framework for Geometry-Preserving Comic Lettering

Abstract Automatic lettering of translated comics is a constrained layout problem in which a fixed visual composition must accommodate target-language text with different lengths, hyphenation patterns, and writing conventions. We present the optimization core of OptiComics, a framework that separates this task into a continuous geometric stage and a discrete typographic stage. A sampled speech-balloon contour is first summarized by Principal Component Analysis and refined through a nonconvex nonlinear program that selects a large text-safe ellipse while keeping the artist's balloon geometry unchanged. The resulting ellipse is then filled with text, and an integer linear programming model assigns ordered syllables to text rows, while accounting for spaces, hyphenation, font size, centering, and visual balance. We provide detailed derivations, worked numerical examples, modeling clarifications concerning rotated coordinates and sample-based containment, and implementation guidance. The framework is evaluated on real pages from Japanese and Italian comics, including highly irregular balloons and full-page production workflows. The results show that mathematical programming can be embedded effectively in an editorial production pipeline for the comics industry, while also identifying important limitations associated with irregular geometry, composite balloons, raster discretization, and human-facing typographic quality.