Progress in Computing Applications Leonie Selbach, Tobias Kowalski, Klaus Gerwert, Maike Buchin, Axel Mosig 14 1 2025 https://doi.org/10.6025/pca/2025/14/1/1-18 https://www.dline.info/pca/fulltext/v14n1/pcav14n1_1.pdf In identifying biomarkers and molecular profiling of diseases, laser capture microdissection serves as an exceptionally efficient method for isolating disease-specific areas from intricate, varied tissue specimens. These areas must be broken down into manageable pieces that meet specific size and shape requirements for successful extraction. We approach the challenge of constrained shape decomposition by calculating optimal feasible decompositions of simple polygons. Our framework is based on a skeleton-oriented method and provides analgorithmic structure that supports the integration of different feasibility criteria and optimization objectives. Driven by our application focus, we explore various constraints and analyze the resulting fragmentations. Additionally, we implement our technique on lung tissue samples and demonstrate its benefits over a heuristic decomposition strategy.