Learning Deformation-Induced Shape Representations for Building Footprints via Self-Supervision

Effective shape representation of building footprints is essential for many geospatial analysis and applications, such as building retrieval, cartographic generalization, and urban morphology analysis. Constrained by scarce and coarse annotations of building shapes, self-supervised learning (SSL) is regarded as a promising paradigm. However, existing SSL approaches primarily infer invariance from augmented views of the same instance without explicitly defined similarity, limiting their ability to capture multi-layered relationships—from geometric regularity to structural layout—across building shapes. Providing reliable and interpretable similarity supervision remains challenging. In this work, we propose Deformation-Induced Self-Supervised Learning (DI-SSL), a framework that explicitly defines similarity through Geometric-Aware Deformations (GAD). GAD constrains deformations along global topology, geometric variation and structural layout, jointly characterizing structural comparability between shapes and ensuring geometrically valid, structurally coherent variants under controlled form deviations. Consequently, similarity is explicitly defined through these constrained deformation processes, yielding an embedding space where structurally similar shapes are consistently organized. Experiments demonstrate that DI-SSL achieves strong performance in retrieval and few-shot generalization. The learned embedding space is well-structured, exhibiting global separability of structural prototypes and local continuity consistent with morphologically meaningful similarities. Ablation studies further highlight the critical role of deformation-induced supervision in shaping this space.