arXiv:2610.28131v1 Announce Type: cross Abstract: Existing feature lifting approaches for open-vocabulary segmentation rely on simple backprojection to assign features to primitives. In the case of 3D Gaussian splatting reconstruction, the primitives overlap heavily, leading to suboptimal reconstructions, governed by many primitives per ray. Backprojection, however, reduces to a least-squares solvable problem, exactly when no two primitives share a ray. Motivated by this insight, we propose OV-Foam, which uses PowerFoam as the underlying representation. This representation uses a power-diagram to partition the scene, resulting in zero overlap between primitives and a substantial reduction in primitives per ray, which ultimately simplifies the lifting problem and allows for closer-to-optimal feature assignment. We show that the space partitioning primitives of OV-Foam reach near-optimal assignment, and our experiments demonstrate improved open-vocabulary segmentation over Gaussian baselines.