Spatial Affordance-Aware Affine Transformation Between Heterogeneous Spaces for Mixed Reality Remote Collaboration

We propose a spatial affordance-aware affine transformation method between heterogeneous spaces for continuous multi-object matching in shared Mixed Reality (MR) spaces. While previous redirection and spatial mapping approaches utilize physical objects and walkable areas, a critical gap remains in enabling continuous mapping between dissimilar physical environments that supports both precise object alignment and seamless locomotion in a shared space. Our method structurally segments heterogeneous spaces into interaction zones and constructs affine patches based on object adjacency and facing configuration, enabling continuous correspondence. We evaluate our method using a dataset of paired dissimilar spaces and demonstrate that, unlike conventional grid-based methods, our approach achieves broader spatial alignment and richer object matching. The results show that our method can serve as an effective mapping framework for shared environments requiring semantic continuity and structural coherence across diverse real-world spaces.