FlexiCoord: Flexible Spatial Representations via Function Reparameterization

Spatial Representations form the foundation of various modern Machine Learning systems in Computer Vision and Graphics, such as image encoding, data compression, and 3D reconstruction. Despite their differences, these methods share a common assumption: spatial functions are evaluated in a fixed coordinate system. We argue that this assumption fundamentally limits representation efficiency, as complex geometric structures must be encoded by increasingly expressive basis functions, which can introduce large memory overhead but marginal performance gain. We introduce FlexiCoord, a general framework that augments a spatial representation via learned function reparameterization, transforming fixed basis functions into adaptive spatial primitives that model complex geometric structures via local coordinate deformation. Unlike architecture-specific improvements, FlexiCoord operates as a universal enhancement that can be attached to arbitrary spatial functions. We validate this hypothesis on three fundamentally different representations: Gaussian kernels for splatting-based novel-view synthesis, multi-resolution hash grids for image encoding, and vector-matrix tensor decompositions for volumetric medical data compression. Across all settings, FlexiCoord yields more efficient representations to capture sharp features with complex geometry. These findings highlight function reparameterization as a broadly applicable mechanism for increasing representational power and suggest a new direction for the design of spatial representations.