Unified Geometric-Spectral Framework for Foveated Immersive Video Compression via Constrained Diffeomorphic Fields

This work introduces a unified theoretical framework for foveated immersive video compression based on constrained geometric transformations. We establish a formal relationship between spatial transformations and entropy variation, showing that geometric operators can act as control mechanisms for bitrate allocation. The framework unifies prior geometric allocation strategies with adaptive learned approaches under a common set of constraints that ensure stability, invertibility, and perceptual consistency. These constraints define the admissible space of transformations for efficient compression under perceptual and physical limits. We propose a hybrid architecture that combines a deterministic geometric prior with an adaptive residual component, enabling content-aware spatial restructuring prior to encoding. This approach operates as a signal-geometry layer, decoupled from specific codecs, and compatible with standard compression pipelines. Experimental results demonstrate substantial bitrate reductions at equivalent perceptual quality in both synthetic and real-world scenarios. Additionally, we identify critical stability boundaries and failure modes that constrain practical deployment in high-latency environments. A reproducibility protocol and evaluation methodology are outlined to enable independent validation, while key implementation details are intentionally abstracted to preserve system-level integrity and deployment constraints. This work suggests a paradigm shift in compression design: from optimizing encoding of a fixed signal to restructuring the signal itself under principled geometric constraints.