Direct Jacobian Control for Geometric Video Compression via Prescribed-Density Diffeomorphic Synthesis

This work introduces a geometric framework for video compression based on deterministic control of spatial transformations. The approach reformulates compression as a forward problem, where a target spatial density is prescribed and a corresponding transformation is constructed under strict mathematical constraints. The method leverages principles from differential geometry and partial differential equations to ensure stability, invertibility, and consistency of the spatial mapping. A constructive pipeline is defined to generate valid transformations that align spatial structure with compression objectives, enabling controlled redistribution of information prior to encoding. The proposed formulation addresses limitations of indirect estimation approaches by providing a structured mechanism for enforcing transformation properties. The framework is compatible with existing video coding pipelines and is designed to operate within practical computational constraints. Experimental validation demonstrates consistency between the prescribed transformation properties and the resulting behavior of the system, supporting the feasibility of the approach.