Non-rigid motion estimation for CGH using the chirped cross-ambiguity function

We present a direct motion estimation method for digital holographic video that operates on interference patterns without intermediate wavefield reconstruction. Extending the chirped cross-ambiguity function (CCAF) from radar signal processing to the holographic domain, our method jointly estimates five rigid motion parameters — lateral translation (t_x, t_y), depth displacement t_z, and rotation angles (θ_x, θ_y) — from two hologram frames. To handle scenes containing multiple independently moving objects, we embed the CCAF within a 2D short-time Fourier transform (STFT) framework. Each space-frequency crop isolates the contribution of a single object, and evaluating the CCAF independently per crop yields a dense motion field without modifying the underlying estimator. We validate the method on a synthetic two-frame sequence of two overlapping coin point clouds with known independent transformations, generated as computer-generated holograms under the Fresnel diffraction approximation. The estimated motion fields for all five parameters show spatially consistent estimates within each object region, demonstrating correct separation of independently moving objects directly in the hologram domain.