Spatial Structure Beyond the Power Spectrum: Amplitude-Adjusted Surrogate Testing in Natural and Synthetic Images

The Fourier power spectrum captures only second-order statistics of an image, leaving most spatial structure encoded in the phase.

Standard phase-randomisation surrogates confound tests of phase-dependent structure because they also Gaussianize the amplitude distribution, producing an ambiguity: separation from surrogates could reflect spatial geometry or could reflect the shift from non-Gaussian to Gaussian, and the surrogate method itself cannot distinguish the two. This study applies iterative amplitude-adjusted Fourier transform (IAAFT) surrogates, which preserve both the power spectrum and the amplitude distribution, to a multi-metric image analysis pipeline spanning fractal, geometric, and topological measures.

The method is validated against a non-Gaussian unstructured control image, with seventeen of eighteen metrics correctly registering no separation. Across six image categories drawn from three domains, human portraits photographic and AI-generated, coral reef tissue, and quasicrystalline materials, the results separate into two distinct layers. Fractal dimension, lacunarity, and junctions detect spatial structure near universally, with large effect sizes regardless of image domain. Persistence homol
ogy metrics computed on edge-extracted point clouds detect a second, more specific layer, the closed-contour edge topology of biological and face images, present
in faces of both photographic and synthetic origin, present in healthy coral, and largely absent in quasicrystal. Bilateral symmetry is shown to be substantially a
frequency-domain property and does not separate under IAAFT.

The two structural layers dissociate across categories, offering a more precise characterisation of spatial structure beyond the power spectrum than any single metric or null model can supply alone