Neural Phase Correlation

• URL: http://arxiv.org/abs/2606.18496v1
• Date: Tue, 16 Jun 2026 21:08:36 GMT
• Title: Neural Phase Correlation
• Abstract summary: Correspondence seeks the unknown transformation between two observations of a common scene, not the content of either.<n>We introduce a learned generalization of phase correlation that lifts this restriction by learning the basis on which the transformation decomposes.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Correspondence is fundamentally relational: it seeks the unknown transformation between two observations of a common scene, not the content of either. Yet the dominant learning-based methods do not represent the transformation as a first-class object in the architecture. They encode each image independently and let a learned similarity function or a deep decoder discover the mapping implicitly. Phase correlation is the canonical exception, measuring the inter-image relationship directly in the Fourier domain, but the rigidity of its fixed basis confines it to global translation. We introduce a learned generalization of phase correlation that lifts this restriction by learning the basis on which the transformation decomposes. The same algebraic primitive extends to dense non-rigid deformations and to unitary dynamics. On the ACDC cardiac-MRI benchmark the framework matches or exceeds prior published baselines on both registration directions. On CAMUS echocardiography it matches state-of-the-art without auxiliary scoring or adaptive-smoothness mechanisms. Applied to time-evolved wavefunction pairs of the 1-D quantum harmonic oscillator, the same framework recovers the Hermite-function eigenstates and the quantized energy levels of the unknown Hamiltonian from observation pairs alone.

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