ОЦІНЮВАННЯ ПАРАМЕТРА ЗСУВУ ДЛЯ НЕЯВНИХ НЕЙРОННИХ РЕПРЕЗЕНТАЦІЙ ЗОБРАЖЕНЬ

Анотація

Implicit neural representations model images as continuous coordinate-based functions, which enables signal processing without discretization. At the same time, verifying whether two images differ only by a translation is usually performed by methods that require a discrete representation or global aggregations, which complicates their direct application to implicit models and contradicts their continuous nature. To propose and substantiate an algorithm that determines whether two implicit neural representations of an image are related by a parallel translation using only derivative values up to the second order, and to provide an estimate of the translation parameter. The proposed approach is based on a local linearization of the translation operator and on the use of analytically available derivatives obtained via automatic differentiation within the implicit model. The consistency criterion is constructed by verifying the stability of the estimated translation over a set of points in the domain. To improve robustness, local estimates are aggregated using robust procedures together with consistency checks that reduce the influence of inhomogeneous regions of the signal. A criterion for detecting translation equivalence of two implicit representations and a procedure for estimating the translation parameter have been developed. It is shown that the criterion is consistent with the continuous nature of implicit models, does not require decoding into a pixel grid, and is applicable to models in which derivatives are analytically available. The proposed approach provides novelty in the form of a test for translation equivalence of implicit neural representations and has practical significance as a tool for fast consistency verification, validation, and preliminary normalization of data in computer vision tasks.

The obtained results are applicable in scenarios where images or fields are already represented as implicit neural representations, also known as neural fields. This includes automated consistency checking of reconstructions, preliminary alignment or normalization prior to further processing, correctness control in field fusion, and data preparation in computer vision tasks. It is recommended to use the first-order method as a fast initialization and the second-order method as a refinement for larger translations or textured regions. For stable use of the second-order method, smooth INR architectures should be selected and the approximation quality of INR should be sufficiently high, as confirmed by MSE and PSNR metrics.