Image Recognition via Vaisman--Neifeld's Geometry

Abstract

We introduce a new approach to the reconstruction of hidden structures from incomplete data, unifying techniques from geometric integration and topological analysis within the frameworks of Vaisman and Neifeld. Our method employs a refined geometric decomposition of configuration spaces into invariant foliations and moment maps, thereby addressing the intrinsic ambiguities of underdetermined inverse problems. By combining Vaisman's insights into symmetry with Neifeld's analytical methodologies, we establish a robust, noise-resistant framework that ensures computational tractability while providing a unified perspective on reconstruction in imaging and structural analysis. This approach enables applications across diverse scientific domains and highlights the interplay between geometry and topology in the solution of inverse problems.