Multiscale Registration

In the seminal paper E. Tadmor, S. Nezzar and L. Vese, A multiscale image representation using hierarchical \((BV, L^2)\) decompositions, Multiscale Model. Simul., 2(4), 554–579, (2004), authors introduce a decomposition model providing of given into sum scale-varying components. line with this framework, we extend approach to case registration, task which consists mapping salient features an onto corresponding ones in another, underlying goal being obtain such kind deformation relating two considered images (—from coarser one that encodes main structural/geometrical deformation, more refined one—). To achieve goal, functional minimisation problem hyperelasticity setting by viewing shapes be matched as Ogden materials. This is complemented hard constraints on \(L^{\infty }\)-norm both Jacobian its inverse, ensuring bi-Lipschitz homeomorphism. Theoretical results emphasising mathematical soundness are provided, among existence minimisers, \(\varGamma \)-convergence result analysis suitable numerical algorithm, along simulations demonstrating ability produce accurate representations deformations.