Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Diffeomorphic registration using optimal control on the diffeomorphism group and on shape spaces has become widely used since the development of the large deformation diffeomorphic metric mapping (LDDMM) algorithm. More recently, a series of algorithms involving sub-Riemannian constraints have been introduced in which the velocity fields that control the shapes in the LDDMM framework are constrained in accordance with a specific deformation model. Here,  extend this setting by considering, for the first time, inequality constraints in order to estimate surface deformations that only allow for atrophy, introducing for this purpose an algorithm that uses the augmented Lagrangian method.  prove the existence of solutions of the associated optimal control problem and the consistency of our approximation scheme. These developments are illustrated by numerical experiments on simulated and real data.
['Sylvain Arguillère', 'Michael I. Miller', 'Laurent Younes']
I am writing a research paper on a idea Diffeomorphic Surface Registration with Atrophy Constraints
[{"from": "human", "value": "I am writing a research paper on a idea Diffeomorphic Surface Registration with Atrophy Constraints"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Diffeomorphic registration using optimal control on the diffeomorphism group and on shape spaces has become widely used since the development of the large deformation diffeomorphic metric mapping (LDDMM) algorithm. More recently, a series of algorithms involving sub-Riemannian constraints have been introduced in which the velocity fields that control the shapes in the LDDMM framework are constrained in accordance with a specific deformation model. Here,  extend this setting by considering, for the first time, inequality constraints in order to estimate surface deformations that only allow for atrophy, introducing for this purpose an algorithm that uses the augmented Lagrangian method.  prove the existence of solutions of the associated optimal control problem and the consistency of our approximation scheme. These developments are illustrated by numerical experiments on simulated and real data."}]