Research On 3D Model Deformation And Registration Algorithms Based On Conformal Mapping

With the development of three-dimensional scanning technology,three-dimensional models are widely used in the fields of film and television,animation,medicine,etc.Because manually drawing three-dimensional model is time-consuming and laborious,and the deformation of three-dimensional model can be quickly achieved by reusing an existing model to create approximate model.Model reuse is a hot research topic for 3D model editing.In addition,whether one-to-one mapping relationship can be found between surfaces(3D model registration)is also a hotspot of 3D model research.In this paper,the problem that it is difficult to deform directly between three-dimensional surfaces,and the local area distortion is large,and the method of conformal mapping is used to study the deformation and registration of three-dimensional models.The main work is:(1)The related theory of conformal mapping and extended quasi-conformal mapping and harmonic mapping are studied.Using the feature of local preserves angles of conformal mapping,the method of conformal mapping is used to parameterize the model,and the dimensionality reduction of the three-dimensional model is paved for the next deformation and registration.(2)This paper proposes a three-dimensional model deformation algorithm based on quasi-conformal mapping.Firstly,the 3D model is parameterized to a 2D plane disk using quasi-conformal mapping.Secondly,the quasi-common iterative algorithm is used to calculate the mapping between two 2D plane disks to construct the deformed 2D model.Finally,the model restoration algorithm is proposed to restore the 3D model from the deformed 2D model,thereby obtaining the 3D model with different appearances.In the experiment,some 3D models from two public datasets are selected for deformation operation,and the proposed method was compared with Laplace based differential coordinate deformation algorithm.The results show that our proposed method can perform a series of operations such as translation,rotation and stretching.The local features of the model are well maintained,the running time is short,the deformation effect is good,and the robustness is strong.(3)This paper proposes a registration algorithm for three-dimensional surfaces based on conformal mapping.Firstly,the genus number and boundary number of the three-dimensional model were calculated,and the three-dimensional model was parameterized to the topological disk or sphere by conformal mapping method.Secondly,the mapping relationship between the parameterized planes was obtained by the quasi-conformal iterative algorithm.Finally,the model restoration algorithm is proposed to restore the 3D model from the deformed 2D model,thereby obtaining the 3D model of registration.In this experiment,face models and brain models are selected for registration experiments and the proposed method was compared with Iterative Closest Point(ICP)registration algorithm.The result show that the proposed method is an effective non-overlapping matching registration algorithm with small conformal distortion and low requirements for the model.It is suitable for models with arbitrary boundaries and closed surfaces with genus of 0 or 1.