Research On Computing Medial Axis Transform From Animated Meshes And Sparse Point Clouds

As an effective method of regional expression in geometry,medial axis transform(MAT)has been widely used to solve problems in the fields of geometric modeling,shape recognition,robot path planning,and surface reconstruction.As a precisely defined skeleton,medial axis of 3D shape not only provides the topological features of the 3D object,but also contains the description of the surface and volume in its structure.With the unique structure and the characteristic of compactness and symmetry,MAT can be used to represent arbitrary shapes,as well as motion and collision of shapes.However,in the current research on the calculation of MAT,almost all of them focus on the calculation of the static shape,and have not applied medial axis to the expression of the dynamic shape to solve the problem such as reconstruction of dynamic shape.In addition,there are mainly two category of static shape expressions currently used to calculate the medial axis.One category takes densely sampled point clouds as input,and the other takes densely sampled closed manifold mesh models as input.This strict requirement for input greatly limits the application of MAT in practical problems.According to the above research background,this paper starts from fitting of different expressions of shapes,and focus on those two objects:the animated surface mesh and sparse point cloud,trying to study on the following two problems:(1)how to approximate the animated surface mesh with medial axis,(2)how to compute medial axis from sparse point cloud,and approximate the shape represented with the point cloud.The main research contents include:(1)An approach for approximating animated surfaces with medial axis,namely Deformable Medial Axis Transform(DMAT)is proposed,which uses a deformable medial axis with constant connectivity and composed of a set of animated spheres.Starting from extracting an accurate and compact representation of a static MAT as the template and partitioning the vertices on the input surface as the correspondences for each primitive,it can obtain the deformed MAT by solving an As-Rigid-As-Possible(ARAP)deformation energy to approximate the animation sequence.(2)A point-to-MAT network is proposed,namely P2MAT-NET.The network converts the input sparse point cloud into spheres with the same number by learning the point-wise displacement vectors of the point cloud to approximate the medial spheres of the same shape.Then it proposes the sphere-bounding strategy and the normalrefinement strategy to optimize the predicted spheres.The experiments shows that P2MAT-NET can not only predict the medial spheres from sparse point clouds in different resolutions sampled on the mesh model,but also could generate the medial spheres from the incomplete noise point cloud.(3)A method for constructing the connectivity of MAT from medial spheres is proposed.After the MAT of the same shape represented by the point cloud is computed from the refined predicted spheres of P2MAT-NET,the constructed MATs could be directly used in the shape classification task,achieving higher classification accuracy than the-state-of-the-art methods.Furthermore,the computed MATs of the sparse point cloud are directly used in the task of shape classification,and the classification accuracy is higher than the existing methods.The main contributions include:(1)It proposes a method for extracting deformable medial axis from mesh sequences with an as-rigid-as-possible deformation field for approximating the mesh sequences,which can improve the approximation accuracy while maintaining the simplicity of medial axis.(2)For the problem of computing medial axis from sparse point cloud,a point-toMAT network P2MAT-NET is proposed,which computes medial spheres from sparse point cloud as well as incomplete noisy point cloud,then a solution for constructing the connectivity of medial spheres computed from sparse point cloud is proposed to construct medial meshes for on-going applications.