Research On Variational Tetrahedral Mesh Generation From Volume Images

With the popular of various medical scan instruments like CT and MRI,it gets more and more easy to collect the attribute information of a given 3D objects.The scanned data not only contain the surface information of the object but also the information within the object,and the output format is always a volume image.However,the volume image representation is independent of the object content as volume image is a regular sampling of the 3D space.A more concise and compact representation is to use non-regular mesh structure to represent the whole 3D object according to its content.It is usually tetrahedral mesh.Moreover,many advanced medical applications prefer the tetrahedral mesh representation rather than the volume image,and the tetrahedral mesh is widely used in numerical simulations across a wide range physical phenomena.In this paper,we propose a method to convert volume image to tetrahedral mesh,which represents the original object well and could be processed by many medical applications.In order to convert volume image to tetrahedral mesh,existing methods always first restore the input raw scanned image,then segment the image and finally construct a tetrahedral mesh.Unfortunately this type of multi-stage methods have some limitations that errors continue to be accumulate.Due to the drawbacks of the multi-stage methods,a more effective and straight-forward way is to construct the tetrahedral mesh directly from the volume image.In this paper,a variational model is proposed for tetrahedral mesh generation.In partic-ular,a total variation term is introduced to regularize the tetrahedral intensity values.As a result,our method adopts augmented Lagrangian method and alternating direction method of multipliers(ADMM)to solve optimization problem and can deal with noisy volumetric data well.