Research On The Properties Of The Skeleton Used In Surface Quadrangulation

A skeleton is an important tool describing 3D model structure information, and widely used in computational geometry and image processing and so on. The surface of three-dimensional model is represented by triangular mesh surface and popular used in graphics images, which is easy to be generated and rendered, and more flexible to deal with. However, in many applications, it is needed to convert the triangular surface mesh into quadrilateral mesh. Firstly, separate the triangular mesh into a number of quadrilateral regions. For this, it is an effective method under study which uses the skeleton information to optimize the generated mesh's topological and geometric properties. Many skeleton algorithms existing, with different conceptions and conclusions, lack of the depth analysis of the skeleton topology and geometric properties, are a stumbling block on the use of the skeleton. Regard of these problems, the paper focus on the improved skeleton based on the thinning algorithm, discusses the properties of the skeleton, and confirms some several relative conceptions and relations. These conclusions are significant for the skeleton in the s quadrilateral segmentation of the discrete surface.Part One, of the paper, summarizes the development status of skeletons, which introduces several skeletons and has a discussion with them. Part Two is a discussion about thinning algorithms of skeleton extraction and some related concepts. And Part Three introduces parallel thinning algorithm, mainly several sub-iteration thinning algorithm. Lastly, it provides conclusions on some properties of the skeleton by thinning algorithm.