Medial Axis Transform Representation And Applications Of 3D Deformable Objects

Researching on 3D deformable objects representation is always a hot topic of computer graphics.With the development of relevant hardware equipment,3D objects can be easily captured.3D deformation representation has plenty of applications,such as shape recognition,motion planning and gesture recognition,etc.However,it is inconvenient to process these data because 3D objects contain rich information.Therefore a concise step shall be implemented as 3D object transformation.After that we can get the compact representation.Medial axis transformation performs well on it.Medial axis transform is a classic concept of computational geometry.It is an efficient tool for shape representation.Its result is a set of center points and radius of spheres.Those spheres are maximal inside object boundaries and have at least two tangent points with boundaries.Medial axis is an alternative form of original object.We can resolve original model from the form of medial axis.However,there are two negative factors for medial axis.First of all,computation of medial axis is a complicated task and time consuming.The other issue is its sensitivity.Small perturbation of boundary may cause dramatic changes.To solve problems mentioned above,we need to complete following tasks.(1)We use medial axis to represent 3D deformable objects,compute the approximate medial axis to solve the inefficient problem.Results will be organized as medial mesh.(2)Voronoi-Diagram-based method is implemented to compute the approximate medial axis.We apply a quantitative analysis on the stability of medial branches.Improved quadric error metric has been adopted to simplify the medial axis.At last concise medial axis can be extracted.(3)We take the improved quadric error metric to simplify medial axis and design experiments based on both 2D and 3D objects respectively.In 2D situation,we propose a novel method to extract skeleton of objects.And experiments based on three benchmarks are designed to prove our algorithm is efficient.We use the algorithm to detect the sharp point of hand images.Then a novel representation method is adopted to describe the image.Our method performs well through our experiment.We can get concise medial axis through our method and can maintain the topology of the shape.In 3D situation,improved quadric error metric is applied for pruning noise branches to prune noise branches and obtain concise medial axis.The experiment shows that our algorithm is efficient in extracting medial axis and is robust for boundary perturbation.In addition,at the extreme level of simplifying,we can still obtain precise result.