Data-driven And Sketch-based Approaches For Realistic Modeling Of Tree Ramifications

Tree modeling play a essential role in Virtual Reality,Landscape design and applications in agriculture and forest.However,modeling tree with realistic ramifications is still a challenging issue for their structural complexity.For easy tree modeling,sketch-based methods are proposed but they need to face the ambiguity problem when converting 2D sketch of trees to 3D ones,which is still an open problem.Data-driven method provide a possibility to solve the ambiguity problem of sketchbased methods by replacing prior models with data mining to approximate the truth,which is worth to be attempted.On the other hand,most of the methods focus on global impression of trees such as topological structure of branches and arrangement of leaves,because generalized cylinder can represent branches effectively,without taking continuity of branch ramifications into consideration.For continous ramifications,some studies have tried to use implict surface,which is difficult to control interactively.To solve the two problems above,this paper presents a new approach based on both data-driven and sketch to convert user-defined sketch into 3D skeletons of tree from a given tree model as an exemplar.After the 3D skeletons similar to the exemplar's are generated,a global optimization method to calculate a suitable control mesh for Catmull-Clark subdivision are proposed.to get a complete tree model with continous ramification structure.The main contributions in this paper are as follows:(1)A solution of the ambiguity when converting 2D sketch of one tree to 3D model is proposed,combining data-driven method with sketch-based one.A Fator Graphic of MRF(Markov Random Filed)was built from an examplar tree by feature analysis.Then,BP-NN(BP Neural Network)is adopted to estimate parameters of MRF for the depth information prediction from a user-defined tree sketch.The 3D skeletons generated by a recursive algorithms contains the features of the tree exemplar.(2)An optimization approach to genarate trees with continuous ramifications surface which can be controled intuitively.As a tree skeleton with thickness has been obtained above,a tree with continuous ramifications is built as following steps.we firstly build a local coordinate system for each joint node,and orient each node properly on the basis of the angle between parent branch and its child branch.Then,we create the corresponding basic ramifications units with cuboid-like quadrilateral mesh,which is mapped back to the world coordinate.To obtain a suitable manifold initial control mesh,the ramifications are classified into main ramifications and additional ramifications,and a bottom-up optimization approach is presented to adjust the positions of the main ramification units for connections.Next,the first round Catmull-Clark subdivision is applied to the main ramifications,and the additional ramifications,which are picked up for visual distortion alleviation,are added back to the main mesh by a cut-paste operation.Finally,the second round Catmull-Clark subdivision is utilized to generate the final quad-mesh of the entire tree.The results showed that our BP-NN for MRF performs high generalization capability and the output tree skeletons is similar to the input examplar tree with a low mean squared error of prediction in test data.In this experiment,the mean squared error of an apple tree,a cherry tree and a maple tree are all acceptable and reasonable.The global optimization method for subdivision surface can generate realistic tree quad-mesh effectively from tree skeletons of different types such as apple,cherry and maple.Comparing with the trees generated by generalized cylinder,our results represent a similar global impression to the generalized cylinder's but own continuous ramificaitons.The same sketch with different examplar can obtain a new tree model similar to the corresponding examplar tree.According to our user study,users can draw a user-defined sketch of a tree by our tree modeling system and a compelete tree mesh are generated with continuous ramifications similar to a given examplar tree in 3 to 6 minutes.