دانلود رایگان مقاله بخش بندی محدب پلی هدرا از طریق تفکیک برآمدگی محدب

Abstract

Decomposing a 3D model into approximately convex components has gained more attention recently due to its ability to efficiently generate small decompositions with controllable concavity bounds. However, current methods are computationally expensive and require many user parameters. These parameters are usually unintuitive thus adding unnecessary obstacles in processing a large number of meshes with various types and shapes or meshes that are generated online within applications such as video games. In this paper, we investigate an approach that decomposes a mesh P based on the identification of convex ridges . Intuitively, convex ridges are the protruding parts of the mesh P. Our method, called CoRiSe, extracts nearly convex components of P by separating each convex ridge from all the other convex ridges through the new concept of residual concavity. CoRiSe takes a single user parameter: concavity tolerance which controls the maximum concavity of the final components, as input, along with other two fixed parameters for encoding the smoothness term of graph cut. We show that our method can generate comparable (sometimes noticeably better) segmentations in significant shorter time than the current state-of-art methods. Finally, we demonstrate applications of CoRiSe, including physically-based simulation, cage generation, model repair and mesh unfolding.

8. Conclusion, limitations and future work

In summary, in this paper we proposed a 3D decomposition method that produces components with bounded concavity. Our method called CoRiSe meets the needs of real-time simulations and computer games better than the existing methods. We also showed that the decomposition results can produce semantically meaningful decomposition with low computation cost when proper concavity tolerances are given. The decomposition is achieved by identifying convex ridges and then solving a graph cut optimization problem formulated with valley separators and must-link regions. Comparing CoRiSe with other methods on the public benchmark dataset, we show that CoRiSe can generate results close to manual decomposition. Comparing CoRiSe with other approximate convex decomposition methods, we show that CoRiSe is significantly more efficient. Known limitations. Each of the major step of CoRiSe is quite robust. For example, the convex ridges are always identified at expected locations for all the models that we tested (see the supplementary material, Appendix A for more examples). A main limitation of CoRiSe is that its semantic meaning of CoRiSe components is significantly influenced by the concavity tolerance τ . When τ is too small, small components are produced and the semantic meaning of these components diminishes. For example in Fig. 17(b) and (c), even though CoRiSe still provides a tight approximation of the initial model using a relatively small concavity tolerance (0.05), many small components do not have significant meanings. Another limitation of CoRiSe is that CoRiSe may not decompose a cup-like shape if none of the valleys reach the bottom of the cup’s concavity (see Fig. 17(d)). This is caused by the fact that a valley is the (approximated) shortest geodesic path. We believe that this can be addressed by ensuring that the vertex p with largest concavity of a valley has the local maximum concavity. If this is not the case, then we iteratively descend p until a point p ′ with local maximum concavity is reached. A new valley is then computed by enforcing it to pass through p ′ .