Topological Analysis And Visualization For Volumetric Data Under Continuous Framework

The topology analysis and visualization are two main research fields for volumetric data. In recent years, topological information of volumetric data is often used to enhance volume rendering results. While the existing approaches to extract topological features are based on discrete framework, which has some drawbacks like low accuracy, non-smoothness and difficult to implement. In this paper, a novel continuous framework is proposed according to the classic Morse theory, and methods for topological analysis and visualization under continuous framework are discussed. The proposed method applies 7-directional box spline to reconstruct the discrete model to a 2-continuous data field, and topological features as critical points and integral lines are computed via numerical method in this data field. The combination of these features results in the topological skeleton of volumetric data. The experiment results show that the skeletons extracted by our method are more smooth and clear compared with discrete method. We also explore the parallelism of critical point extraction, and the performance is acceptable with GPU acceleration.The second half of this paper presents a new volume rendering algorithm with topology enhanced under the continuous framework. Critical points and saddle-extrema arcs are used to build a weighted critical points histogram. And our method adjust the transfer function via enhancing the opacity of points with value near to some critical isovalues in the histogram, so that the interior structures of volumetric data are enhanced in the rendering results. Compared with methods based on discrete framework, our results have better smoothness and the interior structures are clearer.