High-quality topological structure extraction of volumetric data on ^C2-continuous framework

The existing approaches for topological structure analysis of volumetric data are mainly based on discrete methods, and the results usually need to be simplified and smoothened for further use. In this paper we propose a novel framework to extract the topology of volumetric data distinguished from the commonly-used piecewise linear framework. The data is reconstructed into a ^C2-continuous quasi-interpolated space first by 7-directional box spline, where the value evaluation and differential calculations are both direct and accurate. Then Newton-Armijo method and homotopy continuation method are combined to solve critical points, and topological structures are extracted by connecting saddle-extremum arcs generated by a kind of numerical integral method. The parallel architecture of GPU is also applied to ensure the efficiency of our algorithms. A number of examples illustrate that our framework provides much smoother and clearer results compared with the piecewise linear framework.