دانلود رایگان مقاله استخراج ساختار توپولوژیکی داده حجمی در چارچوب C2 - پیوسته

Abstract

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.

6. Conclusion and future work

We presented a novel and practical framework that allows us to apply numerical methods for topological analysis on discrete volumetric data. Compared with the discrete methods, our approach can extract accurate critical points and generate smooth integral lines between critical points. The extracted skeleton is clear for visualization and can be simplified by traditional methods for further analysis. The framework is parallelism-friendly and has good performance. However, for scanned data with large scale, high frequency noise makes the data bumpy in a local region. This phenomenon leads to the increasing number of critical points, which slows down the extraction and makes the skeleton complicated. Though we can apply simplification to the complex skeleton iteratively as the discrete approach does to remove the noise, solving critical points takes too much time. We are exploring new methods in the preprocessing step to remove high frequency noise, so that the number of candidate tetrahedra and the number of polynomial system to be solved are reduced to an acceptable level.