AI Summary & Key Takeaways
AI InsightMoreover, this method can be used with point sets that do not have a regression axis.
📌 3 Key Takeaways
Abstract
In this paper, we propose a dynamic bandwidth selection method for thinning noisy point clouds into curves. Due to the nonhomogeneous distribution of noise or varying curvature of the data, the thinning procedure requires a dynamically adjusted bandwidth along the curve. On the other hand, the selected local region must be sorted along a suitable direction vector for local curve fitting purposes. The contribution of this paper to the field is 2-folded: first, a normalized eigenvalue analysis-based method is used to determine the best local bandwidth. The second task is getting a good regression line of the local region for ordering the data. In this step, a feature that is based on the Euclidean distances between points is used to determine the best regression line in the search space. Finally, a third-order parametric polynomial is fitted to the local data using the least squares method. We adapt and test our algorithm on the widely used k-nearest neighbor and constant radius methods. Our experiments show that the proposed methods automatically produce comparable results with these methods at their best parameter, which is empirically determined. Our methods also do not require any empirically determined parameter to adjust the best bandwidth or to select a good regression axis. Moreover, this method can be used with point sets that do not have a regression axis.
Özet
In this paper, we propose a dynamic bandwidth selection method for thinning noisy point clouds into curves. Due to the nonhomogeneous distribution of noise or varying curvature of the data, the thinning procedure requires a dynamically adjusted bandwidth along the curve. On the other hand, the selected local region must be sorted along a suitable direction vector for local curve fitting purposes. The contribution of this paper to the field is 2-folded: first, a normalized eigenvalue analysis-based method is used to determine the best local bandwidth. The second task is getting a good regression line of the local region for ordering the data. In this step, a feature that is based on the Euclidean distances between points is used to determine the best regression line in the search space. Finally, a third-order parametric polynomial is fitted to the local data using the least squares method. We adapt and test our algorithm on the widely used k-nearest neighbor and constant radius methods. Our experiments show that the proposed methods automatically produce comparable results with these methods at their best parameter, which is empirically determined. Our methods also do not require any empirically determined parameter to adjust the best bandwidth or to select a good regression axis. Moreover, this method can be used with point sets that do not have a regression axis.