Robust principal curvatures using feature adapted integral invariants

Principal curvatures and principal directions are fundamental local geometric properties. They are well defined on smooth surfaces. However, due to the nature as higher order differential quantities, they are known to be sensitive to noise. A recent work by Yang et al. combines principal component analysis with integral invariants and computes robust principal curvatures on multiple scales. Although the freedom of choosing the radius r gives results on different scales, in practice it is not an easy task to choose the most appropriate r for an arbitrary given model. Worse still, if the model contains features of different scales, a single r does not work well at all. In this work, we propose a scheme to automatically assign appropriate radii across the surface based on local surface characteristics. The radius r is not constant and adapts to the scale of local features. An efficient, iterative algorithm is used to approach the optimal assignment and the partition of unity is incorporated to smoothly combine the results with different radii. In this way, we can achieve a better balance between the robustness and the accuracy of feature locations. We demonstrate the effectiveness of our approach with robust principal direction field computation and feature extraction.