Principal curvatures from the integral invariant viewpoint

Principal curvatures from the integral invariant viewpoint

The extraction of curvature information for surfaces is a basic problem of Geometry Processing. Recently an integral invariant solution of this problem was presented, which is based on principal component analysis of local neighbourhoods defined by kernel balls of various sizes. It is not only robust to noise, but also adjusts to the level of detail required. In the present paper we show an asy...

Principal Curvatures of Surfaces

A Fast Method For Computing Principal Curvatures From Range Images

Estimation of surface curvature from range data is important for a range of tasks in computer vision and robotics, object segmentation, object recognition and robotic grasping estimation. This work presents a fast method of robustly computing accurate metric principal curvature values from noisy point clouds which was implemented on GPU. In contrast to existing readily available solutions which...

Affine Integral Geometry from a Differentiable Viewpoint

The notion of a homogeneous contour integral is introduced and used to construct affine integral invariants of convex bodies. Earlier descriptions of this construction rely on a Euclidean structure on the ambient vector space, so the behavior under linear transformations is established after the fact. The description presented here relies only on the linear structure and a Lebesgue measure on t...

Principal Curvatures of Fibers and Heegaard Surfaces

We study principal curvatures of fibers and Heeagaard surfaces smoothly embedded in hyperbolic 3-manifolds. It is well known that a fiber or a Heegaard surface in a hyperbolic 3-manifold cannot have principal curvatures everywhere less than one in absolute value. We show that given an upper bound on the genus of a minimally embedded fiber or Heegaard surface and a lower bound on the injectivity...