Integral based Curvature Estimators in Digital Geometry

International audienceIn many geometry processing applications, the estimation of differential geometric quantities such as curvature or normal vector field is an essential step. When designing such estimators, we have to pay attention to both its theoretical properties and practical effectiveness. In this paper, we investigate a new class of estimators on digital shape boundaries based on Integral Invariants. More precisely, we provide proofs of multigrid convergence of curvature estimators which are easy to implement on digital data. Furthermore, we discuss about some algorithmic optimisations and detail a complete experimental evaluation

Integral based Curvature Estimators in Digital Geometry

International audienceIn many geometry processing applications, the estimation of differential geometric quantities such as curvature or normal vector field is an essential step. When designing such estimators, we have to pay attention to both its theoretical properties and practical effectiveness. In this paper, we investigate a new class of estimators on digital shape boundaries based on Integral Invariants. More precisely, we provide proofs of multigrid convergence of curvature estimators which are easy to implement on digital data. Furthermore, we discuss about some algorithmic optimisations and detail a complete experimental evaluation

Implementation of Integral based Digital Curvature Estimators in DGtal

In many geometry processing applications, differential geometric quantities estimation such as curvature or normal vector field is an essential step. In [1], we have defined curvature estimators on digital shape boundaries based on Integral Invariants. In this paper, we focus on implementation details of these estimators

Estimation of Minkowski tensors from digital grey-scale images

It has been shown that local algorithms based on grey-scale images sometimes lead to asymptotically unbiased estimators for surface area and integrated mean curvature. This paper extends the results to estimators for Minkowski tensors. In particular, asymptotically unbiased local algorithms for estimation of all volume and surface tensors and certain mean curvature tensors are given. This requires an extension of the known asymptotic formulas to estimators with position dependent weights.Comment: 15 page