Properties of Gauss Digitized Shapes and Digital Surface Integration

摘要: This paper presents new topological and geometric properties of Gauss digitizations Euclidean shapes, most them holding in arbitrary dimension d. We focus on r-regular shapes sampled by digitization at gridstep h. The digitized boundary is shown to be close the Hausdorff sense, minimum distance $$\frac{\sqrt{d}}{2}h$$d2h being achieved projection map $$\xi $$? induced distance. Although it known that boundaries may not manifold when $$d \ge 3$$d?3, we show non-manifoldness only occur places where normal vector almost aligned with some axis, limit angle decreases then have a closer look onto continuous $$?. size its non-injective part tends zero leads us study classical digital surface integration scheme, which allocates measure each element proportional cosine between an estimated trivial vector. convergent whenever estimator multigrid convergent, explicit convergence speed. Since estimators are now available literature, provides for objects.