Lattice Points in Three-Dimensional Convex Bodies

Integral Based Curvature Estimators in Digital Geometry

“…Similar results hold in 3D, γ = 1 is the general case (e.g. see [11]) while γ = 243 158 for smoother boundary [7]. In fact, preceding equations hold whenever the shape boundary can be decomposed in a finite number of convex pieces [9].…”

On the distribution of squares of integral Cayley numbers

“…where Re(a) = a 0 is the real part and Im(a) := (a 1 , a 2 , a 3 , a 4 , a 5 , a 6 , a 7 ) is the imaginary part of the octave a = (a 0 , a 1 , a 2 , a 3 , a 4 , a 5 , a 6 , a 7 ), and | · | is the Euclidean norm.…”

“…It is plain that 4 √ X and |v| ≤ η(X; |u|), and that E 6 (X; u, v) = ∅ otherwise. By applying (3.3) and (3.6) for n = 6, and (2.1) we derive…”

Multigrid convergent principal curvature estimators in digital geometry

“…see [38] where µ 0 = 38 25 − , or [39], Theorem 1, where µ 0 = 66 43 − ). We wish to apply this formula to the set A = B R (x) ∩ X, whose size decreases with h. Big "O" notation in Eq.…”