Fuzzy Methods in Nonlinear Signal Processing: Part II—Applications - Nonlinear Signal and Image Processing: Theory, Methods and Applications - page 102

(a) (b) (c) (d)

(e) (f) (g) (h)

FIGURE 3.24
Surface smoothing of cylinder ( V 484): (a) and (e)

original objects; (b) and (f) noise-corrupted objects; (c) and (g) following FMED v

= 365, F = 726) and cube ( V = 244, F =

face normal

smoothing; (f) and (h) following vertex position update.

(a) (b) (c) (d)

(e) (f) (g) (h)

FIGURE 3.25
Smoothing of cube: (a) Taubin's normal smoothing; (b) vertex update operating on Taubin's result;
(c) FMED normal smoothing; (d) vertex update operating on FMED result. The triangular

v v

meshes for a to d are shown in e to h.

To illustrate the surface normal smoothing process, Figure 3.24 shows ex-
periments on two synthetic objects: a cylinder and a cube. Figure 3.24a and
e show the original objects, whose vertex positions are then corrupted by
additive Gaussian noise, Figure 3.24b and f. Note that both the vertex posi-
tions and face normals (represented by stubs on the surface) contain noise.
The noisy face normals are smoothed by 50 iterations of fuzzy vector median