Concepto de nutrición

The proposed algorithm uses the best VMC vertices since they are closer to the actual surface than vertices of intersection octants, and the number of vertices are considerably reduced. On the other hand, the octree vertices are used to define a local convexity from MC vertices and their connections. In order to represent an object as a piecewise convex set, the data is sliced along the z axis and the slicing interval is defined by the height of the smallest octant, i.e., w. Even though a MC surface has twice finer resolution, the same slicing level is used to keep the correspondence between an octree and a MC slice. The sliced results are stored as a set of binary images planes called MC slices

Smc _{= {I}mc

0 ,· · · , Iimc}, where i denotes z index. Similarly, the corresponding octree

vertices are also grouped into slices and the results are stored in a set of octree slices, i.e.,

Soc={I0oc,· · · , Iioc}.

Suppose that a functionobj(·) indicates whether a VH contains a 3D pointp!w₌

[x y z 1]T_{, i.e.,} obj(p!w) =        1 if!pw_∈VH 0 otherwise . (6.2)

                 _                    _ Ioc i I ocq i Figure 6.6: (a)Ioc

i where ‘×’ and ‘◦’ respectively represent a vertex of an intersection

octant and internal octant in i-th octree slice. (b)Ioc

i where total number of points are

reduced from 29 to 17. The value ofIoc

0 at point (m, n) is then given by

Iioc(m, n) =obj(x, y, z)δ(x−mt, y−nt, z−it), (6.3)

wherem,n, andi∈Z, andδ(·) is a 3D delta function, which has a samplling interval4_t.

An interesting observation of a sliced octree data is that every four nonzero points, forming the 4-connected neighbours inIoc

i , are from the same octant. To treat these points

equally and reduce the number of processing data,Ioc

i is transformed to a quantised octree

slice, i.e., Iiocq[u, v] = 1 / j,k=0 Iioc(u+j, v+k). (6.4)

An example of an octree slice is illustrated in Figure 6.6(a), where vertices of intersec- tion octants (marked as×) and nine vertices of four internal octants (marked as ◦) are represented by 29 points inIoc

i . Since every four points belong to the identical octant,

a quantised octree sliceI_iocqremoves redundant vertices so that a nonzero point in I_iocq

represents four vertices from the same octant [see Figure 6.6(b)].

On the other hand, to represent MC data by the same slice index even though its sampling period is half oft, a binary image plane S_imcq[u, v] is only set to 1 when a MC vertex is found withinut≤x < (u+ 1)t, vt≤y <(v+ 1)t and it≤z <(i+ 1)t.

4

Thus, the volume of an octant associated with four nonzero points in Iiocq is t3, whilst

the volume of nonzero points at [u, v] in the quantised MC slice is bounded by

T3 8 ≤vol(I mcq i [u, v])≤ 7T3 8 , (6.5)

wherevol(·) is a function which estimates the volume of nonzero points in the quantised MC slice. The actual volume of an objectvobj is smaller than the volume of MC slices,

and which is smaller than the volume of the octree slices, i.e.,

vobj < . i,u,v ? vol(I_imcq[u, v]) +t3(I_iocq[u, v] − I_imcq[u, v]I_iocq[u, v])}<. i,u,v ? I_iocq[u, v]t3@ . (6.6)

In practice, however, the volume of MC slices often violate (6.6) because the erroneous classification of octree vertices fails to correctly locate MC vertices.

Another observation from a sliced octree data is that each quantised octree slice of a non-convex object can have multiple clusters that are linked 8-neighbouring points on the quantised octree slice. These multiple clusters need to be connected to other clusters in adjacent slices to define a local convexity. The clustering in a quantised octree slice is trivial because points belonging to the same cluster are conglomerated in accordance with the presence of internal octants. Thus, identifying a cluster in I_iocq is simply a search for connected nonzero points among eight neighbours. However, clustering inImcq

is not similarly straightforward. A decision on the clustering and connecting of clusters inI_imcq is based on the Bayesian decision making rule [104] and a priori information of the decision is obtained fromIiocq.

Four examples of imperfect silhouettes which are obtained by simple threshold- ing are shown in the second row of Figure 6.7(a) with the corresponding actual images shown in the first row. An octree of a dummy from sixty silhouettes is illustrated in Figure 6.7(b). The octree is obtained from a seven-level of octree construction from a 40[cm]x40[cm]x40[cm] initial octant, i.e., the smallest size of octant is 0.625[cm]. When the traditional MC is applied to Figure 6.7(b) it produces holes on the resultant surface in addition to unattached segments. furthermore, some holes still remain in the VMC with

85% voting threshold, which produces the best surface as shown in Figure 6.7(c). The pro- posed method connects imperfect surface (e.g., holes) using the connectivity information obtained from Figure 6.7(b).

A total of 29 quantised octree slices and 60 clusters are found in Figure 6.7(b). Some slices of the octree,I_iocq, are illustrated in Figure 6.8 where each nonzero pixel in a slice indicates an octant, and octants belonging to the same cluster identification (ID) have identical grey value. For example, the slice 11 is for z = 6.875[cm], which is at shoulder height of the dummy.