Digital Geometry in Image Processing

204 Digital Geometry in Image Processing

effectively make the time complexity of O(n). As poly gon filling [84] is done

efficiently with the help of special hardware and architecture by g raphics pro -

cessors, we may consider it as a unit task. Moreover, since the polygons of

the disks are convex, the computation could be further optimized. In our dis-

cussion, we consider the cost of polygon filling is a unit cost, ignor ing its

cove rage.

Since the vertices of the rotated convex polygons are disc retized, and the

vertices themse lves are computed using appr oximations as discussed in Section

2.5.5.2 of Chapter 2, it is of inter est to obse rve how the ...