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The Constrained Maximum Rectangular

Parallelepiped Representation of a 3D Object

from Multiple Views

**Young-Hua Fenh ^{*}, Jun S. Huang and Jau-Yien Lee^{*}**

National Cheng Kung University,

Tainan, Taiwan, R.O.C.

In this study, the goal was to develop an algorithm to geneerate the constrained maximum rectangular parallelepiped (MRP) representation of a 3D object from multiple views. The construction of the MRP code was by the volume intersection of three sets of sweeping MRPs which are converted from the 2D maximumempty rectangular code in three orthogonal views. In the two-dimensional rectangular coding, we have developed an algorithm to obtain the maximum empty rectangular code. The use of the maximum empty rectangular code is to minimize the effects of boundary noise. An O(N^{2}) algotithm is discussed here and a modified algorithm is used to generate the maximum empty rectangle contained in the boundary of the object.

The MRP code is then refined by additional views by projecting the MRPs noto the additional view and by forming the area intersections, or by volume intersections with the sweeping volumes of the additional views.

Some experimental results are shown with line drawings for visual evaluation. These results show that our algorithm forconstructing the MRP code is quite reliable and that the MRP code is an efficient, stable and compact representation.

Keywords: rectangular prarllelepiped coding, object silhouette, 2D rectangular boding, the mazimum empty rectangle problem, volume intersection, refinement by additional views

Received January 25, 1991; revised October 7, 1991.

Communicated by Wen-Hsiang Tsai.