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<p>A fast, efficient, algorithm that processes polyhedral cones from views of an object to produce an octree representation of the object is proposed. A polyhedral cone defined by both a viewpoint and a polygonal contour of the object in the image for each view always contains the object. Thus the common region of the cones for multiple views is considered to be an approximating one of the object. The octree representation controls all cubic regions in three-dimensional space as a set of nodes with a hierarchical description in positioning, and therefore is suitable for registration of the common region. The computational complexity of the algorithm is directly proportional to the common region surface area and exponentially proportional to the finest resolution level of the octree. The calculation time of the algorithm is determined for illustrative examples of three-dimensional objects.</p>
3-D objects; computerized pattern recognition; computerized picture processing; polyhedral cones; octree representation; polygonal contour; nodes; hierarchical description; computational complexity; resolution level; computational complexity; computerised pattern recognition; computerised picture processing; trees (mathematics)

S. Arimoto, S. Fukuda and H. Noborio, "Construction of the Octree Approximating a Three-Dimensional Object by Using Multiple Views," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 10, no. , pp. 769-782, 1988.
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