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Computing the Aspect Graph for Line Drawings of Polyhedral Objects
February 1990 (vol. 12 no. 2)
pp. 113-122

An algorithm for computing the aspect graph for polyhedral objects is described. The aspects graph is a representation of three-dimensional objects by a set of two-dimensional views. The set of viewpoints on the Gaussian sphere is partitioned into regions such that in each region the qualitative structure of the line drawing remains the same. At the boundaries between adjacent regions are the accidental viewpoints where the structure for the line drawing changes. It is shown that for polyhedral objects there are two fundamental visual events: (1) the projections of an edge and a vertex coincide; and (2) the projections of three nonadjacent edges intersect at a point. The geometry of the object is reflected in the locus of the accidental viewpoints. The algorithm computes the partition together with a representative view for each region of the partition.

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Index Terms:
3D object representation; picture processing; edge projection; pattern recognition; aspect graph; line drawings; polyhedral objects; Gaussian sphere; accidental viewpoints; vertex; geometry; computational geometry; graph theory; pattern recognition; picture processing
Citation:
Z. Gigus, J. Malik, "Computing the Aspect Graph for Line Drawings of Polyhedral Objects," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 2, pp. 113-122, Feb. 1990, doi:10.1109/34.44399
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