A difficult, error-prone, and time consuming problem in brachytherapy is the determination of the three-dimensional (3-D) positions of implanted seeds. To triangulate 3-D seed positions, the corresponding seed images in radiographs taken at different parallax (gantry) angles must be identified (matched). With only two radiographs, there is an inherent problem of ambiguity in matching individual seed images. The use of the assignment algorithm cannot bypass this ambiguity. However, when seeds are implanted within ribbons, their positions in 3-D space can be determined accurately and (almost always) without ambiguity. This follows because the matching of ribbon images is much less ambiguous than the matching of individual seed images. We describe a semi-automated procedure to match the ribbon images on two radiographs, determine the 3-D loci of the ribbons, and locate the 3-D position of each seed on each ribbon. The ribbon matching problem involves a double application of the assignment algorithm. After image matching, the 3-D locus of each ribbon is found from the intersection of the ray sets from its radiographic images and the analysis of a 3-D spanning tree through the derived ray set intersection points. The seed positions on a ribbon locus are determined by interpolation of equally spaced seed intervals along the 3-D ribbon locus. Experiments with a phantom show that for two radiographs separated by any parallax between 20 degrees and 90 degrees, our technique provides a systematic error in 3-D seed location of 3.0 mm, and a random error of less than 2 mm.