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In this paper, we propose a segment-based triangulation method for building parallel-perspective stereo mosaics using ray interpolation. The currently available fast parallel ray interpolation for stereo mosaicing uses a uniform or regular triangulation technique that does not take advantage of the spatial information. This works well when the interframe displacement in the video is small. However, for large interframe displacements, hence large motion parallax, we observe visual artifacts in the mosaics when the source triangles in the video frames are warped into destination triangles in the mosaics using affine transformations. Our method uses the edge information present in the scene to ensure that triangles do not cross over from one planar facet to the other. The video frames are segmented, and the edges are obtained from the inner boundaries of different segments. A mesh is designed in each segment or region, over which motion between consecutive video frames is constant. Hence, this method avoids unwanted warping of objects with large motion parallax in the scene and reduces the visual artifacts. The performance of our proposed technique is demonstrated on a series of simple-to-complex video imagery collected by utilizing cameras and airborne sensors.