Analysis of echoes in single-image random-dot-stereograms

Three-dimensional depth information of a surface can be encoded in a two-dimensional image called autostereograms. The encoded surface can be reconstructed from an autostereogram by using the correspondences between pixels in human brains or computer algorithms. However, in some cases, the reconstructed surface is not unique because of "echoes". In the presence of echoes, reconstruction of the original surface from the autostereogram cannot be guaranteed since no cue of the original surface is available in autostereograms. In this paper, the causes of echoes are investigated and conditions for echo-free reconstruction are derived. Based on these conditions, autostereogram generation algorithm is revised to guarantee echo-free autostereograms. Besides, the surface reconstruction algorithm is modified such that original surfaces encoded are always reconstructed from echo-free autostereograms.