Analysis of echoes in single-image random-dot stereograms

Three-dimensional depth information of a surface can be encoded in two-dimensional images called single-image random-dot-stereograms or, more widely known, autostereograms. It is achieved by using the correlations of pixels in the horizontal direction. Using the correspondences between pixels in human brains or computer algorithms, surfaces can be reconstructed from autostereograms. However, in some cases, the reconstructed surfaces are not unique because of "echoes". In the presence of echoes, reconstruction of the original surface from an autostereogram cannot be guaranteed since no cue of the original surface is available in autostereograms. The causes of echoes are investigated and conditions for echo-free reconstructions are derived. Based on these conditions, an improved autostereogram generation algorithm is proposed to guarantee echo-free autostereograms. Besides, the surface reconstruction algorithm is modified such that the originally encoded surfaces can always be reconstructed from echo-free autostereograms