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The two-stage transform provides a unique description of the object. The object in the left panel (line and dot) was varied by moving the dot exhaustively to all positions in the panel. For each position, the two-stage transform was applied. The difference in output from the pattern at left was computed as a Euclidian distance and color coded (red, most different; blue, most similar). The only similar output (blue region at bottom left) is produced by a rotation of the original image.
