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George Sperling, Arvin Hsu; Revisiting the Lincoln Picture Problem. Journal of Vision 2004;4(8):53. doi: 10.1167/4.8.53.
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© ARVO (1962-2015); The Authors (2016-present)
When Lincoln's portrait is represented by square tiles (sub-sampling), with each tile of uniform luminance equal to the average luminance in the area it covers, Lincoln is unrecognizable. Using image processing to remove the high spatial frequencies generated by the tiles, or equivalently, squinting or viewing at a distance, restores Lincoln to visibility in the residual low frequencies (Harmon & Julesz, Science, 1973). Thus, Lincoln's image is present in the tiled image, but not visually accessible. Why? Findings: 1. The ratio of tile size to object size is critical. Too-small tiles permit easy identification; too-large tiles so attenuate low spatial frequencies that Lincoln remains invisible even when the high spatial frequencies are filtered from the tiled image. 2. Subjective judgments of the appearance of different transformations of a particular picture (Lincoln) generalize only imperfectly to the objective ability to identify familiar objects from their tile representations. 3. Object sillouettes survive tiling. To perform objective tests of identification accuracy, photographs of 100 common objects that were not identifiable by their outlines were represented by optimal tiles for the LPP. 4. For our 100 images, masking of low spatial frequencies by tile-generated high spatial frequencies accounted for only about 1/3 of the tile masking effect. 5. Local-negative masks generated from the sub-sampling algorithm did not account for any of the tile-masking effect. 6. Contours created by the tiling process account for about 2/3 of the tile-masking effect. 7. Contours created by random-mosaic tiles or by triangular tiles had a stronger effect(objects were less identifiable) than contours created by square tiles. 8. The masking effectiveness of tile-generated contours is not simply a function of their energy; it occurs at a “feature” level of perceptual processing where high- and low-spatial frequency information about an object is combined.
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