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Peter Thompson, Kyriaki Mikellidou; The 3-D Helmholtz Square illusion: more reasons to wear horizontal stripes. Journal of Vision 2009;9(8):50. doi: https://doi.org/10.1167/9.8.50.
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The ‘Helmholtz Square’ illusion demonstrates that a square comprising horizontal stripes looks taller and narrower than an identical square comprising vertical stripes. Thompson (vss 2008) showed that this illusion persists when applied to 2-D female figures, challenging the popular belief that horizontal stripes make us look fat. However Taya & Miura (2007) have demonstrated that in 2-D representations of vertical cylinders the apparent depth of the cylinder correlates inversely with apparent width, i.e. the more the apparent depth the narrower the cylinder. They propose that a vertically-striped cylinder presents more cues to its 3-dimensionality than a horizontally-striped cylinder, thus it appears narrower and this effect outweighs the Helmholtz illusion. However Li & Zaidi (2000) have shown that patterns containing contours lying along the lines of maximum curvature of the surface are critical for conveying shape. That is, depth in a vertically oriented cylinder (or human body) would be best revealed by horizontal not vertical lines. We have measured the perceived widths of real 3-D cylinders covered with horizontal or vertical lines and a uniform grey colour. 15 participants matched the perceived width of a range of cylinders (varying in real diameter from 2 – 12cm) to the separation of a pair of vertical lines on a computer screen. We find that the Helmholtz illusion persists, with the horizontal cylinders appearing up to 6% narrower than the vertical cylinders, a similar magnitude to the 2-D case. This contradicts Taya & Miura's expectation that vertical lines will give more depth cues in a 3-D vertical human, and hence will have a slimming effect. We suspect that our cylinders contained sufficient depth cues in both vertical and horizontal versions to eliminate any illusion from a disparity in perceived depth. Further experiments explore the influence of pattern spatial frequency and colour on the illusion.
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