The Pursuit of Leonardo's Constraint

Ono, Hiroshi; Wade, Nicholas; Lillakas, Linda

doi:10.1068/p3079

Cited by 20 publications

(18 citation statements)

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“…Moreover, several studies have proposed that misadoption of the processing of depth information in a picture on a flat plane contributes to certain geometrical illusions. For instance, occlusion would cause the Poggendorff illusion in terms of inappropriate correction to compensate the monocular region in three-dimensional space when viewing a two-dimensional drawing (Ono et al 2002). The processing of depth information extracted from the T-junction and Y-junction in the drawing as effective signatures, respectively, for occlusion and three-dimensional apex would cause the Shepard's table illusion by specifying the same parallelograms in two-dimensional drawing as rectangular parts of different three-dimensional objects (Shepard 1981).…”

Section: Discussionmentioning

confidence: 99%

Angle Illusion in a Straight Road

et al. 2011

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We report a new angle illusion observed when viewing a real scene involving a straight road. The scene portrays two white lines which outline a traffic lane on a road and converge to a vanishing point. In experiment 1, observers estimated the angle created by these converging lines in this scene or in its image projected onto a screen. Results showed strong underestimation of the angle, ie over 50% for observations of both the real scene and its projected image. Experiment 2 assessed how depth cues in projected images influence the angle illusion. Results showed that this angle illusion disappeared when scene information surrounding convergent lines was removed. In addition, the illusion was attenuated with projection of an inverted scene image. These findings are interpreted in terms of a misadoption of depth information in the processing of angle perception in a flat image; in turn, this induces a massive angle illusion.

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Section: Discussionmentioning

confidence: 99%

Angle Illusion in a Straight Road

et al. 2011

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“…(For a recent discussion, see Mapp et al, 2002;Ono, Lillakas, & Mapp, 2003;Ono, Wade, & Lillakas, 2002.) The double vision on a nonfixated plane is due to the stimulus being displaced perceptually in two directions.…”

Section: Resultsmentioning

confidence: 99%

“…Despite the long list of studies regarding da Vinci stereopsis cited above, researchers' understanding of what we see in these stimulus arrangements remains incomplete. On the basis of the results of several informal demonstrations, Ono, Wade, and Lillakas (2002) argued that what observers see in these stimulus situations is better understood by also considering egocentric visual direction rather than visual distance alone. Although observers view the world from two distinct vantage points (the two eyes), directions of objects are perceived as though from a single vantage point, often called the cyclopean eye.…”

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Leonardo's constraint: Two opaque objects cannot be seen in the same direction.

Ono

Lillakas²,

Grove³

et al. 2003

Journal of Experimental Psychology: General

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Given Leonardo's constraint that 2 opaque objects cannot be seen in the same direction, how are the regions of objects occluded to 1 eye included in perception? To answer this question, the authors presented 3-dimensional stimuli, similar to the ones that concerned Leonardo, and measured the visual directions of their monocular and binocular regions. When the distance between near and far objects was large, the nonfixated object was seen as double and blurry. Leonardo's constraint was met by seeing the near object as double and transparent or the distant object as double and superimposed. When the distance between near and far objects was small, the constraint was met by a perceptual displacement and compression of parts of the nonfixated object.Leonardo da Vinci considered a painter's task to be the reproduction of the visual world onto canvas, and being a painter himself, he was interested in discovering nature's laws to apply them to his work (Richter, 1952). In searching for these laws, Leonardo noted that when looking with two eyes one can (a) see around and behind a small near object, thereby seeing more of both the near object and the background than is possible with either eye alone, and (b) see more through an aperture than when looking with one eye only. On the basis of these observations, he concluded that it is impossible for a painter to depict on canvas what he sees with two eyes. (See the caption of Figure 1 for a direct quote from Leonardo's notebooks.) In this article, we argue that it is also impossible for a human observer to see all objects in the visual world in their correct location at any given moment. This is so because the visual system, like a painter, cannot represent two objects as being in the same direction.Because of its implications for depth perception, Leonardo's insight received some attention from early vision researchers and has recently seen a revival of interest by researchers. Wheatstone (1838) speculated that the concept of retinal disparity (two retinal images falling on slightly different positions in the two eyes) would have forced itself upon Leonardo if he had considered a cube instead of a sphere as the small near object shown in Figure 1. The view to each eye is noticeably different when viewing a cube rather than a sphere because of the corners of the cube. In reviewing early work on binocular vision, Boring (1942) discussed Leonardo's notes with respect to Wheatstone's discovery of retinal disparity as a cue to depth and coined the term Leonardo's paradox. According to Boring, the stimulus situation depicted in Figure 1 produces a paradox, because all of the background behind the sphere is seen even though the near object (sphere) is opaque. Without addressing the issue of transparency raised by Boring, recent researchers have shown that depth perception can depend on monocularly seen areas that lack retinal disparity (e.g

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“…The green jar in his Still Life with Commode ( Figure 4) is an example: In reality, one would have to be looking down on the scene in order to see the opening of the jug as an ellipse; from this perspective, the bottom of the jug should be more circular than the top, not less as Cezanne depicts it. As with the eye-centering, one wonders whether this is a conscious or unconscious aesthetic trope, or whether it simply comes as a byproduct of painting from life, where the artist's eyes and head are in constant motion, governed by regions of interest and biased by meaning, unconstrained by the 'correctness' in painting advocated by Leonardo da Vinci [13]-the jug sits securely on the table, so the bottom of it must be flat; we pour liquids out of the jug, so the top must be round.…”

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confidence: 99%

Perspectives on science and art

Conway¹,

Livingstone²

2007

Current Opinion in Neurobiology

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Artists try to understand how we see, sometimes explicitly exploring rules of perspective or color, visual illusions, or iconography, and conversely, scientists who study vision sometimes address the perceptual questions and discoveries raised by the works of art, as we do here.The integration of visual art with the experimental study of vision has its roots in formal analysis of painting, but this approach has gone out of vogue in art-historical circles because it ignores the impact of cultural context on art appreciation. Advances in our understanding of how the brain works have resuscitated interest in linking art with vision science. Here we review some of these new links, with the caveat that we will not address visual aesthetics, but rather some nuts and bolts of making and looking at art, in an endeavor to enrich our understanding of art 'in much the same way as a knowledge of bones and muscles has for centuries enhanced the ability of artists to portray the human body' [1]. Some recent studies may even illuminate why cultural context is so important in visual art.When we look at the world, or at a work of art, our eyes, and our visual attention, are constantly and alternately moving and fixating [2]. Our fixations are not randomly distributed across a scene, but rather concentrate on key regions-to a first approximation, on the areas of high local contrast [3]. The visual machinery that directs the eyes where to look can have two impacts on art. On the one hand, artists have developed techniques to direct your gaze; on the other hand, the unconscious machinery directing the gaze of the artist may influence which parts of the scene the artist portrays or emphasizes. Leonards et al. [4] have argued that Renaissance artists used gold for its special reflective quality under candlelight to control the viewers' gaze. The authors argue that 'the glow of the gold induced shifts in fixations to symbolically important regions of the painting' (Figure 1). Candle illumination introduces areas of local contrast that is not apparent under daylight conditions-the thin lines of gold extending into the bodies of the two subjects. It is these regions that show increased fixations under low illumination, raising the possibility that the viewer's gaze and attention are drawn to these regions not because of their symbolism, as Leonards et al. argue, but rather because of their low-level visual salience.Eyes are especially potent in attracting the gaze, both because of their behavioral significance and because they are the regions of high local contrast. Tyler [5•] examined 265 portraits spanning the past 600 years and found a strong tendency for one eye to be centered on the vertical midline of the painting (Figure 2). A recent critique of Tyler's observations asserts that 'one eye tends to be relatively close to the vertical midline because of geometric constraints on the placing of a relatively large object, the head, within a pictorial frame' suggesting that there is no behavioral significance to eye-centering [...

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The Pursuit of Leonardo's Constraint

Cited by 20 publications

References 46 publications

Angle Illusion in a Straight Road

Angle Illusion in a Straight Road

Leonardo's constraint: Two opaque objects cannot be seen in the same direction.

Perspectives on science and art

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