The Pursuit of Leonardo's Constraint

Leonardo da Vinci (1452–1519) identified two stimulus situations that cannot be painted faithfully on a canvas: (a) when two objects are located in the same direction with respect to the painter's head, and (b) when parts of a surface are visible to one eye, but occluded from the other eye. He analysed these situations in terms of rays being emitted from the two eyes and, aside from the origin of the rays, the projective geometry he used was correct. His analyses showed that what can be seen from two vantage points cannot be represented on a canvas, because a ‘correct’ painting must be created from a single ‘station point’. He was struck by the consequence of this fact that the depth seen on a canvas cannot match that of viewing the scene with two eyes. Subsequent visual scientists focused on Leonardo's observation about the lack of vivid depth in a picture. We argue that a complete understanding of what we see in the two stimulus situations requires consideration of visual direction in addition to visual depth. More specifically, we argue that the visual directions of the two objects, (a) above, and the visual direction of the monocular areas, (b) above, are dependent upon the constraint that two opaque objects cannot be represented in the same direction. Demonstrations that readers can perform, and that support this argument, are provided on the Perception website at http://www.perceptionweb.com/perc0102/ono.html.

[1]  Robert E. Bannon,et al.  SPATIAL SENSE AND MOVEMENTS OF THE EYE , 1948 .

[2]  R. W. Ditchburn.  Seeing is Deceiving: The Psychology of Visual Illusions , 1979 .

[3]  C. Tyler.  Stereoscopic Vision: Cortical Limitations and a Disparity Scaling Effect , 1973, Science.

[4]  O J Braddick,et al.  Binocular single vision and perceptual processing , 1979, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[5]  Casper J. Erkelens,et al.  Binocular Visual Direction , 1994, Vision Research.

[6]  R. Lawson,et al.  Stereopsis and anomalous contour. , 1967, Vision research.

[7]  M. Hollins,et al.  The effect of contrast on the completeness of binocular rivalry suppression , 1980, Perception & psychophysics.

[8]  B. Julesz,et al.  A disparity gradient limit for binocular fusion. , 1980, Science.

[9]  CASPER J ERKELENS,et al.  Binocular Alignment in Different Depth Planes , 1996, Vision Research.

[10]  Misalignment effects in 3-D versions of Poggendorff displays , 1995, Perception & psychophysics.

[11]  R B Lawson,et al.  The Poggendorf Illusion in Stereoscopic Space , 1976, Perceptual and motor skills.

[12]  B. Julesz,et al.  A THEORETICAL ANALYSIS OF ILLUSORY CONTOUR FORMATION IN STEREOPSIS , 1995 .

[13]  M S Banks,et al.  The computation of binocular visual direction: a re-examination of Mansfield and Legge (1996) , 1997, Vision research.

[14]  H. Ono,et al.  Occlusion as a depth cue in the Wheatstone-Panum limiting case , 1992, Perception & psychophysics.

[15]  D. Lindberg,et al.  Theories of vision from Al-Kindi to Kepler , 1977, Medical History.

[16]  Frank Jewett Mather,et al.  The literary works of Leonardo Da Vinci , 1939 .

[17]  H. Ono,et al.  Ecologically Invalid Monocular Texture Leads to Longer Perceptual Latencies in Random-Dot Stereograms , 1999, Perception.

[18]  Hiroshi Ono,et al.  Wondering about the wandering cyclopean eye , 1999, Vision Research.

[19]  I. Howard,et al.  Ptolemy's Contributions to the Geometry of Binocular Vision , 1996, Perception.

[20]  N. Wade,et al.  An Investigation of Line and Dot Forms of the Muller-Lyer and Poggendorff Illusions , 1981 .

[21]  W. PEDDIE,et al.  Helmholtz's Treatise on Physiological Optics , 1926, Nature.

[22]  B Gillam,et al.  The Role of Monocular Regions in Stereoscopic Displays , 1988, Perception.

[23]  J. Leconte.  On some phenomena of binocular vision , 1869, American Journal of Science and Arts.

[24]  Charles Wheatstone.  On some remarkable and hitherto unobserved phenomena of binocular vision. , 1962 .

[25]  Hiroshi Ono,et al.  The Making of a Direction Sensing System for the Howard Eggmobile , 2003 .

[26]  K. Nakayama,et al.  Real world occlusion constraints and binocular rivalry , 1990, Vision Research.

[27]  K Nakayama,et al.  Experiencing and perceiving visual surfaces. , 1992, Science.

[28]  Shinsuke Shimojo,et al.  Da vinci stereopsis: Depth and subjective occluding contours from unpaired image points , 1990, Vision Research.

[29]  B. Julesz,et al.  Modifications of the Classical Notion of Panum's Fusional Area , 1980, Perception.

[30]  Shinsuke Shimojo,et al.  Interocularly unpaired zones escape local binocular matching , 1994, Vision Research.

[31]  Lei Liu,et al.  Quantitative stereoscopic depth without binocular correspondence , 1994, Nature.

[32]  H. Leibowitz,et al.  The effect of rotation and tilt on the magnitude of the Poggendorf illusion. , 1966, Vision research.

[33]  B. S. Anton.  Poggendorff Illusion as a Function of Orientation of Transversal and Parallel Lines , 1976, Perceptual and motor skills.

[34]  On the Late Invention of the Stereoscope , 1987, Perception.

[35]  C J Erkelens,et al.  Perceived direction during monocular viewing is based on signals of the viewing eye only , 2000, Vision Research.

[36]  A. P. Mapp,et al.  A Restatement and Modification of Wells-Hering's Laws of Visual Direction , 1995, Perception.

[37]  H. Ono,et al.  Leonardo da Vinci's Struggles with Representations of Reality , 2001, Leonardo.

[38]  D. Topper.  The Poggendorff Illusion in Descent from the Cross by Rubens , 1984, Perception.

[39]  C. Erkelens,et al.  Is there an interaction between perceived direction and perceived aspect ratio in stereoscopic vision? , 2000, Perception & psychophysics.

[40]  S. Gilman,et al.  The notebooks of Leonardo da Vinci , 1978, Medical History.

[41]  Ken Nakayama,et al.  Quantitative depth for a phantom surface can be based on cyclopean occlusion cues alone , 1999, Vision Research.

[42]  E. Boring.  Sensation and Perception. (Scientific Books: Sensation and Perception in the History of Experimental Psychology) , 1943 .

[43]  N J Wade,et al.  Early studies of eye dominances. , 1998, Laterality.

[44]  Barton L. Anderson,et al.  The role of partial occlusion in stereopsis , 1994, Nature.

[45]  nd cent Ptolemy,et al.  Ptolemy's theory of visual perception : an English translation of the Optics : with introduction and commentary , 1996 .

[46]  G. Nyman,et al.  Occlusion Constraints and Stereoscopic Slant , 1997, Perception.

[47]  Raymond van Ee,et al.  The role of the cyclopean eye in vision: sometimes inappropriate, always irrelevant , 2002, Vision Research.

[48]  J. M. Foley,et al.  Effects of voluntary eye movement and convergence on the binocular appreciation of depth , 1972 .

[49]  Jitendra Malik,et al.  Stereoscopic occlusion junctions , 1999, Nature Neuroscience.

[50]  K. Nakayama,et al.  Toward a general theory of stereopsis: binocular matching, occluding contours, and fusion. , 1994, Psychological review.

[51]  Gordon E. Legge,et al.  The binocular computation of visual direction , 1996, Vision Research.

[52]  N J Wade,et al.  Descriptions of Visual Phenomena from Aristotle to Wheatstone , 1996, Perception.

[53]  C. Wheatstone.  XVIII. Contributions to the physiology of vision. —Part the first. On some remarkable, and hitherto unobserved, phenomena of binocular vision , 1962, Philosophical Transactions of the Royal Society of London.