Depth Perception Part II Depth Perception 1 Binocular Cues to Depth Depth Information Oculomotor Visual Accomodation Convergence Binocular Monocular Static Cues Motion Parallax Perspective Size Interposition Shading Binocular Vision: Vision with Two Eyes Fixating an Object Binocular cues to depth: Binocular cues are based on the fact that we have two forward facing eyes that are laterally separated This provides slightly displaced images in each eye Fovea Fovea This information can be converted into a signal about relative depth Based on the geometry of the images reaching the eye Important concepts in binocular depth vision: Corresponding and non-corresponding points Fixation plane Horopter etinal disparity Diplopia Stereopsis Stereoacuity Stereopsis: Definitions Our brains convert overlapping flat images projected onto the retina of each eye into a 3-D model of the surrounding world. This creation of a 3-D world from the combining of information from the two eyes is called Stereopsis - from the Greek words stereos - for solid and opsis for vision - solid vision or solid sight. Stereopsis - is the ability to perceive depth or relative object distance based on retinal disparity.
Depth Perception 2 binocular stereopsis Not the most important cue for depth Why study it? Because its the only aspect of depth of which we have some physiological understanding Eavesdropping on binocular cells using electrophysiology The Early Stage of Stereopsis When we look at an object with two eyes we converge our eyes so the the image of the object falls on the fovea of each eye - the retinal locus with the highest resolving power. This convergence of the eyes so that the image of the object of interest falls on the foveas is called bifoveal fixation and is generally considered to be the first stage in binocular function. The foveas can be considered to be corresponding points on the two retinas. Thus any object you fixate will fall on corresponding points on the two retinas - i.e. the foveas. Corresponding and noncorresponding points When fixating, image of target falls on fovea of each eye The images of an object at the same distance as the fixation plane will fall on the same relative position in the two eyes Images that fall on different relative locations are said to fall on noncorresponding points Corresponding points and the horopter: The horopter is an imaginary plane through the fixation point that joins all corresponding points
The Horopter Points Falling on the Horopter Fall on Corresponding Points on the etinae Depth Perception 3 Non-corresponding Points and etinal Disparity If a target is closer or more distant than the fixation plane, its image falls on noncorresponding points in the two eyes etinal Disparity and Depth: There is a systematic relationship between the amount of retinal disparity on the retina and the distance of a target relative to the fixation plane If images fall on noncorresponding points, then there is retinal disparity and the potential for stereopsis definition of disparity = θ θ θ θ fixating here a b Fusion & Panum s Area The process by which we merge these retinally disparate images into a single percept is called fusion. Not all images that fall on disparate points lead to double vision-- which is also known as diplopia. ab a b left eye view right eye view There is a narrow region on either side of the horopter that includes all points in visual space that are fused into single images. This region is called Panum's area -the region where fusion occurs. perceived depth increases with increasing disparity (minus, closer than horopter, plus, farther than horopter)
Depth Perception 4 Panum s fusional space ocus of corresponding retinal points - Horopter Points that don't fall on the horopter fall on disparate (non corresponding) points in the two eyes. That is, objects located nearer or farther than the fixated target form images in different positions on each retina giving rise to disparity. The difference in the location of two retinal images of the same object is called binocular disparity. Crossed disparity Uncrossed disparity Stereoacuity andom Dot Stereogram The smallest disparity that can be resolved = Stereoacuity = 10-20 seconds of arc Invented by Bela Julesz 1956 emigre engineer from Hungary First innovative use of a computer for research in perception
How a andom Dot Stereogram Works: Depth Perception 5 random black and white pixels which are essentially the same in each eye some, however, are shifted laterally with respect to the others 1 0 1 0 1 0 1 1 0 1 0 1 1 0 0 1 1 1 1 1 1 0 1 1 0 0 1 1 0 1 left eye 1 0 1 0 1 0 1 0 1 0 1 1 1 0 1 1 1 1 1 1 0 1 0 1 0 0 1 1 0 1 right eye E E 1 0 1 0 1 0 1 0 1 0 1 0 row 1 1 1 0 1 0 1 1 0 1 0 1 1 row 2 Wheatstone s invention of the stereoscope (c. 1836) mirrors mirrors top view Some other methods to show stereo pictures Polaroid glasses method P+ P+ eft eye image mirrors ight eye image P- P- front view aluminized screen free fusion, w/o optical aids divergent convergent Each eye receives a separate image How does it work? notice that each eye receives a separate image of just two lines having a different separation. Brewster stereoscope
Plane of Fixation Disparity-Tuned Cell esponses C A B C' A' B' Depth Perception 6 Subject fixating B Individual neurons were tuned for different amounts and directions of disparity Stimulation ocation (A,A') (B,B') (C,C') Stimulation ocation Cell esponses "Near" cell Cell tuned to fixation plane "Far" cell Several different classes of neuron, some finely tuned for small amounts of disparity, others simply responding to near or far Autostereograms: In autostereograms we use our vergence eye movements as the stereoscope A Simplified Example of How An Autostereogram Works By converging or diverging we shift the image in one eye relative to the other With the correct amount of vergence we are now superimposing two parts of a repeating image which has been designed to contain disparity when viewed this way Simplified Magic Eye Autostereogram
Depth Perception 7 Binocular parallax a b Notice the difference in angular separation Size constancy Size constancy The perception of size is closely related to the perception of distance. The brain is remarkably good at compensating for changes in retinal image size with distance in order to keep the perceived size constant Why does someone walking away not appear to shrink?
Size constancy: Given the size of the image on the retina (visual angle) and its distance, it is possible to compute the physical size of an object Depth Perception 8 The Holway-Boring experiment: Size constancy is the mechanism that makes this computation Holway & Boring demonstrated the crucial importance of depth perception in an experiment Observer views Test Disks located at different distances Task is to adjust size of Comparison Disk to match physical size of Test Disk Test disks all set to subtend 1 o of visual angle Test under several condition in which the availability of depth cues is varied Observers matched closer to visual angle as cues removed elationship between size perception and perceived distance: Emmert s aw Generate afterimage on retina View afterimage against surfaces at different distances Note changed size of afterimage The perceived size of an afterimage is related to the distance of the viewing surface from the eye
Depth Perception 9 Emmer t's law: Sp = k x Sr x Dp (Sp = pe rceived size; Sr = retinal size; Dp = perceived d istance; k = constant) Ponzo Illusion This picture looks odd because the size and distance cues are in conflict Size perception and visual illusions: A number of visual illusions may result from the misapplication of constancy scaling Gregory has argued that the misjudgement of size is because the illusory figure contains information that activates the constancy scaling mechanism Consequently, an object is seen as larger or smaller than it should be Muller-yer Illusion: If the arrowheads are seen as internal and external contours, the closer, external corner should appear bigger
Depth Perception 10 The moon illusion: Moon (or sun) seems larger at the horizon than at the zenith ecognised in classical times, many theories Assumption: if two objects have the same retinal image size, the one that appears closer will look smaller That means horizon moon must look more distant Some evidence that horizon looks further away than zenith sky Current most-accepted explanation in terms of apparent distance, although issue is still controversial If zenith sky appears closer, then moon will seem to be smaller