Can you believe that the grays are the same?

Fourier Fun

It is well known that the shadow of the tip of a rotating rod traces out a sine wave:

SINEWAVE

It’s also well known that the Fourier components of a square wave are:
So consider a rotating arm, of length 1 and rotation rate 1.  On the arm a hand of length 1/3 rotates at a rate of 3.  On the hand a finger of length 1/5 rotates at a rate of 5… and so on.

Question:  What path in space will the tip of the set of rotating arms trace out?

SQUARE WAVE

The Fourier components of a sawtooth wave are:

SAWTOOTH WAVE

And here is a full wave rectified sinewave:

RECTIFIED SINEWAVE

With strict fixation of the center spot, each letter is equally legible because it is about ten times its threshold size. This is true at any viewing distance. Chart shows the increasingly coarse grain of the retinal periphery. Each letter is viewed by an equal area of visual cortex (“cortical magnification factor”) (Anstis, S.M., Vision Research 1974).  

The left hand picture shows the San Diego skyline. The right hand picture is progressively blurred from the center to the periphery. When fixated at their respective centers, both pictures look equally sharp because the progressive blurring in the right hand picture just matches the progressive loss of acuity with eccentricity caused by the increasingly coarse grain of the peripheral retina.

The retinal image undergoes barrel distortion in the retinal ganglion layer and in the visual cortex V1. This barrel distortion, or greater magnification of the center than the periphery, reflects the “cortical magnification factor”.

Even men use this trick!

What do babies and fish have in common?

Patrick Cavanagh, Stuart Anstis, Daphne Maurer, Terri Lewis

Fishes and babies can neither read nor speak, yet we persuaded them to tell us what colors they see. We showed them special moving colored patterns on a computer screen. If they saw the colors, the babies followed the movement with their eyes, and the fishes followed it by moving their whole bodies, swimming after the patterns in an innate optomotor response.

We made a movie only four frames long which looped repetitively. Each frame filled the whole computer screen with vertical colored stripes. In the left hand column, the stripes at Time 1 were light red and dark green, and at Time 2 they were light & dark yellow. The yellow stripes were shifted sideways by half a bar width, so the stripes appeared to jump sideways — but which way? The brain could not pair up succcessive stripes on the basis of color, because all the stripes at Time 2 were the same color (yellow). So the brain had to pair them up on the basis of luminance. If the red stripes were lighter than the green, the stripes appeared to jump to the right toward the nearest light yellow stripe (left-hand column). If the red stripes were darker than the green, the stripes appeared to jump to the left toward the nearest dark yellow stripe (right-hand column). The movie translates lightness into motion.

We titrated red against green luminance until, at equiluminance, perceived motion disappeared for adult obsesrvers, babies stopped making pursuit eye movements, and fishes stopped swimming in circles. Red-deficient observers rquire more red to make an equiluminous mathc, and green-deficients require more green. We were able to identify individual color-defective babies. Conclusions: Outputs from cones into the luminance pathways were in place within the first months of life. Also, guppy fish are more green-sensitive and less red-senstivie than humans.

[quicktime width=”500″ height=”400″]http://quote.ucsd.edu/anstislab/files/2012/11/Camoflouge.mov[/quicktime]
The hidden word is well camouflaged until it moves, whereupon the visual system easily picks it out. That’s why gazelles freeze when predators are about!

Who What makes your heart flutter?

[quicktime width=”600″ height=”400″]http://quote.ucsd.edu/anstislab/files/2012/11/Tram1.mov[/quicktime]

Motion looks different in the periphery!  Look straight at the red & yellow spots, and you can see they move horizontally.  But look away & view them in peripheral vision (out of the corner of your eye).  Their paths appear curved!  The yellow spots seem to bow outwards, the red spots inwards, attracted toward the background stripes.

[quicktime width=”600″ height=”300″]http://quote.ucsd.edu/anstislab/files/2012/11/Circular1.mov[/quicktime]

The spots move in straight parallel lines, but in peripheral vision their paths look like circular arcs.

[quicktime width=”600″ height=”300″]http://quote.ucsd.edu/anstislab/files/2012/11/CircularOccluders1.mov[/quicktime]

Left: Spots move straight, & look straight — no illusion.  Right: In peripheral vision the spot paths look curved.  Conclusion: Background must be local,not global, and spots must touch the stripes, not just be near them.

[quicktime width=”500″ height=”400″]http://quote.ucsd.edu/anstislab/files/2012/11/CircleSlide.mov[/quicktime]

Spots move in circles on horizontal or vertical stripes.  In peripheral vision the spots appear to slide and shear on elliptical paths.

[quicktime width=”450″ height=”250″]http://quote.ucsd.edu/anstislab/files/2012/11/SizeChange.mov[/quicktime]

Moving bar, viewed peripherally, seems to change its length.

[quicktime width=”500″ height=”400″]http://quote.ucsd.edu/anstislab/files/2012/11/Rays.Vert1Hering.mov[/quicktime]

Red vertical lines appear to bow slightly outwards like sides of a barrel because of Hering’s (1861) geometrical illusion.  Red lines are repelled by radiating lines (orientation contrast).  Motion is illusion is opposite to this!  The spots kiss the red lines, but in peripheral vision they appear to bow inwards like a pincushion.  This is orientation assimilation, not contrast.

[quicktime width=”600″ height=”400″]http://quote.ucsd.edu/anstislab/files/2012/11/Footsteps.Not_.mov[/quicktime]

Top:  Footsteps illusion (Anstis 2001).  Blue & yellow squares move at constant speed, but appear to speed up and slow down.  Reason:  When dark blue edges lie on black stripes they have low luminance contrast and appear to slow down.  On white stripes they have high contrast and appear to speed up.
Bottom: Motion illusion.  In peripheral vision their speed does not change, but their perceived direction of motion does.  So the two illusions are different.

[quicktime width=”600″ height=”400″]http://quote.ucsd.edu/anstislab/files/2012/11/Oblique.mov[/quicktime]

In central vision the spot is correctly seen as moving vertically.  But as you view it more & more peripherally, its perceived angle increases, up to a maximum of 45° in this case.