Transcript Spatial Frequency

Understanding Psychophysics:
Spatial Frequency & Contrast
How does differential neural firing to differing
orientations of “bars” cause us to “perceive” our
environment?
Understanding the relation between physical
stimuli (i.e., what is “Spatial Frequency” and
“contrast”?) and our perceptions of the world.
•Low Spatial Frequency:
–Shapes of buildings
–Closer buildings
•high Spatial Frequency:
–Size of the windows
–Far buildings
•Large Contrast:
–Dark building among
light-colored buildings
•Small Contrast:
–Shading differences
among small
background buildings
Frequency - cycles per second (time domain)
Spatial Frequency – cycles per degree of visual
angle (space domain)
square-wave grating
sine-wave gratings
the unit of measure is cycles per degree (of visual angle)
Visual Angle and Spatial Frequency: The angle of an object
relative to the observer’s eye
A
<A
The closer an object is, the larger it’s visual angle, or
The larger an object is (relative to smaller object) the larger the
visual angle
Size (visual angle) is related to distance from the
viewer (e.g. how “big” are the windows?)
2x cycles/deg
x cycles/deg
Low-contrast
High-contrast
I
M
A
contrast = A/M
Our sensitivity to contrast varies as a function
of spatial frequency
Contrast
Sensitivity
Function
0.1 0.2
1
10
Spatial Frequency
50
Panel (a): strips are wider
than photoreceptors, hence
brain can “reconstruct”
vertical lines.
Panel (b): strips are
narrower than
photoreceptors, resulting
in perception of gray.
Retinal ganglion cells and
striate cortex have
“frequency sensitive” cells
Lowest contrast with
lowest spatial frequency
highest contrast with
lowest spatial frequency
Contrast Sensitivity
Function
Lowest contrast with
highest spatial frequency
Highest contrast with
highest spatial frequency
How does the brain analyze visual information?
How does the brain analyze
visual information? Breakdown
the scene by its spatial frequency
(and contrast) “components”
How does the brain analyze visual information?
Mathematical technique call Fourier Analysis
scene
Breakdown
of spatial
frequencies
& contrast
components
How the brain analyzes visual information
-any scene can be broken down into spatial
frequency components - a series of sine
waves
= Fourier analysis
square-wave
Freq= f; Amp = a
=
sine-wave f, a
+
3rd harmonic 3f, a/3
+
5th harmonic 5f, a/5
+ all odd harmonics
Our brain does Fourier Transfer Functions via “firing preferences” of different
(1) retinal, (2) LGN receptive field sizes and (3) cortical “frequency
analyzers”
Adaptation & physiological measurement
experiments reveal -- Spatial Frequency Channels
(Spatial Freq. “Analyzers”)
0.1 0.2
1
10
50
Spatial Frequency
-single-cell recording experiments show that simple
cells in visual cortex respond to a narrow range of spatial frequencies
Retinal ganglion
cells are also
sensitive to specific
spatial frequencies
as a function of the
size of the centersurround field.
How does the brain analyze visual information?
Mathematical technique call Fourier Analysis
scene
Breakdown
of spatial
frequencies
& contrast
components
Organization of Visual Cortex
1.
Retinotopic Maps
Figure 4.13 Retinotopic mapping of neurons in the cortex. When the electrode penetrates the cortex obliquely,
the receptive fields of the neurons recorded from the numbered positions along the track are displaced, as
indicated by the numbered receptive fields; neurons near each other in the cortex have receptive fields near
each other on the retina.
Retinotopic Organization
vertical penetration
Visual Field
ABC D
E
F
A
A
A
A
A
oblique penetration
B
C
D
E
F
Organization of Visual Cortex
1.
Retinotopic Maps
2.
Magnification Factor
Magnification of the fovea in the
visual cortex
• 50,000 Ganglion cells are found in 1 mm from
the fovea
• 1,000 Ganglion cells are found in 1 mm from the
periphery of the retina
• Need for a lot more cortex to process foveal
information
Magnification Factor
Figure 4.14 The magnification factor in the visual system: The
small area of the fovea is represented by a large area on the
visual cortex.
The apportioning of proportionally more space on
the cortex to central vision (cones), compared to
peripheral vision (rods).
Copyright © 2002 Wadsworth Group. Wadsworth is an imprint of the
Wadsworth Group, a division of Thomson Learning
Figure 3.26, page 95
Magnification factor, packing density
Magnification of the Fovea
vertical penetration
Visual Field
ABC D
E
F
A
A
A
A
A
oblique penetration
B
C
D
E
F
Organization of Visual Cortex
1.
Retinotopic Maps
2.
Magnification Factor
3.
Orientation Columns
“Location column” (A): all receptive fields are from the same
point on the retina
A
“Orientation column”: includes
simple, complex and end-stopped
cells (informing about spatial
frequency, contrast, movement &
length) that are sensitive to only
one orientation
Organization of Visual Cortex
1.
Retinotopic Maps
2.
Magnification Factor
3.
Orientation Columns
4.
Ocular Dominance Columns
5.
Hypercolumns (location Columns)
Ocular Dominance & Hypercolumns
• Ocular (left or right eye) Dominance Columns
– 80 percent of cells fire to both eyes, but…
– Cells have preference for left or right eyes
– Left v. right preference set up in columns
• Hypercolumns – one spot on the retina
– Full set of everything
• Orientation
• Ocular Dominance (preference for left v. right)
The Hypercolumn
1 mm
color blobs
(pegs)
R
Ocular
dominance
columns
(R or L)
L
Retinotopic Organization indicates the existence of
“location columns”
vertical penetration
Visual Field
ABC D
E
F
A
A
A
A
A
oblique penetration
B
C
D
E
F
“Location column” (A): all receptive fields are from the same
point on the retina
A
“Orientation column”: includes
simple, complex and end-stopped
cells (informing about spatial
frequency, contrast, movement &
length) that are sensitive to only
one orientation
“L” left eye dominant
“R” right eye dominant
Figure 4.22 Schematic diagram of a hypercolumn as pictured in Hubel and Wiesel’s ice-cube model. The light
area on the left is one hypercolumn, and the darkened area on the right is another hypercolumn. The darkened
area is labeled to show that it consists of one location column, right and left ocular dominance columns, and a
complete set of orientation columns.
Short-, Medium- & Long-Cone densities
Only pieces of an object overlap with
any one hypercolumn
Figure 4.24 How a tree creates an image on the retina and a pattern of activation on the cortex. See text for
details.
Figure 4.25 How the trunk of the tree pictured in Figure 4.24 would activate a number of different orientation
columns in the cortex.