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 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 Size (visual angle) is related to distance from the viewer (e.g. how “big” are the windows?)

I x cycles/deg 2x cycles/deg Low-contrast High-contrast M A contrast = A/M

Our sensitivity to contrast varies as a function of spatial frequency Contrast Sensitivity 0.1 0.2 1 10 50 Spatial Frequency

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

Contrast Sensitivity Function Lowest contrast with lowest spatial frequency Contrast Sensitivity Function Lowest contrast with highest spatial frequency highest contrast with lowest spatial frequency Highest contrast with highest spatial frequency

How does the brain analyze visual information?

How does the brain analyze visual information How does the brain analyze visual information? Breakdown the scene by its spatial frequency (and contrast) “components”

Breakdown of spatial frequencies & contrast components scene How does the brain analyze visual information? Mathematical technique call Fourier Analysis Breakdown of spatial frequencies & contrast components scene

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”) Contrast Sensitivity 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 center-surround field.

Breakdown of spatial frequencies & contrast components scene How does the brain analyze visual information? Mathematical technique call Fourier Analysis Breakdown of spatial frequencies & contrast components scene

Organization of Visual Cortex 1. Retinotopic Maps

Figure 4. 13 Retinotopic mapping of neurons in the cortex 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 A B C F E D oblique penetration A A 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 The apportioning of proportionally more space on the cortex to central vision (cones), compared to peripheral vision (rods). 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.

Figure 3.26, page 95 Magnification factor, packing density Copyright © 2002 Wadsworth Group. Wadsworth is an imprint of the Wadsworth Group, a division of Thomson Learning

Magnification of the Fovea vertical penetration Visual Field A B C D E F oblique penetration A B C A D A E A F A

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 “Orientation column”: includes simple, complex and end-stopped cells (informing about spatial frequency, contrast, movement & length) that are sensitive to only one orientation A

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 L Ocular dominance columns (R or L)

Retinotopic Organization indicates the existence of “location columns” vertical penetration Visual Field A B C F E D oblique penetration A A B C D E F

“Location column” (A): all receptive fields are from the same point on the retina “Orientation column”: includes simple, complex and end-stopped cells (informing about spatial frequency, contrast, movement & length) that are sensitive to only one orientation A

“L” left eye dominant “R” right eye dominant Loc 3 Loc 2 Loc 1 Across the retinal field (each L/R pair is one retinal location) Loc 3 Loc 2 Loc 1 “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 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.