Lecture of 26 August 1994

Human Visual System -- The Eye

• Structure of the Eye includes the following critical parts:
  • cornea & sclera (outer casing)
  • choroid (inner dark lining and blood supply)
  • retina (sensor layer)
  • ciliary body and iris diaphragm (to control amount of light entering eye.
  • lens (to focus light onto the retina)
  • about 75 to 150 million rods (for monochrome, scotopic sensing)
  • about 6 to 7 million cones (for color, photopic imaging)
• Figure 2.3 shows the distribution of rods and cones as a function of angle from the fovea (central focal region of the retina).
• Figure 2.4 shows the extremely large range of brightness (as measured in millilamberts) over with the eye can function. It also demonstrates that given any ambient light level (i.e. average illumination value over the field of view), the eye is only sensitive to a small subrange of this total brightness range. This phenomenon is known as brightness adaptation.
• Figure 2.5 gives a schematic of the kind of image that can be used to demonstrate the minimal perceptable change in brightness. Please note that any change in illumination is said to be subliminal, that is, below the limit of perception. Although many metaphysically challenged people have spoken for years about subliminal communication, it is clear that no communication can take place by employing signals that cannot be perceived by the sender. Thus subliminal communication is by its very nature a contradiction in terms and impossible.
• Figure 2.6 plots the Weber ratio (the percentage change in brightness that is perceptable 50% of the time) as a function of ambient light level. It demonstrates that at high ambient levels, changes in brightness are more easily discerned.
• Figure 2.7 shows that although seeing may be believing, one cannot rely on visual perceptions as absolutely reliable indicators of fact. It shows some problems associated with boundaries of regions of varying brightness, such as Mach banding.

  Simple Image Model

• Gonzalez and Woods present their 2D image model which involves two components:
  • i(x,y): the amount of illumination incident upon the object imaged at point (x,y)
  • r(x,y): the reflectance of the object imaged at point (x,y).
  This model is somewhat crude in that it does not consider the kinds of issues one might be familiar with from computer graphics, such as orientation and polarization of light sources, object orientation, multiple light sources, etc. But it does give a rough idea of what's going on in an image containing no energy radiating sources.
• The values for i(x,y) vary between 0 and infinity.
• The values for r(x,y) vary between 0 and 1.
• The image value f(x,y) is the product of these.

  Sampling and Quantization

• To be digitized, a continuous image must be sampled and quantized. That is, values of the image must be chosen at finitely many locations (sampling), and those values must be finitely representable (quantized).
• A point (x,y) and the value of the image at that point a(x,y), together are called a picture element or pixel. (The term pel is really only used as a combining form in such words as megapel.)
• Tables 2.1 and 2.2 show the storage requirements for images with given values for N (image height), M (image width), and G (number of gray values) given a rectangular sampling array.
• Figures 2.9 and 2.10 show how varying N and M or G can affect the presentation quality of an image.
• Figure 2.12 shows lines of isopreference (or same preference) for several pictures of varying complexity. It essentially shows that the more complicated a picture, the less dependent is its presentation quality on having a large value for G. It also shows that a less complex image (containing fewer and larger regions) can actually be deemed to be more desirable if presented with lower values for G than necessary.
• In considering non-uniform sampling, remember that the human visual system uses a non-uniform sampling sensor (the eye). With several types of sensors (rods and cones). And that the sensor is actively steered in a goal-directed way.

  Relationships Between Pixels

• Points in a set may be connected or not. In no sense are pixels inherently connected. When one discusses connectivity of pixels or sets of pixels, one must first determine what points are in the set of interest, then determine if those points are connected.
• The point (x,y) in a subset of Z-2 is said to be N-4 connected to the following set of points:
  • (x+1, y)
  • (x-1, y)
  • (x, y+1)
  • (x, y-1)
  it is said to be N-D connected to the following set of points:
  • (x+1, y+1)
  • (x+1, y-1)
  • (x-1, y+1)
  • (x-1, y-1)
  and it is said to be N-8 connected to the set which is the union of N-4 and N-8.
• To find the m-connectivity of a set, connect all 8-connected points in the set, then remove the diagonal connections between any points p and q such that there is a point r in the set which is a 4-neighbor of both p and q.