A pixel is not a little square

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A pixel is not a little square A voxel is not a
little cube

• 2000.01.10
• Chung ji hye

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abstract

• gtPurpose
• Rid the world of the misconception that a
  pixel is a little geometric square.
• Everything I say about little squares and
  pixels in the 2D case applies equally well to
  little cubes and voxels in 3D.

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The little square model

• The little square model pretends to represents a
  pixel as a geometric square.
• Pixel is assumed to correspond to the area of the
  plane bounded by the square
• (x,y)i-.5xi05,j-.5yj.5
• gt(x,y)ixi1,jyj1

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So what is a pixel?

• A pixel is a point sample. It exists only at a
  point.
• At color picture for example pixel might actually
  contain three samples
• An image is a rectilinear array of point samples
  (pixel).

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So what is a pixel?

• We can reconstruct a continuous entity from such
  a discrete entity using an appropriate
  reconstruction filter

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So what is a pixel?
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So what is a pixel?
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So what is a pixel?
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Why is the little square model so persistent?

• gtprincipal reasons
• ?geometry-based computer graphics uses it. (3D,
  CGI etc)
• ?video magnification of computer displays appears
  to show it.

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Why is the little square model so persistent?

• rendering
• -rendering is the process of converting abstract
  geometry into viewable pixels that can be
  dispaled on a computer screen or written to film
  or video for display.
• modern computer graphics model

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When magnifies or zooms in on

• When Magnifies or Zooms in on, each pixel appears
  to be a little square.
• each point sample is being replicated M M
  times. for magnification factor M.
• When you look at an image consisting of MM
  pixels all of the same color, guess what you see.

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How does a scanner digitize a picture

• Principle of work
• 1.light source illuminates a piece of paper
  containing a colored picture.
• 2.light reflected from the paper is collected
  and measured by color sensitive devices.

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How does a scanner digitize a picture

• 3. Incoming light a shape or both? ?? ?? ?? ???
  image? ??? ? ??. Its not square think as
  Gaussian
• In general, overlapping shapes are averaged to
  get neighboring pixel samples.
• So, scanning should not contribute any weight to
  the little square model.

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How does a printer print a digital image?

• Consider halftone printing of ink on paper.
• gtconvert a pixel with many values to a dot of
  ink on paper such that the area of the dot
  relative to a little square of paper occupied by
  the dot is in the ratio of the intensity
• although there are little squares in each
  color separation, there are none for the final
  result.

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How does a printer print a digital image?

• Little square model?? ???
• the different primaries are printed at an
  angle to each other.
• The point here is that use of the little square
  is a printing technology decision, not something
  inherent in the model of the image being imaged.
• In fact, the image being imaged is simply an
  array of point samples in all cases.

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How is an image displayed on a monitor?

• Color monitor often has little triads of dots
  that cause the perception of color at normal
  viewing distances
• gtprincipal
• 1.The value of a pixel is converted, for each
  primary color, to a voltage level.
• 2.This stepped voltage is passed through
  electronics which , by its very nature, rounds
  off the edges of the level step.

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How is an image displayed on a monitor?

• 3. eye integrates the light pattern from a group
  of triads into a color.
• gtIt is obvious that there are no little squares
  involved at any step of the process.

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What is a discrete to continuous mapping that
works?

• Assume the samples are mapped to the integers.
• Then, the outer extremes of the image are bounded
  by a rectangle whose all edges.
• It uses symmetric filters gt but, asymmetric
  filters are useful because of perspective
  transformation.

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What is a discrete to continuous mapping that
works

• We display from top to bottom on millions of TVs
  and computer displays.
• We read from top to bottom
• We compute on matrices the natural container for
  image from top to bottom. Nearly all popular
  image file formats store image form top to bottom

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Image broadening

• Minimal enclosing rectangle of a reconstructed
  image were the most natural representation of it
  ?fall out to a discussion of image broadening.
• Minimal enclosing rectangle uses symmetric filter
  ?
• The filter is asymmetric, then so is the
  broadening.
• The amount of broadening is dependent on the
  filter used.

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Summary

• Pixel is not a square.
• -scanner digitize a picture
• -printer print a digital image.
• -display on monitor
• the triads on a display screen are not pixel
  they do not even map one to one to pixels.