A Pixel is Not a Little Square, A Pixel is Not a Little Square, A Pixel is Not a Little Square, and a Voxel is Not a Little Cube

This was the title of an classic article  about image reconstruction written by Dr. Alvy Ray Smith from July 17, 1995, well before the advent of PenTile technology, but still technically accurate and on-point with respect to what pixels really are.  In this classic article he clearly explains why it is wrong to look at pixels as little squares.

http://alvyray.com/Memos/CG/Microsoft/6_pixel.pdf

Dr Alvy Ray Smith cofounded – or was present at the beginning of – four centers of computer graphics excellence http://alvyray.com/.

• Altamira Software Corporation: CEO and Founder 1991-1994 (Purchased by Microsoft)
• Pixar: Executive Vice President and Cofounder 1986-1991 (Now a multi-billion-dollar company) - see Pixar founding documents
• Lucasfilm Ltd, Computer Division: Director of Computer Graphics Research 1980-1986
• NYIT = New York Institute of Technology, Computer Graphics Laboratory: Senior Scientist 1975-1979

After that he became the first Graphics Fellow at Microsoft, 1994-1999, and before the four centers he was Visiting Scientist with Xerox PARC = Palo Alto Research Center (1974), during its heyday, and a professor of computer science at New York University (1969-73) and the University of California at Berkeley (1974). He worked briefly with Jim Blinn at Cal Tech’s Jet Propulsion Laboratory in 1979 on special effects for Carl Sagan’s Cosmos series for public television.

Still we have seen many bloggers referring to pixels as little squares.  One example of this is blog below with a key figure from this blog reproduced in the following image.

http://arstechnica.com/gadgets/news/2010/03/secrets-of-the-nexus-ones-screen-science-color-and-hacks.ars/

Illustration from ARS Technical Blog by Luke Hutchison in 2010

In Dr.Smith’s article it is well explained that pixels are actually points of image reconstruction and nothing else.  To make this even clearer he reminds us that the real world does not have little squares.  And, that scanners, when capturing this information, do not have little squares.  Consequently, the representation as little squares is rather arbitrary.

Quoting from a couple sections of this article  Dr. Smith said:

“…Just to be sure that I eradicate the notion of little square(s) everywhere, let’s look at the scanning process.  I want to be sure that nobody thinks that scanners work with little squares and that, therefore, it is all right to use the model.

A scanner works like this:  A light source illuminates a piece of paper containing a colored picture.  Light reflected from the paper is collected and measured by color sensitive devices.  Is the picture on the paper divided up into little squares, each of which is measured and converted to a single pixel?  Not at all.  In fact this would be very hard to accomplish physically.  What happens instead is that the illuminating light source has a shape or the receiving device has an aperture that gives the incoming light a shape or both, and the device integrates across this shape.  The shape is never a square.  It is not necessarily accurate, but will give you the correct flavor, to think of the shape as a Gaussian.  In general, overlapping shapes are averaged to get neighboring pixel samples.

So scanning should not contribute any weight to the little square model…”

****

Dr. Smith went on to say:

“…It has been shown that the little square model does not arise naturally in sampling theory, the main underpinning of everything we do.  It does not arise in scanning or display.  It arises in printing only in restricted cases.  The geometry world uses it a great deal because they have had to simplify in order to accomplish.  Their simplified model of contributions to a pixel should not be confused with or identified with the pixel.  Magnified screen pixels that look like little squares have been shown to be a quick and dirty trick (pixel replication) by graphics boards designers, but not the truth.  In short, the little square model should be suspect whenever it is encountered.  It should be used with great care, if at all, and certainly not offered to the world as “standard” in image computing…”

This is precisely the point I have been trying to make about PenTile.  We have demonstrated a way to reconstruct a pixel imaging point with the average of two subpixels per pixel.  For field sequential displays you can only count a single dot for each pixel at any point in time.  PenTile technology uses as many as 10 subpixels to reconstruct the chroma information for any pixel.  Counting squares has nothing at all do with the number of pixels on the screen.  Only contrast modulation matters for determining  resolution or the number of pixels that are possible on a given display with PenTile display architecture.  Pattern visibility resulting from larger subpixels may be apparent upon looking at displays closely enough to see subpixels, but this is not the same as saying there are fewer reconstruction points or fewer pixels.

It is time to stop counting dot when referring to resolution.