Digital BW, The Print

Austin writes:

> No, with most people that's true ...

The truth of the principle does not vary by person, since it is based on
objective logic.

> East is simply a universal standard (well,
> for most people), and most people know what
> direction East is...

Really?  Most people would define east as being ... the part of the sky in
which the sun rises.

But what distinguishes a "universal standard" that apparently doesn't
require corroboration for you from something that does?

> Because I KNOW so.

Because you say so.  I have no way of assessing the state of your occult
knowledge just by reading your posts.

> I understand that.  That does not make your
> assertion valid though.

A fortiori, your simple assertion that I am wrong doesn't make me wrong,
either.

> Any transition that appears smooth is simply
> of higher resolution (in one or two dimensions)
> than you can discern.  The fact is, you CAN
> discern that smoothness.

These two statements contradict each other.  You can see it, but you can't?
Right.

> So what?  That doesn't define the field of
> vision of a human.

I know; that has nothing to do with this discussion.  It does, however,
define the number of pixels required to satisfy human vision in the image,
and that number is 6-8 million.

> If the eye can only discern, at high resolution,
> a 1" circle, then why are you limiting the FOV
> to 10" x10" ?

I have no idea what you mean by a one-inch circle.  Dimensions are measured
in angular measure in the human visual field, i.e., objects are so many
minutes or degrees of arc in diameter, and so on.  A one-inch circle could
be any size at all in the visual field, depending on the distance at which
it is viewed.

> You obviously don't get it, and are missing why
> what you say is wrong.

I'll leave that determination for the reader.  I know that your mind will
not change, so I won't quarrel with you; I'll let my exposition of the facts
speak for itself, and each reader of these posts will be able to decide on
his own who is correct, and who isn't.

> You are taking the human eye's ability to have a
> particular resolution over a VERY small arc, and
> extrapolating it to 10 x 10, and the problem is, you
> have to SCAN over that 10x10 area to even see the
> entire 10x10 area at the higher resolution.

That isn't a problem.  That's how vision works.  My figures assume that a
viewer will scan the entire area of an image in order to view it (because
that's exactly what a human viewer with human eyes will do).  Thus, the
resolution required is many orders of magnitude above what would be required
if he just stared at one point on the image without looking at the rest of
it; in this latter case, only the pointed stared at would be in focus, and
the rest would be a useless blur ... and the resolution required to support
that in a print would of course be extremely low.

> Yes, it is...but that has nothing to do with
> your claim.

It has everything to do with it.  It turns out the limits of acuity
precisely match the limits imposed by the dimensions of cone cells.  That
is, in a good eye with perfect vision, it's the size of these cells that
limits resolving power, not the lens or cornea or anything else.

> The physiology text gives the resolution for a
> VERY SMALL area ...

Yes, the fovea centralis, part of the macula.  That's the only part of the
retina with cones in very high density, and it's the only part of the retina
upon which images can be accurately focused.

> ... and you are extrapolating that out to some
> arbitrary area.

Because all human vision involves scanning with the eyes in order to move
the entire image past the fovea.  That's what allows you to read an entire
page of a book without moving your head; your eyes scan the page, drawing
the fovea past each word in sequence so that you can actually see the word
in focus.  Without this scanning--if you just stared at the center of the
page without moving your eyes--you'd only be able to see a few words on the
page, and the rest would be a blur.  Try it, and you'll see.

When human beings view images, they do so by scanning them, just as they do
for everything else.  Thus, the resolution required in the image is that of
the fovea, multiplied by the area of the image.  This turns out to be 6-8
million pixels.  If you wish to calculate the resolution required for a
non-scanning view of the image, it's only a few thousand pixels.  But nobody
looks at images without scanning them with his eyes, so this latter exercise
serves no purpose.

> Why?  Who determined that as the "limit"?

You have to set some sort of arbitrary distance, or you cannot compute the
amount of resolution required for the print.  To have an image that works at
any distance, you need infinite resolution, but infinite resolution is not
achievable; so you decided on some arbitrary viewing distance, and you
calculate for that.

For most prints, it turns out that a good choice for the arbitrary viewing
distance is equal to the diagonal of the print.  Most people will not view
it more closely than that (indeed, they often can't, since they'd have to
turn their heads to scan it at closer distances), although many might view
it from farther away (but required resolution drops with distance, so that
isn't a problem).  The same calculation is used to prepare DOF tables and
markings.

> That is not what you initially said.

It is what I initially said; it just isn't what you understood.

> You said that 6M pixels WAS THE limit
> of human vision, and I said it is not,
> and it simply is not.  You didn't
> qualify it with a particular area.

I didn't have to, as anyone with a knowledge of the physiology of vision
already knows how I arrived at that figure.

> What defines a "full frame image"?

The entire image seen at any one time with movements of the eyes alone,
without cropping and without turning the head.

> Why?

Because if the resolution is less than the resolving power of the eye, a
lack of detail is discernable.  If the resolution is higher than the
resolving power of the eye, the additional detail beyond that
resolving-power limit is invisible (to human eyes).

> I understand all that, but that doesn't negate
> my disagreement with your statements.

It does, however, make your disagreement moot.

> Yes you are.

Because you say so?  I think not.

Others reading these posts can judge for themselves.  I've explained all
these principles exhaustively; you have explained virtually nothing.  The
weight of facts and reason thus work in my favor.  But the final
determination is made by the reader.

> Obviously, you can't, or you would.

That is flawed logic as well.