Megapixels and resolution

Let’s say that you have a 1,000-square-foot or 100qm house and you add a second storey to it so now you have a 2,000-square-foot or 200qm house. Is it only 50% larger? Instead of adding the second storey, let’s say you add the 1,000 square feet on the ground floor, say on the back and along one side, but the final size is still 2,000 square feet. Don’t you still have twice the area rather than only 50% more? Sure, it’s only 50% bigger if you look at only one wall, but the living area doubles.

With that in mind, why is the increase in pixel area seen in one dimensional terms rather than two? Do the eye and brain perceive horizontal resolution as separate from vertical? I’ve read here and there the statement that 12 megapixels only yields 50% more resolution than six megapixels, since the size increases only 50% in each dimension. However, it would seem to me that the brain perceives both of a picture’s two dimensions simultaneously, so the apparent increase in resolution is 100%, just as the jump from six to 12 megapixels would imply.

At 266 dpi for 133 lpi magazine printing, the six-megapixel image is almost large enough for a full page and the 12-megapixel image is almost enough for a double truck (without interpolation). That looks like double the resolution to me.

What is it that I don’t understand?

Don Douglas said:

At 266 dpi for 133 lpi magazine printing, the six-megapixel image
is almost large enough for a full page and the 12-megapixel image
is almost enough for a double truck (without interpolation). That
looks like double the resolution to me.

What is it that I don’t understand?

Click to expand...

Well, seems to me you have only doubled the area, (by doubling the width alone) when going double truck with the image. Doubling REAL resolution needs to have the height doubled too!!

A four-up sheet, not a two-up sheet. ;-)

Remember, you could NOT use the same photograph in horizontal and vertical orientation. Flopping a vertical shot onto its side is not the same thing as increasing its resolution.

So, whilst I see the logic behind your reasoning, and your point is nicely argued) I subscribe to the 4x school of resolution doubling, not the 2x.
--
Regards,
Baz

as resolution is refered to as "pixels per inch",a linear measurement,If we refered to resolution as "pixels per square inch" then the resolution figure would have doubled.
Frank Perry

Don Douglas said:

With that in mind, why is the increase in pixel area seen in one
dimensional terms rather than two? Do the eye and brain perceive
horizontal resolution as separate from vertical? I’ve read here and
there the statement that 12 megapixels only yields 50% more
resolution than six megapixels, since the size increases only 50%
in each dimension. However, it would seem to me that the brain
perceives both of a picture’s two dimensions simultaneously, so the
apparent increase in resolution is 100%, just as the jump from six
to 12 megapixels would imply.

At 266 dpi for 133 lpi magazine printing, the six-megapixel image
is almost large enough for a full page and the 12-megapixel image
is almost enough for a double truck (without interpolation). That
looks like double the resolution to me.

What is it that I don’t understand?

Click to expand...

History perhaps?

First off, megapixels and resolution are only loosely related to each other, and even less related to what the brain perceives.

Second, most photographers and most scientists and engineers (most of the time) use resolution as a measure of 1-dimensional rather than 2-dimensional detail.

Resolution describes the ability of an instrument to distinguish (resolve) closely separated objects. For a telescope it might be the angular separation of two adjacant stars that are just far enough apart to appear as two objects, rather than a single fuzzy circle. For a spectrometer it is the smallest wavelength or frequency separation that can be resolved.

This usage was adopted by photographers long before the digital era. Resolutions of lenses and emulsions are often characterised by the shortest period of black and white zebra-stripes that achieves a specified contrast ratio (line-pairs per mm).

If you double the linear resolution (more accurately the resolving power) you get 4 times as much detail in the same area, or you can enlarge 4 times and still get the same sharpness in the enlarged image.

Strictly speaking, the resolution of a digital camera should take account of the modulation transfer function of the lens (contrast and resolution), the influence of the anti-aliasing filter above the sensor, and how the sensor elements are arranged (Monochrome, Foveon or Bayer array). It is certainly NOT just the separation of adjacent pixels.

You seem to want a term that describes the total number of resolvable points in the image. A useful concept, but I don't know that we have a word for it.

Hope this helps
--
Alan Robinson

Then given equivalent lenses, the same film emulsion, and the same aspect ratio, a 4x5 chrome would have only four times the resolution of a 24x30mm crop from a 35mm chrome. Somehow, to me, quite subjectively, the 4x5 seems more than four times “better,” the difference being more closely related to the fact that it has 16 times the film area. So many people have blogged on about how increases in pixel count are “hype” (or gentler words to that effect) that I have to wonder whether subjective perception of graphic quality isn’t more accurately represented by two-dimensional area than by linear resolution.

Those of us brought up on the european 'A' system are trained to think that each paper size is a doubling of the previous size and half the next size

e.g. A3 is double the size of A4 because it is like two A4 sheets joined together and 2 A4 sheets are twice one A4 sheet.

I get a strong impression that a lot of Americans on these forums think of a doubling as doubling both height and width (what I would call 4x the size).

As a Brit (and therefore european) I respond in the European way i.e. 12MP is twice 6MP and will yield equal quality prints at twice the size (area) but many Americans would be up in arms over this insisting that doubling the resolution requires 24MP...

I don't think there is really an argument either way here; it's just a case of agreeing conventions before starting a debate in order to avoid confusion.

I believe there is a phrase that sums up this process: "Good communication".

Don Douglas said:

Let’s say that you have a 1,000-square-foot or 100qm house and you
add a second storey to it so now you have a 2,000-square-foot or
200qm house. Is it only 50% larger? Instead of adding the second
storey, let’s say you add the 1,000 square feet on the ground
floor, say on the back and along one side, but the final size is
still 2,000 square feet. Don’t you still have twice the area rather
than only 50% more? Sure, it’s only 50% bigger if you look at only
one wall, but the living area doubles.

With that in mind, why is the increase in pixel area seen in one
dimensional terms rather than two? Do the eye and brain perceive
horizontal resolution as separate from vertical? I’ve read here and
there the statement that 12 megapixels only yields 50% more
resolution than six megapixels, since the size increases only 50%
in each dimension. However, it would seem to me that the brain
perceives both of a picture’s two dimensions simultaneously, so the
apparent increase in resolution is 100%, just as the jump from six
to 12 megapixels would imply.

At 266 dpi for 133 lpi magazine printing, the six-megapixel image
is almost large enough for a full page and the 12-megapixel image
is almost enough for a double truck (without interpolation). That
looks like double the resolution to me.

What is it that I don’t understand?

Click to expand...

--
Galleries and website: http://www.whisperingcat.co.uk/mainindex.htm

It all depends...

Apparently, if Canon do it it's a 100% increase, but if other manufacturers do then it's actually LESS than 50%, because you lose a stop due to the crop factor.

Leastways, after some of the arguments I've ploughed through on here, that's how it looks.

Seriously, it all depends on BOTH linear measurements?

And yes, 6 to 12 is a 100% increase.
--
http://catmangler.smugmug.com/

Don Douglas said:

Then given equivalent lenses, the same film emulsion, and the same
aspect ratio, a 4x5 chrome would have only four times the
resolution of a 24x30mm crop from a 35mm chrome.

Click to expand...

Yes.

Don Douglas said:

Somehow, to me,
quite subjectively, the 4x5 seems more than four times “better,”
the difference being more closely related to the fact that it has
16 times the film area.

Click to expand...

Agreed.
4x linear resolution gives 16x 'useful detail'

Don Douglas said:

So many people have blogged on about how
increases in pixel count are “hype” (or gentler words to that
effect) ...

Click to expand...

If you don't crop, only ever view your images on a monitor at 1600x1200 pixels, or you only ever look at 6x4 inch prints, then you don't need more than 2-3 Mpixels.

If you want a stunning 2 metre wide print, then extra megapixels will be a big help.

Don Douglas said:

I have to wonder whether subjective perception of
graphic quality isn’t more accurately represented by
two-dimensional area than by linear resolution.

Click to expand...

Here we get to the nub of your problem. I don't regard linear resolution as a subjective measure of graphic quality. It measures the ability to distinguish fine detail, which is not the same, though it obviously contributes to the quality.

It seems you are looking for 'total detail available' or some such. Resolution is often used rather loosely in this context, but it has a well-established (and useful) meaning as a 1-dimensional concept.

We need a different term.

--
Alan Robinson

What about "pixel area" -- the number of pixels times the size of each in microns, which would take into account the improvement in quality delivered by larger pixels.

Don Douglas said:

What about "pixel area" -- the number of pixels times the size of
each in microns, which would take into account the improvement in
quality delivered by larger pixels.

Click to expand...

Now we are moving away from 'image quality' to 'light gathering ability'. Ignoring fill-factor and microlens effects, pixel count x pixel area gives total sensor area. Your new metric won't distinguish between an APC sensor with a small number of photosites (great for low light / high ISO, but limited resolution) from an APC sensor with a large number of photosites (capable of high resolution in good light).

There is not a single number which predicts how good an image will be.

Resolution defines the ability to resolve fine detail, and depends on lens quality as well as sensor performance.

Pixel count sets a limit to the detail, provided everything else is as good as possible. We still need to be careful here: a 6 Mp Foveon sensor will give roughly the same detail as a 12 Mp Bayer sensor, due to differences in the way colour information is extracted. (Arguably the definition of pixel count used by most manufacturers is broken, but that is a separate argument, lost long ago).

Noise, dynamic range and tonal range are important too, as are contrast and sharpness.

Cheers,
--
Alan Robinson

Thanks to all for your thoughtful responses. The way this question came up is this: I’ve been shooting since the sixties and have been telling myself I’d go digital when a camera came along which I could afford that would give me the resolution I need, something that rivals film.

Recently, a photograph done for an A4 printed piece ended up being used by the client additionally as an A2 poster. I was glad to be able to get the film drum scanned to the larger size. A similar thing happened when someone ordered large prints – fairly large anyway, 70x100cm – from images whose original purpose was again A4. So I figure I don’t know what will come up and it doesn’t hurt to go for more quality than I think I need at the time of shooting. But I get confused by statements such as, “You’d need 24 megapixels to get double the resolution of six.” Wait a minute. A Sinarback 54 gives only twice the resolution of an $800 plastic toy? Maybe I’m too old to understand.
Cheers,
Don
dondouglas.com

Don Douglas said:

Thanks to all for your thoughtful responses. The way this question
came up is this: I’ve been shooting since the sixties and have been
telling myself I’d go digital when a camera came along which I
could afford that would give me the resolution I need, something
that rivals film.
Recently, a photograph done for an A4 printed piece ended up being
used by the client additionally as an A2 poster. I was glad to be
able to get the film drum scanned to the larger size.

Click to expand...

A common guideline is that the eye can't resolve detail smaller than around 300 dpi. Many professional photo-printers work at about this resolution. On this basis, for A4 you need something like 3500 x 2500 pixels. In practice, 4 Mpixel can look pretty good, depending on the subject matter.

The rule is based on the eye resolving about 1 minute of arc, corresponding to around 0.003 inch at 10 inches (0.007 mm at 25 cm distance). For A2 and larger sizes, the image probably won't be viewed from 25 cm, or with a magnifying glass, so you don't need as much as 35 Mp.

Threads regularly appear discussing at what resolution digital matches film, for example http://forums.dpreview.com/forums/read.asp?forum=1021&message=15940076

I don't believe there is a consensus yet.. If you have a few hours to spare, type 'Film resolution' in the search engine on this site.

Regards,
--
Alan Robinson