pixels

All About Pixels

The concept of pixels can be intimidating to novices in digital photography. Many issues revolve around them. Most important is the confusion between pixels per inch (ppi) and dots per inch (dpi) when considering digital printers. This document intends to give some background about pixels and hopefully ease some of the confusion.

What are pixels?

A digital image is made up of an array of discrete spots. It is essentially a grid of columns and rows of spots, or pixels. Each pixel is contained in a certain row and column of that grid, or array. Further, each pixel represents, with a number, the color and brightness of the portion of the image contained in that spot. If the image is a black and white image, the number refers ONLY to the brightness.

In general, the resolution, or fineness of detail, in an image is related to the total number of pixels in the image. I say in general because the subject of resolution is a complicated one, discussed in more detail later. Some of the earliest digital images were only a hundred pixels total, in a ten by ten array (ten rows and ten columns). Now consumer digital cameras create images containing millions of pixels.

The above image is 20 x 20 pixels. you can just make out that it is a human face- a young girl

What are ‘dots’?

Ah, here is when we get into problems. There are two different meanings of the term dot when we are working with digital photographs and digital graphics. One is an old term, long predating digital graphics. It is the halftone dot. I will explain halftone dots later, but it refers to a method of printing pictures on a printing press. This brings up another problem. The term ‘printing’ can mean two things. The first is the process of duplicating books, magazines, newspapers, etc., on a printing press. The second means the action of creating a hard-copy of an image from your computer on your computer’s printer- usually an ink-jet or a laser printer. The problem can arise because in the old halftone process a dot was in a sense a pixel, so the term pixels per inch and dots per inch could be used interchangably. This is NOT the case for an ink-jet or laser printer. Only certain types of special artwork (not photographs) can be printed by an ink-jet or laser printer with one dot per pixel. Normal images take a number of dots to create each pixel.

The halftone process.

After the invention of the printing press the printing of images required a laborious preparation of a ‘plate.’ Printing ink is black- strictly black (or, at least, a single color). One cannot directly print lots of shades of grey using black ink on a printing press.

An image plate was created by hand carving a flat-surfaced block of wood, or engraving a metal plate. Dark areas were depicted by closely spaced fine lines. Medium grey areas had a less dense array of such lines. The carved wood plates were known as woodcuts, the engraved metal plates by any of several names depending on the exact method of preparing them and the exact printing process used. One name for a high-quality process was the gravure.

After the invention of photography people wanted to print photographs in newspapers, magazines, and books. At first the photograph was used strictly as an aid to engravers working on metal plates (the woodcut having become obsolete by this time). Newspapers and magazines employed a large number of these graphic artists (using today’s term for such people).

Finally the halftone process automated the printing of photographs. By exposing a negative through a fine screen (a halftone screen) onto a photo-sensitive printing plate, a new kind of printing plate was produced- the halftone plate. In areas where the image was dark, the plate would print large dots of ink- so large the dots even overlapped. In areas where the image was light, only the smallest dot of ink was printed.

The finer the halftone screen- that is the more halftone dots per linear inch the screen produced, the higher the quality of the image printed- that is, there was higher detail. But the higher the number of dots per inch, the more finicky the process.

This image is part of a picture in a 1946 magazine. One can clearly see the individual halftone dots. Note too that the dots are laid out in a diagonal pattern (at 45 degrees) rather than in horizontal rows and vertical columns. This is supposed to make the pattern a bit less noticable to the human eye. The smaller dots look like they are a lighter shade of grey than the larger ones, but this is an artifact of the scanning process. The shade of black is actually the same for the large and small dots in the actual printed page.

Newspaper photographs used a coarse screen, maybe seventy five dots per inch. Ordinary magazines and books used maybe a hundred dots per inch, while high quality mags used a finer screen yet, with maybe 130 or thereabouts dots per inch.

While the term ‘pixel’ did not yet exist in the early halftone days, in fact each halftone dot was a pixel, and a halftone image can be analyzed by the same mathematics used to analyze digital images.

Computer printers

When home computers became powerful enough to work on digital image files, people sought out a way to print such images from the computer. Unfortunately, ink-jet and laser printers, the common home and small business types, have the same problem as a printing press. Lets stick for a moment with black and white images- they are easier to understand, and we can extend the concepts to colored images later. But black and white laser and ink-jet printers can only print black or not print black. A printed dot is black, whereas a spot that has no printed dot is white (assuming of course we are printing on white paper).

How then to print an image containing many shades of grey? The first attempt was to create a fake ‘halftone dot’. In this technique the developers decided on a certain ‘dot’ size, say a four by four array of sixteen dots. This would allow the printing of sixteen shades of grey, from full white (no dots printed) to the darkest black (all sixteen dots in the array printed). A medium grey would have eight of the sixteen possible dots printed.

Now, a typical printer in that day could only print maybe 120 dots per inch. If we take up four lines and four columns for each fake halftone dot or pixel, we could only print 30 pixels per inch with such a technique. The large patterns, far larger than in a newspaper photo, were easily visible to the eye and quite distracting. Further, sixteen shades of grey does not create a very high quality image even if printed at high resolution.

This is a mock halftone dot pattern made from a 4 x 4 matrix (one cell outlined in magenta). It represents dark on left of image, with a vertical edge and lighter tone to left. This is how first PC printers printed images. The "halftone" pattern was very coarse, even worse than for newspaper pictures, and very irritating to the eye. Something else was needed.

The solution to this problem took two parallel efforts. One effort kept improving the fineness with which computer printers could print. Nowadays consumer printers have reached 1200 to even 2400 dots per inch. The second direction was to find some other way to depict shades of grey rather than the hard and fast N x M rectangular array of dots or subpixels.

Developers came up with a method called dithering, where only a statistical relationship between the number of actually printed black dots in a given reference area correlated with the shade of grey. Two adjacent areas might well have different numbers of dots printed, but the average number over and area had a fixed relationship with the shade of grey. The resulting somewhat random pattern was far less noticable to the eye, and presents a much higher quality image. One mathematical technique is called ‘error diffusion dither.’ While the technique does allow a much better image quality with a given number of printer dots per inch, it still, on the average, takes a number of printer dots to equal one pixel. That is, a 600 dpi printer CANNOT print a 600 pixel per inch image.

Unfortunately, the fineness of the dither pattern is so fine that my closeup lens on my film camera cannot copy it well. Until I get a photo-microscope (which I hope to some day) I can't show you what the dither pattern looks like. If you have a really strong magnifying glass, you may be able to see it in the output of your printer.

How many ppi should I scan at for a (whatever) sized print.

Well, the only downsides to scanning at very high resolution are that it will take up more bytes in storage on your hard drive, and take more time, both in scanning and in any computer processing of image. But in these days of 20 GB hard drives and 750 Mhz Pentium III computers that isn’t as big of a drawback as it used to be.

It is sometimes easier to figure how many pixels per inch you need to print at and work backwards. Some programs default to a pixels per inch of 72 when you go to print. Some programs even say the image resolution is 72 dots per inch. That is poor terminology- they should say pixels per inch. The reason they use dpi is that the 72 ppi or 72 dpi comes from days when the printers were CRT types that COULD print true halftones. These were pretty fancy machines. Remember, with a true halftone screen a dot IS a pixel.

That 72 ppi figure comes from the very early days of digital image manipulation in computerized graphics arts printing. The equipment was primitive and 72 ppi was about as good as the first ones could do. However, that is only adequate for advertisements or for cheap newspapers and tabloids. It is not magazine quality.

You need at least 150 ppi to get magazine quality and at least 200 to get anywhere near even Instamatic quality prints. Some folks even recommend a minimum of about 300 ppi, but I find 200 is not bad- usually adequate. So, how many pixels do we need for a decent sized print?

If we want to make a 200 dpi print in a 5 x 7 size (lets assume landscape format for the moment) we then need an image that is 1400 x 1000 pixels wide and high. That is a 1.4 Mpixel camera if you are talking about a digital camera. An 8 x 10 print (again, assume landscape) requires a 2000 x 1600 pixel image. That is more than a 3 MPixel image. See why you need a really good digital camera to make a decent 8 x 10 print?

Is there any downside to having too high a resolution (ppi) when printing?

Actually, there is. First of all, the higher the number of dots per inch the printer is capable of, the better. However, a file with lots of pixels, and a printer with insufficient dpi can lead to problems. Lets say you have an image that you are trying to print at 300 ppi, and your printer is only capable of 600 dpi. That only allows a range of four dots in each color (or four dots of black with a B & W image). Even though the modern dither algorithms do give you more than four shades of grey when they dither, they do not give that many. So if you have an image which you are printing at a high ppi on a low dpi printer you will still find that the quality suffers because of insufficient shades of grey or colors.

So you have to run tests on high ppi images. High ppi will give you high spatial resolution (sharpness) but limits the number of shades of colors available. If you get a sharp picture, but notice edges to colors where there should be a continuous shading, as in a blue sky (this is called posterization) you may get better results by resizing the picture to a smaller ppi. You will lose sharpness but may gain and more subtle shading of colors.

How do I resize, and/or change the number of pixels, in an image file.

This is a tough one. You have to be willing to do a little arithmetic. And, furthermore, it depends on what software you are using. The better photo editing programs give you great flexibility in resizing or resampling images, while cheaper ones may not. By the way, resampling is what we call changing the number of pixels in an image while not changing the physical size of a printout.

First of all, we need to say something about the physical size of an image file. The first graphics file formats did not contain any information about the physical size of the image. They only contained a number for the total number of pixels and/or the number of rows and columns. If, however, you wanted to make a print with your printer, the computer now does not know how large you want the print to be.

Some software, if it encounters a file that does not contain a physical size, will by default assign a value of 72 pixels per inch (again, that holdover from the early days of computer graphic arts). But you are not bound by that.

With most software you can change the physical size of an image (which, of course, only has meaning when you print it), the number of total pixels, and/or the pixels per inch. The exact steps to do this depend on exactly what software you are using. However, this is one of the most important editing steps you will be taking, so you need to read your software manual carefully on the subject of resizing or resampling.
How can the computer resample the image?

Your computer can either decrease or increase the number of pixels in an image. Decreasing it is easy. Lets say you have a 1 million pixel image, and you would like to reduce it to a 250, 000 pixel image. This is easy. The computer looks at square groups of four pixels (two high by two wide) and takes the average brightness (and color) of those four pixels and assigns it to a new pixel. If the reduction is not by an even number, as in the above example, it is more complicated mathematically, but still involves a sort of average.

The surprising thing is that the computer can also INCREASE the number of pixels! That is, it can generate new information! Well, to some degree it can. Let’s say we wish to increase the number of pixels in each direction by 50 %. The resulting image will have a bit over twice as many pixels as the old one (1.5 x 1.5 = 2.25). The process is called interpolation. The easiest way is to look at any two adjacent pixels and create a new pixel, halfway between the old two, and having a value of the average of the two original pixels.

Now, actual algorithms tend to be a bit more complex than that mathematically. And, they are limited in how well they work. You really cannot get something for nothing indefinitely. You can about double the total number of pixels in an image by interpolation. Much beyond that and it just doesn’t improve the image. Oh, the new file will have many more pixels. Say you asked to double the number of pixels in each direction (that is, four times as many pixels as the original). If you actually ran a resolution test on the process (say, by photographing a test chart) you would find that the new resolution was only about 50% higher than the original, not 100% higher. So go easy on interpolation. Doubling the number of pixels is about the limit in practice.

Is interpolating the same thing as sharpening?

Not quite, but very similar. In the same way, a little sharpening can improve an image, especially one from a scanner or digicam with poor optics, but you can only go so far. One application of sharpening may improve things, doing it over doesn’t add anything (or sometimes adds noise- salt and pepper artifacts).