Digital Images The fundamental properties of the digital photographic image. * Monochrome Images * Color Images * What is a halftone?

Display of Images The phosphor dots are arranged into triangular groups of three ( R,G and B dots). See Figure 1. They are sufficiently small to be unresolvable by a human eye, instead, what we perceive at each point on the screen is a mixture of light from the red, green and blue phosphors of a triplet. Images are normally viewed on a monitor employing cathode- ray tube ( CRT) technology.

Cathode-ray Tube (CRT) Colors are represented using Red, Green, and Blue components. The CRT has a mechanism for displaying these three components – Figure 1. Grayscale.The Table list the specifications for intensity codes for a four –level grayscale system. With 3 bits per pixel, we can accommodate 8 gray levels. Intensity CodesStored Intensity Values in The Frame Buffer (Binary Code) Display Grayscale 0.00 (00)Black (01)Dark gray (10)Light gray 1.03 (11) Intensity = 0.5[min(r,g,b) + max(r,g,b)]

In the RGB color model, the frame buffer stores the RGB components for every pixel Figure 2

In the indexed color model, the frame buffer stores an index into a color-lookup table Figure 3

Gamma Intensity output is not a linear function of voltage input The shape of the curve may be represented by a power function y = x 1/  - x is the input voltage -  is the gamma parameter - typically y is the light intensity output GammaAppendix.html

Gamma Correction When we "compute" colors we generally assume that they are linear quanities. Unfortunately, most display devices are nonlinear. The most common correction method is called gamma correction.

High resolution 24-bit images display 16.7 million colors. Each pixel in a 24-bit image has one of 256 brightness values for red, green and blue.

How many bits do we need to store an image? For number of bits b, we need to store an image of size N x N with 2 m different grey levels is : b=N x N x m So for a typical 512 x 512 image with 256 grey levels (m=8) we need 2,097,152 bits. That is why we often try to reduce m and N without significant loss in the quality of the picture. The resolution of an image expresses how much detail we can see in it and clearly depends on both N and m. Keeping m constant and decreasing N results in the checkerboard effect. Keeping N constant and reducing m results in false contouring.

Common Values ParameterSymbolTypical values RowsN256,512,525,625,1024,1035 ColumnsM256,512,768,1024,1320 Gray LevelsL2,64,256,1024,4096,16384 Table 1: Common values of digital image parameters Quite frequently we see cases of M=N=2 K where {K = 8,9,10}. This can be motivated by digital circuitry or by the use of certain algorithms such as the (fast) Fourier transform. The number of distinct gray levels is usually a power of 2, that is, L=2 B where B is the number of bits in the binary representation of the brightness levels. When B>1 we speak of a gray-level image; when B=1 we speak of a binary image. In a binary image there are just two gray levels which can be referred to, for example, as "black" and "white" or "0" and "1".

What resolution should I use for my images? This is a frustrating question because it all depends on your final print output, and more specifically, what line screen frequency, better known as lpi, your commercial printer uses. Since most people pick a printer after their project has been completed, this can be tricky. Use a resolution that is too low, and you end up with poor quality graphics. With a resolution that is too high, you end up with longer process time and little gain on the overall quality of the halftone. There are, however, some typical line screen frequencies that are used as general guidelines: Newspapers or publications printed on newspaper stock use a 65 or 85 lpiBooks printed on uncoated stock use a 120 or 133 lpiBooks and magazines printed on coated stock use a 133 or 150 lpiHigh quality books with lots of graphics (art books), calendars, etc. on coated stock will use 150 or higher lpi

What resolution should I use for my images? When determining resolution, the basic rule is that final image resolution should be twice that of your intended commercial printer's lpi. In general, a higher screen frequency produces a smoother, more detailed image. However, for certain types of paper a higher screen frequency is not better. Typically newsprint uses an LPI of is the norm for glossy paper such as in magazines. Check with your printer to determine the best LPI settings to use for their equipment and your paper. So, for example, if you are creating a family history book with black and white images, you can't go wrong with an image resolution of 300 ppi. However, 267 ppi is the most popular ppi for most book projects with grayscale graphics.

The limit to display 24-bit RGM images There is a trade-off between spatial and color resolution. If spatial resolution is increased so that larger images can be displayed on-screen, then color resolution may need to be reduced.

What is a halftone? Halftoning is the process of turning continuous tone grayscale or color images into a series of dots for printing that fool the eye. Halftones are images made up of a series of dots in a specific pattern that simulates the look of a continuous tone image. Because printers cannot print continuous tones -- whether it's the many shades of gray in a grayscale image or the millions of colors in a color photograph -- images must be converted to halftones. Another term for halftoning is dithering

White Paper, Black Ink Some ideas can be conveyed effectively with only the most basic materials. For example, the theme of "Good vs. Evil" is easy to represent graphically using only white paper and black ink. Where we want to illustrate "good," we allow the white paper to remain pure and unblemished. Where we want to illustrate evil, we smother the paper with black ink.

Halftone Screening The solution to our dilemma is to use "halftone screening" a process that allows us to approximate shades of gray while using only black ink. If we want to see a light gray, we print a bunch of small black dots, evenly spaced. If we want to see a medium gray, we print larger black dots. If we want a dark gray, we print black dots that are large enough to overlap, covering most, but not all of the surface with black ink. If we want black, the spaces in between the dots disappear, and the ink covers the surface completely. The dots are printed small enough to escape the individual attention of the human eye. The eye mixes the color of the ink and the color of the paper showing through together. We call the mixture a "tint" of the original ink, a term that comes down to us from the traditional practice of mixing colored paint with white to produce a lighter color

Patterning The previous arrangement uses cells of 4 pixels each, and yields 5 possible gray-levels. The disadvantage of patterning is the loss of spatial resolution, making it acceptable only if the resolution of the image is lower than the resolution of the display. The use of patterning with the previous cells, results in a new image, with doubled dimensions. To obtain 256x256 new images, we have to use 128x128 original images: Left: original image 128x128, 5 gray levels; Right: resultant 256x256 binary image

Patterning Left: original image 128x128, 5 gray levels; Right: resultant 256x256 binary image

The most used halftoning techniques The images we will work on are given below: Left: 256 gray-levels bird's image; Right: some gray values

Thresholding The simplest technique for improving visual resolution is to use a threshold pattern. We create this pattern and compare with the original image. If the pixel in the original image exceeds the correspondent pixel in the threshold pattern, it is replaced by 1(white), otherwise, it is replaced by 0 ( black).

Constant Threshold In this case, the treshold pattern is a constant. For example, if T = 127, we have the following results: Left: binary bird; Right: the levels are divided in 2: black or white

Gaussian Pattern In this step, we change the constant pattern by the gaussian pattern showed below: Pattern for threshold: each cell in the image represents a gaussian curve

Gaussian Pattern The results obtained with this pattern are showed below: Left: binary bird; Right: the gray-levels, binarized by thresholding with the gaussian pattern

Noise pattern for thresholding To better see the effect of the threshold's pattern in the resultant binary image, we can, for example, use a noise pattern: The results, as can be seen below, are noisy binary images: Left: binary bird; Right: the gray-levels, binarized by thresholding with the noise pattern

Order Dithering This technique attempts to introduce a random error into the image. This error is represented by a dither matrix, which is compared with the image in a repeating checkerboard pattern (actually, we do the threshold with the pattern given by the dither matrix). The smallest ordered dither pattern is: A n*n gray levels image can be reproduced from a dither pattern Dn. Our examples are images of 256 gray levels; so, to use D8, we must reduce our number of gray levels to 64.

Order Dithering The elements of the dither matrix are thresholds The matrix is laid like a tile over the entire image and each pixel value is compared with the corresponding threshold from the matrix. The pixel becomes white if its value exceeds the threshold or black otherwise

Order Dithering The pattern given by D8 is: The results, as can be seen below, are better than the results with the thresholding techniques.

Which graphic file format is best for halftones? Macintosh or PC, you can't go wrong with TIFF format, and it is the preferred and the most widely supported printing format. PICT files are sometimes used and have been known to cause problems in QuarkXPress. Avoid PICT; stick with TIFF. Even if you are able to place a JPEG image into a desktop publishing application like Quark or Pagemaker, convert it to TIFF first, and you'll save yourself some heartache later.

See: -tech/dithering13.html m For color image see: