What digital characteristics affect the number of shades of gray available for image display?

1. Basic  Terminology

Key Concepts

digital images
resolution
pixel dimensions
bit depth
dynamic range
file size
compression
file formats

additional reading

BIT DEPTH is determined by the number of bits used to define each pixel. The greater the bit depth, the greater the number of tones (grayscale or color) that can be represented. Digital images may be produced in black and white (bitonal), grayscale, or color.

A bitonal image is represented by pixels consisting of 1 bit each, which can represent two tones (typically black and white), using the values 0 for black and 1 for white or vice versa.

A grayscale image is composed of pixels represented by multiple bits of information, typically ranging from 2 to 8 bits or more.

Example: In a 2-bit image, there are four possible combinations: 00, 01, 10, and 11. If "00" represents black, and "11" represents white, then "01" equals dark gray and "10" equals light gray. The bit depth is two, but the number of tones that can be represented is 2 2 or 4. At 8 bits, 256 (2 8 ) different tones can be assigned to each pixel.

A color image is typically represented by a bit depth ranging from 8 to 24 or higher. With a 24-bit image, the bits are often divided into three groupings: 8 for red, 8 for green, and 8 for blue. Combinations of those bits are used to represent other colors. A 24-bit image offers 16.7 million (2 24 ) color values. Increasingly scanners are capturing 10 bits or more per color channel and often outputting 8 bits to compensate for "noise" in the scanner and to present an image that more closely mimics human perception.

Bit Depth: Left to right - 1-bit bitonal, 8-bit grayscale, and 24-bit color images.

Binary calculations for the number of tones represented by common bit depths:

© 2000-2003 Cornell University Library/Research Department

We can write ten different digits, 0,1,2,3,4,5,6,7,8, and 9, .  This system probably developed because we have ten fingers.

When we write larger numbers (more than one digit) the position of a digit within the number has a certain value, 1, 10, 100, 1000 etc as shown here.

The value of a number we have written is just the sum of the values represented by each digit position.

In this example, 8000 + 500 + 30 + 4 =8,534.

The photograph of Roentgen shown above was obtained with a photographic film, and is an analog image. The brightness at any location is a continuous variable that ranges from a minimum (black) to a maximum (white), and can take on any intermediate value. The image intensity can be obtained at any location.

A digital version of this photograph can be obtained by sampling the light intensity along a two dimensional grid (middle). The sampling grid has 40 squares pixels) on the horizontal axis, and 60 grids on the vertical axis, so that there are a total of 40 x 60 squares in the grid. Each square (pixel) can take on a discrete value; for example, the intensity can range from 0 to 255 for a total of 256 shades of gray (see case 3 below). Suppose the grid is superimposed on the photograph, and the average intensity in each square is measured. Each square will take on a discrete value ranging from 0 (i.e., black) to 255 (white), with a value of 127 being an intermediate gray. The digital image is made up of 40 x 60 such discrete numbers and is shown on the right.

Digital image characteristics

Matrix and pixel size

Consider a conventional photograph that has dimensions of 20 cm x 20 cm (this is often referred to as the Field of View). When the photograph is acquired in a digital form with a matrix size of 1000 x 1000, then each pixel has a linear dimension of (20/1000) cm, or 200 micron (um). Increasing the matrix size to 2000 x 2000, reduces the pixel size to 100 m, whereas reducing the matrix size to 500 x 500 increases the pixel size to 400 m.

Pixel depth

Each pixel must take on a discrete value. Use of 1 bit (binary digit) to "code" for the pixel value means that the pixel can take on one of two discrete values (1 or 0), which would correspond to a pixel that is either black (0) or white (1). If two bits are used to code for a pixel, then four discrete values are possible (i.e., 00, 01, 10, and 11). In general, if n bits are used to code for one pixel, the number of discrete values is 2n. 8 bits (equal to one Byte) can code for 256 discrete values (shades of gray); adding an extra bit will double the number of discrete values (i.e., 9 bits codes for 512 shades of gray), whereas subtracting one bit halves the number of shades of gray (i.e., 7 bits allows 128 shades of gray).

Image size

Computers normally store information using a discrete number of bytes; accordingly, the value of any given pixel will use 1 byte, 2 byte, 3 byte etc. The total number of pixels is given by M x N, where M is the matrix size in the horizontal direction, and N is the matrix size in the vertical direction. The total data in an image is thus given by N x M x bytes/pixel. For a 1000 x 1000 matrix size, with 256 shades of gray (1 byte), the storage requirements would be 1 Mbyte; increasing the shades of gray from 256 to 1024 would mean increasing the number of bytes per pixel from 1 to 2, and the image size to 2 Mbyte (note that using 9 bit, 10 bit, 11 bit …. 16 bit to code for one pixel would all require 2 Byte).

Which of the following factors influence the grayscale of a digital radiograph?

What determines the number of gray tones available within each individual element?

What are the characteristics of digital radiographic image receptors?

Which factors affect spatial resolution in digital imaging?