Raster images

A vector image comprises data describing a set of geometric primitives, each of which is associated with grey or colour values.

A process of interpretation – rasterizing, or raster image processing, or ripping – is necessary to convert

a vector image to a raster. Vector suggests a straight line but paradoxically, “vector” images commonly contain primitives describing curves.

A digital image is represented by a rectangular array (matrix) of picture elements (pels, or pixels). Pixel arrays of several image standards are sketched in Figure 1.1. In a greyscale system each pixel comprises a single component whose value is related to what is loosely called brightness. In a colour system each pixel comprises several components – usually three – whose values are closely related to human colour perception.

Historically, a video image was acquired at the camera, conveyed through the channel, and displayed using analog scanning; there was no explicit pixel array. Modern cameras and modern displays directly represent the discrete elements of an image array having fixed structure. Signal processing at the camera, in the pipeline, or at the display may perform spatial and/or temporal resampling to adapt to different formats.

[0, 0]

480i29.97 (SD) Video, 300 Kpx

HDV

HD, 1 Mpx

Workstation, 1 Mpx

SXGA, 1.25 Mpx

HD, 2 Mpx

UXGA, 2 Mpx

In art, the frame surrounds the picture; in video, the frame is the picture.

A computer enthusiast refers to the image column and row counts (width× height) as resolution. An image engineer reserves the term resolution for the image detail that is acquired, conveyed, and/or delivered. Pixel count imposes an upper limit to the image detail; however, many other factors are involved.

The pixel array is for one image is a frame. In video, digital memory used to store one image is called

a framestore; in computing, it’s a framebuffer. The total pixel count in an image is the number of image columns

NC (or in video, samples per active line, SAL) times the number of image rows NR (or active lines, LA). The total pixel count is usually expressed in megapixels (Mpx).

In video and in computing, a pixel comprises the set of all components necessary to represent colour (typically red, green, and blue). In the mosaic sensors typical of digital still cameras (DSCs) a pixel is any colour component individually; the process of demosaicking interpolates the missing components to create a fully populated image array. In digital cinema cameras the DSC interpretation of pixel is used; however, in a digital cinema projector, a pixel is a triad.

The value of each pixel component represents brightness and colour in a small region surrounding the corresponding point in the sampling lattice.

Pixel component values are quantized, typically to an integer value that occupies between 1 and 16 bits – and often 8 or 10 bits – of digital storage. The number of bits per component, or per pixel, is called the bit depth. (We use bit depth instead of width to avoid confusion: The term width refers to the entire picture.)

Aspect ratio

Aspect ratio is simply the ratio of an image’s width to its height. Standard aspect ratios for film and video are sketched, to scale, in Figure 1.2. What I call simply aspect ratio is sometimes called display aspect ratio

Film 35 mm still film

image 3:2 Cinema film

1.5:1 1.85:1

Figure 1.2 Aspect ratio of video, HD, and film are compared. Aspect ratio is properly written width:height (not height:width). Conversion among aspect ratios is fraught with difficulty.

Cinema film

2.4:1

In Europe and Asia, 1.66:1 was the historical standard for cinema, though 1.85 is increasingly used owing to the worldwide market for entertainment imagery.

FHA: Full-height anamorphic

Schubin, Mark (1996), “Searching for the perfect aspect ratio,” in SMPTE Journal 105 (8): 460–478 (Aug.).

Figure 1.3 The choice of 16:9 aspect ratio for HD came about because 16:9 is very close to the geometric mean of the 4:3 picture aspect ratio of conventional television and the 2:4:1 picture aspect ratio of CinemaScope movies.

(DAR) or picture aspect ratio (PAR). Standard-definition

(SD) television has an aspect ratio of 4:3.

Equation 1.1 relates picture and sample aspect ratios. To assign n square-sampled pixels to a picture having aspect ratio AR, choose image column and image row counts (c and r, respectively) according to Equation 1.2.

Cinema film commonly uses 1.85:1 (which for historical reasons is called either flat or spherical), or 2.4:1 (“CinemaScope,” or colloquially, ’scope). Many films are 1.85:1, but “blockbusters” are usually 2.4:1. Film at 2.4:1 aspect ratio was historically acquired using an aspherical lens that squeezes the horizontal dimension of the image by a factor of two. The projector is equipped with a similar lens, to restore the horizontal dimension of the projected image. The lens and the technique are called anamorphic. In principle, an anamorphic lens can have any ratio; in practice, a ratio of exactly two is ubiquitous in cinema.

Widescreen refers to an aspect ratio wider than 4:3. High-definition (HD) television is standardized with an aspect ratio of 16:9. In video, the term anamorphic usually refers to a 16:9 widescreen variant of a base video standard, where the horizontal dimension of the 16:9 image occupies the same width as the 4:3 aspect ratio standard. Consumer electronic equipment rarely recovers the correct aspect ratio of such conversions (as we will explore later in the chapter.)

HD is standardized with an aspect ratio of 16:9 (about 1.78:1), fairly close to the 1.85:1 ordinary movie aspect ratio. Figure 1.3 below illustrates the origin of the 16:9 aspect ratio. Through a numerological coincidence apparently first revealed by Kerns Powers, the

4:3

16:9

≈2.4:1

y

II I

III IV

Figure 1.4 Cartesian coordinates [x, y] define four quadrants. Quadrant I contains points having positive x and y values. Coordinates in quadrant I are used in some imaging systems. Quadrant IV contains points having positive x and negative y. Raster image coordinates are ordinarily represented with image row numbers increasing down the height of the image – that is, in quadrant IV, but omitting the negative sign on the y values.

geometric mean of 4:3 (the standard aspect ratio of conventional television) and 2.4 (the aspect ratio of a CinemaScope movie) is very close – within a fraction

of a percent – to 16:9. (The calculation is shown in the lower right corner of the figure.) A choice of 16:9 for HD meant that SD, HD, and CinemaScope shared the same “image circle”: 16:9 was a compromise between the vertical cropping required for SD and the horizontal cropping required for CinemaScope.

Geometry

In mathematics, coordinate values of the (two-dimen- sional) plane range both positive and negative. The plane is thereby divided into four quadrants (see Figure 1.4). Quadrants are denoted by Roman numerals in the counterclockwise direction. In the continuous image plane, locations are described using Cartesian coordinates [x, y] – the first coordinate is associated with the horizontal direction, the second with the vertical. When both x and y are positive, the location is in the first quadrant (quadrant I). In image science, the image lies in this quadrant. (Adobe’s Postscript system uses first-quadrant coordinates.)

In matrix indexing, axis ordering is reversed from Cartesian coordinates: A matrix is indexed by row then column. The top row of a matrix has the smallest index, so matrix indices lie in quadrant IV. In mathematics, matrix elements are ordinarily identified using 1-origin indexing. Some image processing software packages use 1-origin indexing – in particular, matlab and Mathematica, both of which have deep roots in mathematics. The scan line order of conventional video and image processing usually adheres to the matrix convention, but with zero-origin indexing: Rows and columns are usually numbered [r, c] from [0, 0] at the top left. In other words, the image is in quadrant IV (but eliding the negative sign on the y-coordinate), but ordinarily using zero-origin indexing.

Digital image sampling structures are denoted width× height. For example, a 1920× 1080 system has columns numbered 0 through 1919 and rows (historically, “picture lines”) numbered 0 through 1079.