Antialiasing: A technique for smoothing jagged lines on a computer graphics image—an implementation on the Amiga

PETER P. TANNER 0 1 2 PIERRE JOLICOEUR 0 1 2 WILLIAM B. COWAN 0 1 2 KELLOGG BOOTH 0 1 2 FLYNN D. FISHMAN 0 1 2 0 maybe addressed to PierreJolicoeur, Psychology Department, University of Waterloo , Waterloo, Ontario N2L 3Gl , Canada 1 University of Waterloo , Waterloo, Ontario , Canada 2 TANNER , JOLICOEUR, COWAN, BOOTH, AND FISHMAN Images displayed on computer graphics displays often suffer from the presence of aliasing artifacts that give a jagged appearance to lines or polygonedges displayed on the screen. This paper details the problemsassociatedwith these artifacts and presents a method for drawing antialiased lines-ones in which the artifacts have been considerably reduced. The line-drawing routine is further developed to incorporate gamma correction, to take into account the nonlinear relationship between the intensity of the light emission from the phosphor of the monitor and the grayscale values used to control the intensity on the screen. - Aliasing Raster display systemsthat use cathode-ray tube (CRT) displays, ink jet, electrostatic, or laser printers create im ages with arrangements of colored dots. The resulting im ages, therefore, are only approximate, apart from the rare case in which it is actually desired to create an image that really appears to be made up of dots. The quality of the approximation depends on the resolution of the screen, the resolution of the color informationthat can be stored for each dot, and the care taken to eliminate the effects caused by using this approximation of the desired image. Figure I showsa collection of "straight lines" as drawn on the screen of a personal computer using Bresenham's algorithm, an algorithmtypical of thoseused to draw lines on computer displays (Bresenham, 1965). The jaggies (i.e., the staircase effect) visible on these lines are the result of drawing the line into a matrix of pixels with no attention given to line smoothing or antialiasing. The presence of jaggies has a number of consequences. First, it may give a viewer strong cues as to whether a line is perfectly horizontal or vertical or not. While this cue may be helpful in certain computer graphics applications, it is an artificial information aid whose presence is normally not intended by the experimenter. Second, it may reduce the subject's capacity to understand the image on the dis play. For example, Booth, Bryden, Cowan, Morgan, and Plante (1987) showed that, under certain conditions, there was a significant improvement in a subject's ability to count the number of local elements in an image when that image was processed to reduce the aliasing artifacts. Third, the location and number of jaggies change substan tially when a line moves or changes orientation. A sub ject who views a rotating line receives significant cues that indicate the onset and speed of the rotation from the movement of the jaggies along the line. A subject com paring images A and B, where B is a rotated version of A, may well conclude that they are different images, be cause of the different positions of the steps on the lines within the image. Fourth, for objects that are small in re lation to the pixel grid, the staircase artifacts can cause different parts of an image to change their spatial rela tionships. An example of this occurred in an air traffic simulation system in which distant airplanes, covering only a few pixels, would change shape as they moved. Their wings would drop from one row of pixels to the next at a different time than would the rest of the plane, leading to confusion as to whether it was a midwing plane or an upperwing plane (for another example, see Lind holm, 1988). Finally (although this list is not exhaustive), jaggies result in Moire patterns (Crow, 1977) if there are several near-parallel lines drawn close together. Antialiasing techniques make the aliasing artifacts in rendered images less noticeable. One such technique is to defocus the picture tube on which the image is dis played. Although this approach does work to some ex tent, it does so at the cost of a considerable reduction in the viewable resolution of the image. A second approach is to use a higher-resolution display. For example, changing from 512 x 512 to 1,024 x 1,024 resolution will improve the image. However, such an ap proach is very expensive, it only reduces the aliasing er ror by a factor of two, and it still leaves the aliasing ar tifacts quite visible. Supersarnpling is a third antialiasing technique, in which the display is treated as if it has a higher resolution than is actually the case. Each pixel on the display is composed of several higher-resolution pixels or subpixels. The values of the subpixels for this virtual higher-resolution display are computed in the manner described above, each sub pixel being assigned a value of full on or full off. Then the values of the set of subpixels that constitute each pixel of the actual display are averaged according to some rule, the result being a display pixel that may be set to a gray level between full on and full off. Thus the use of this technique requires the ability to set the intensity of in dividual pixels to intermediate values between full on and full off. This technique increases the time required to draw a line. Increasing the virtual resolution of the display by a factor of n requires n2 subpixels per pixel, with a com putational load also increasing by a factor of n", which is unacceptably high. The fourth and final technique consists of prefiltering the data before sampling. As is described in the next sec tion, this method takes into account the reasons for the aliasing artifacts and takes steps to remove them. Most antialiasing methods in common use employ prefiltering. In particular, the common implementation of the anti aliased paintbrush is filtered to smooth its edges. As with the supersampling technique, prefiltering tech niques require the ability to set the intensity level of any pixel to intermediate values between full on and full off. A consequence of this requirement is that the framebuffer must have more than one bit to represent the gray level or color of each pixel. A further discussion of the aliasing problem and of ap proaches to antialiasing can be found in Rogers (1985) and Foley and Van Dam (1981). Antialiased Lines The term aliasing is used to describe the result of a sig nal being sampled at a rate lower than twice its frequency, as illustrated in Figure 2. The signal at the top of Figure 2 is sampled at a frequency indicated by the dots on the waveform. The result of this sampling (Figure 2, bottom) is a signal that is an alias of the original and bears little obvious relation to the original. The line-drawing al gorithm used to draw the lines in Figure 1 can be thought of as taking a sample at the center point of each pixel. If the line (modeled as a polygon or band with a width of one pixel) crosses this center point, the pixel is turned on, if the line does not cro (...truncated)