Abstract
Jaggies (staircasing effects) along slanted lines or curved edges are omnipresent in digital imaging. They are so widespread in digital display devices that very often they are associated with the modern “computerized” world (and sometimes even intentionally introduced into artworks such as logos, advertisements, etc. to convey a modern “pixelized” look). Although this subject is not new, it still remains an important issue in the design of modern digital display and printing devices. In the classical literature, jaggies are often considered as aliasing artifacts; and yet some other references consider them instead as reconstruction artifacts. The present tutorial revisits this question and tries to elucidate the real nature of this phenomenon using Fourier-based considerations. It shows that the jaggies can be either aliasing artifacts due to poor sampling in capture, or the result of poor reconstruction; and it explains the implications thereof on the elimination of unwanted jaggies.
Highlights
It is well known that the approximation of continuous lines or shapes by pixels on a discrete raster grid may cause the appearance of jagged edges on the shape’s borders
Rendering of digital text and graphics on such devices involves conversions from analog to digital and back, yielding jaggies as unavoidable artifacts. This phenomenon is not new, it still remains an important issue in the design of modern digital display and printing devices
The present tutorial sheds some light on this phenomenon
Summary
It is well known that the approximation of continuous lines or shapes by pixels on a discrete raster grid may cause the appearance of jagged edges ( known as “jaggies” or “staircasing effects”) on the shape’s borders (see Refs. 1 and 2, p. 14). Such jaggies often occur during the sampling process (analog-to-digital conversion) along slanted or curved lines We will see that in many cases, jaggies are aliasing phenomena, but in other cases they are only generated in the reconstruction stage, i.e., when the display device recreates a continuous-world signal from the sampled one Note that throughout this tutorial, we assume that the jaggies in question are sufficiently big to be seen by the unaided eye, and we do not discuss issues related to the human visual system, modulation transfer functions, etc. This tutorial does not intend to provide formal theorems and proofs, but rather favors an informal approach using Fourier-based considerations and pictorial illustrations
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