Computer Science
Image Representation
Image representation refers to the methods used to store and manipulate visual data in a digital format. It involves converting images into a form that can be processed by computers, often using pixels to represent color and intensity. Common image representations include bitmap, vector, and digital signal processing techniques.
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eBook - PDF- Wesley E. Snyder, Hairong Qi(Authors)
- 2010(Publication Date)
- Cambridge University Press(Publisher)
4 Images: Formation and representation Computers are useless. They can only give us answers Pablo Picasso In this chapter, we describe how images are formed and how they are represented. Representations include both mathematical representations for the information con-tained in an image and for the ways in which images are stored and manipulated in a digital machine. In this chapter, we also introduce a way of thinking about images – as surfaces with varying height – which we will find to be a powerful way to describe both the properties of images as well as operations on those images. 4.1 Image Representations In this section, we discuss several ways to represent the information in an image. These representations include: iconic, functional, linear, probabilistic, spatial fre-quency, and relational representations. 4.1.1 Iconic representations (an image) An iconic representation of the information in an image is an image. “Yeah, right; and a rose is a rose is a rose.” When you see what we mean by functional, linear, and relational representations, you will realize we need a word 1 for a representa-tion which is itself a picture. Some examples of iconic representations include the following. 2D brightness images, also called luminance images. The things you are used to x y f ( x , y ) calling “images.” These might be color or gray-scale. (Be careful with the words “black and white,” as that might be interpreted as “binary”). We usually denote the brightness at a point x , y as f ( x , y ). Note: x and y could be integers (in this case, we are referring to discrete points in a sampled image; these points are called “pixels,” short for “picture elements”), or real numbers (in this case, we are thinking of the image as a function). 1 “Iconic” comes from the Greek word meaning picture. 38
eBook - PDF- Vojin G. Oklobdzija(Author)
- 2019(Publication Date)
- CRC Press(Publisher)
12.4 Image Sequence Representation 12.4.1 What Does Representation Mean? The term ‘‘representation’’ may require some explanation. Perhaps the best way to do so is to consider some examples of familiar representations. For simplicity, 2-D examples are used. Extension to 3-D is relatively straightforward. 12.4.1.1 Pixel Representation The pixel representation is so common and intuitive that it is usually considered to be ‘‘the image.’’ More precisely, however, it is a linear sum of weighted impulses: u ( m , n ) ¼ X N 1 m 0 ¼ 0 X N 1 n 0 ¼ 0 u ( m 0 , n 0 ) d ( m m 0 , n n 0 ) (12 : 25) where u ( m , n ) is the image, u ( m 0 , n 0 ) are the coefficients of the representation (numerically equal to the pixel values in this case) and the d ( m m 0 , n n 0 ) play the role of basis functions. 12.4.1.2 DFT The next most familiar representation (at least to engineers) is the DFT, in which the image is expressed in terms of complex exponentials: u ( m , n ) ¼ 1 N 2 X N 1 h ¼ 0 X N 1 k ¼ 0 v ( h , k ) W hm N W kn N (12 : 26) where 0 m , n N 1 and W N ¼ e j 2 p N (12 : 27) In this case, v ( h , k ) are the coefficients of the representation and the 2-D complex exponentials W hm N W kn N are the basis functions. The choice of one representation over the other (pixel vs. Fourier) for a given application depends on the image characteristics that are of most interest. The pixel representation makes the spatial organization of intensities in the image explicit. Since this is the basis of the visual stimulus, it seems more natural. The Fourier representation makes the composition of the image in terms of complex exponentials (frequency components) explicit. The two representations emphasize their respective characteristics (spatial vs. frequency), to the exclusion of all others. If a mixture of characteristics is desired, different representations must be used.
eBook - PDF- Henry M. Walker(Author)
- 2012(Publication Date)
- Chapman and Hall/CRC(Publisher)
59 C H A P T E R 3 How Are Images Represented (and Does It Matter)? Y ou scanned an image of your cats, Shamrock and Muffin, and put it on the Web, and now you want to print out a copy. As you try to print the image, you encounter two problems: First, your computer is taking a very long time to open the image on your Web site, and, second, the printed image doesn’t look nearly as good as the one you viewed in your Web browser. This example illustrates that the way computers store images can have a significant impact on how a picture might be used. Pictures stored in a small file save space but may look fuzzy or blurred; those stored in an intermediate-sized file may display well on a com-puter monitor, but appear grainy or fuzzy when printed. Pictures stored in a large-sized format may display nicely on paper, but may consume considerable space and require much time to move between machines (e.g., download over the Internet). Further, computers can store pictures in several common formats. Each format has advantages for some purposes, but each format also has limitations. We begin this chapter by considering several basic ideas behind the storage of images, and we then review several different approaches for image storage. When storing pictures, a user often must make decisions regarding file format and file size, and these decisions can affect how effectively the picture can be used in various contexts. How are images created on a computer monitor or on paper with a printer? When an artist paints a picture, the artist may vary color continuously over a region. In mixing paints, the painter has complete control of the combinations and hues of each color, allowing a seemingly infinite range of possibilities. Further, the painter can apply paint anywhere; for example, a bowl may be quite round, with its silhouette curving smoothly.
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