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82 2 Image formation

ratio (PSNR), which is derived from the average mean square error,
1 2
ˆ
MSE = I(x) − I(x) , (2.117)
n
x
ˆ
where I(x) is the original uncompressed image and I(x) is its compressed counterpart, or
equivalently, the root mean square error (RMS error), which is defined as
√
RMS = MSE. (2.118)

The PSNR is defined as
2
I max I max
PSNR = 10 log 10 = 20 log 10 , (2.119)
MSE RMS
where I max is the maximum signal extent, e.g., 255 for eight-bit images.
While this is just a high-level sketch of how image compression works, it is useful to
understand so that the artifacts introduced by such techniques can be compensated for in
various computer vision applications.

2.4 Additional reading

As we mentioned at the beginning of this chapter, it provides but a brief summary of a very
rich and deep set of topics, traditionally covered in a number of separate fields.
A more thorough introduction to the geometry of points, lines, planes, and projections
can be found in textbooks on multi-view geometry (Hartley and Zisserman 2004; Faugeras
and Luong 2001) and computer graphics (Foley, van Dam, Feiner et al. 1995; Watt 1995;
OpenGL-ARB 1997). Topics covered in more depth include higher-order primitives such as
quadrics, conics, and cubics, as well as three-view and multi-view geometry.
The image formation (synthesis) process is traditionally taught as part of a computer
graphics curriculum (Foley, van Dam, Feiner et al. 1995; Glassner 1995; Watt 1995; Shirley
2005) but it is also studied in physics-based computer vision (Wolff, Shafer, and Healey
1992a).
The behavior of camera lens systems is studied in optics (M¨ oller 1988; Hecht 2001; Ray
2002).
Some good books on color theory have been written by Healey and Shafer (1992); Wyszecki
and Stiles (2000); Fairchild (2005), with Livingstone (2008) providing a more fun and infor-
mal introduction to the topic of color perception. Mark Fairchild’s page of color books and
links 25 lists many other sources.
Topics relating to sampling and aliasing are covered in textbooks on signal and image
processing (Crane 1997; J¨ ahne 1997; Oppenheim and Schafer 1996; Oppenheim, Schafer,
and Buck 1999; Pratt 2007; Russ 2007; Burger and Burge 2008; Gonzales and Woods 2008).

2.5 Exercises

A note to students: This chapter is relatively light on exercises since it contains mostly
background material and not that many usable techniques. If you really want to understand
25 http://www.cis.rit.edu/fairchild/WhyIsColor/books links.html.