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1.5 A note on notation 25

1.5 A note on notation

For better or worse, the notation found in computer vision and multi-view geometry textbooks
tends to vary all over the map (Faugeras 1993; Hartley and Zisserman 2004; Girod, Greiner,
and Niemann 2000; Faugeras and Luong 2001; Forsyth and Ponce 2003). In this book, I
use the convention I first learned in my high school physics class (and later multi-variate
calculus and computer graphics courses), which is that vectors v are lower case bold, matrices
M are upper case bold, and scalars (T, s) are mixed case italic. Unless otherwise noted,
vectors operate as column vectors, i.e., they post-multiply matrices, Mv, although they are
sometimes written as comma-separated parenthesized lists x =(x, y) instead of bracketed
T
column vectors x =[xy] . Some commonly used matrices are R for rotations, K for
calibration matrices, and I for the identity matrix. Homogeneous coordinates (Section 2.1)
2
are denoted with a tilde over the vector, e.g., ˜x =(˜x, ˜y, ˜w)= ˜w(x, y, 1) = ˜w¯x in P . The
cross product operator in matrix form is denoted by [] .
×

1.6 Additional reading

This book attempts to be self-contained, so that students can implement the basic assignments
and algorithms described here without the need for outside references. However, it does pre-
suppose a general familiarity with basic concepts in linear algebra and numerical techniques,
which are reviewed in Appendix A, and image processing, which is reviewed in Chapter 3.
Students who want to delve more deeply into these topics can look in (Golub and Van
Loan 1996) for matrix algebra and (Strang 1988) for linear algebra. In image processing,
there are a number of popular textbooks, including (Crane 1997; Gomes and Velho 1997;
J¨ ahne 1997; Pratt 2007; Russ 2007; Burger and Burge 2008; Gonzales and Woods 2008). For
computer graphics, popular texts include (Foley, van Dam, Feiner et al. 1995; Watt 1995),
with (Glassner 1995) providing a more in-depth look at image formation and rendering. For
statistics and machine learning, Chris Bishop’s (2006) book is a wonderful and comprehen-
sive introduction with a wealth of exercises. Students may also want to look in other textbooks
on computer vision for material that we do not cover here, as well as for additional project
ideas (Ballard and Brown 1982; Faugeras 1993; Nalwa 1993; Trucco and Verri 1998; Forsyth
and Ponce 2003).
There is, however, no substitute for reading the latest research literature, both for the lat-
est ideas and techniques and for the most up-to-date references to related literature. 15 In this
book, I have attempted to cite the most recent work in each field so that students can read them
directly and use them as inspiration for their own work. Browsing the last few years’ con-
ference proceedings from the major vision and graphics conferences, such as CVPR, ECCV,
ICCV, and SIGGRAPH, will provide a wealth of new ideas. The tutorials offered at these
conferences, for which slides or notes are often available on-line, are also an invaluable re-
source.

15 For a comprehensive bibliography and taxonomy of computer vision research, Keith Price’s Annotated Com-
puter Vision Bibliography http://www.visionbib.com/bibliography/contents.html is an invaluable resource.