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Preface xxvi

TABLE 4: A syllabus for students who are primarily interested in the applications of
computer vision.
Week Chapter Sections Key topics
1 1, 2 1.1, 2.1, 2.2.4 pinhole cameras, pixel shading models,
photometric stereo
2 3 3.1–3.5 human color perception, color physics, color spaces,
image color model
3 4 all linear filters
4 5 all building local features
5 6 6.3, 6.4 texture synthesis, image denoising
6 7 7.1, 7.2 binocular geometry, stereopsis
7 7 7.4, 7.5 advanced stereo methods
8 8, 9 8.1, 9.1–9.2 structure from motion with perspective cameras,
segmentation ideas, applications
9 10 10.1–10.4 Hough transform, fitting lines, robustness, RANSAC,
10 12 all registration
11 14 all range data
12 16 all classifying images
13 19 all image based modeling and rendering
14 20 all looking at people
15 21 all image search and retrieval

usually denoted by Roman or Greek bold-italic letters (e.g., v, P ,or ξ), but the
−−→
vector joining two points P and Q is often denoted by PQ. Lower-case letters are
normally used to denote geometric figures in the image plane (e.g., p, p, δ), and
upper-case letters are used for scene objects (e.g., P, Π). Matrices are denoted by
Roman letters in calligraphic font (e.g., U).
3
The familiar three-dimensional Euclidean space is denoted by E ,and the
vector space formed by n-tuples of real numbers with the usual laws of addition
n
and multiplication by a scalar is denoted by R , with 0 being used to denote the
zero vector. Likewise, the vector space formed by m × n matrices with real entries
is denoted by R m×n .When m = n, Id is used to denote the identity matrix—
that is, the n × n matrix whose diagonal entries are equal to 1 and nondiagonal
entries are equal to 0. The transpose of the m × n matrix U with coefficients u ij
T n
is the n × m matrix denoted by U with coefficients u ji . Elements of R are often
T
identified with column vectors or n × 1 matrices, for example, a =(a 1 ,a 2 ,a 3 ) is
the transpose of a 1 × 3 matrix (or row vector), i.e., an 3 × 1 matrix (or column
3
vector), or equivalently an element of R .
The dot product (or inner product) of two vectors a =(a 1 ,... ,a n ) T and
T
n
b =(b 1 ,... ,b n ) in R is defined by
a · b = a 1 b 1 + ··· + a n b n ,
T
T
and it can also be written as a matrix product, i.e., a · b = a b = b a.We denote
2
by |a| = a · a the square of the Euclidean norm of the vector a and denote by d
−−→
n
the distance function induced by the Euclidean norm in E , i.e., d(P, Q)= |PQ|.
Given a matrix U in R m×n , we generally use |U| to denote its Frobenius norm, i.e.,
the square root of the sum of its squared entries.