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Preface xxvii

TABLE 5: For students of cognitive science or artificial intelligence who want a basic
outline of the important notions of computer vision.
Week Chapter Sections Key topics
1 1, 2 1.1, 2.1, 2.2.x pinhole cameras, pixel shading models,
one inference from shading example
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 6.1, 6.2 texture representations from filters,
from vector quantization
6 7 7.1, 7.2 binocular geometry, stereopsis
8 9 9.1–9.3 segmentation ideas, applications,
segmentation by clustering pixels
9 11 11.1, 11.2 simple tracking strategies, tracking using matching,
optical flow
10 15 all classification
11 16 all classifying images
12 20 all looking at people
13 21 all image search and retrieval
14 17 all detection
15 18 all topics in object recognition

When the vector a has unit norm, the dot product a·b is equal to the (signed)
length of the projection of b onto a. More generally,
a · b = |a||b| cos θ,

where θ is the angle between the two vectors, which shows that a necessary and
sufficient condition for two vectors to be orthogonal is that their dot product be
zero.
The cross product (or outer product) of two vectors a =(a 1 ,a 2 ,a 3 ) T and
3
T
b =(b 1 ,b 2 ,b 3) in R is the vector
⎛ ⎞
a 2 b 3 − a 3 b 2
def
a × b = ⎝ a 3 b 1 − a 1 b 3 .
⎠
a 1 b 2 − a 2 b 1
Note that a × b =[a × ]b,where
⎛ ⎞
0 −a 3 a 2
def
[a × ] = ⎝ a 3 0 −a 1 .
⎠
−a 2 a 1 0
3
The cross product of two vectors a and b in R is orthogonal to these two
vectors, and a necessary and sufficient condition for a and b to have the same
direction is that a × b = 0.If θ denotes as before the angle between the vectors a
and b,itcan be shown that
|a × b| = |a||b||sin θ|.