Image Processing Reference

In-Depth Information

Fig. B.4
Right-angled

triangle

For this particular problem it might seem to be faster to do it by hand, as above,

instead of using Eq.
B.28
. This might also be true for such a simple problem, but

in general using Eq.
B.28
is definitely more efficient. Recall that you just have to

define the matrix and vectors, then the computer solves them for you—independent

of the number of equations and unknowns.

When implementing linear algebra in software, it is highly recommended to ap-

ply a built-in library as opposed to implementing the solution from scratch. This

is especially true for linear systems with more than three dimensions, since these

require iterative solutions.

B.8

Right-Angled Triangle

In Fig.
B.4
a right-angled triangle is shown. A right-angled triangle is defined as

θ
1
=

θ
2
. The three points
A
,
B
and
C
define the corners of the

triangle. The relationship between the lengths of the three edges is defined using

Pythagoras' theorem:

90° and
θ
3
=

90°

−

−
AB

+
−
AC

=
−
BC

2

2

2

(B.30)

From trigonometry we have

=
−
AC

=
−
AB

=
−
AC

−
BC

−
BC

−
AB

sin
(θ
2
)

,

cos
(θ
2
)

,

tan
(θ
2
)

(B.31)

B.9

Similar Triangles

In Fig.
B.5
two triangles are present. The outer triangle defined by the three points

ABC
and the inner triangle defined by the three points
DBE
. If the two triangles

have the same angles, i.e.,
θ
1
=

θ
4
,
θ
3
=

θ
5
, and
θ
2
=

θ
2
, then the triangles are said

to be
equiangular
or
similar
.

If we look at the outer triangle then we know from trigonometry that

−
BC

sin
(θ
1
)
=

−
CA

sin
(θ
2
)
=

−
AB

sin
(θ
3
)

(B.32)