Camera Calibration for 3D Reconstruction and View Transformation - 3D Modeling and Animation: Synthesis and Analysis Techniques for the Human Body - page 114

p

1

− p

3

x

im
r

− p

1

+ p

3
1

x

im
r

− p

1

+ p

3

x

im
r

− p

1

+ p

3

x

im
r

r 4 r 4 r 1 r r 2 r 2 r 3 r 3 w

x

p

2

− p

3
4

y

im
r

− p

2
1

+ p

3
1

y

im
r

− p

2

+ p

3

y

im
r

− p

2
3

+ p

3

y

im
r

r 4 r r r r 2 r 2 r r 3 w

= y

1 3

4

im
l

1
1

3
1

im
l

1
2

3 im

l

1 3

3

im
l

p − p x − p + p x − p + p x − p + p x

l 4 l l l l l 2 l 3 l w

z

. (51)

2
4

3
4

im
l

2
1

3
1

im
l

2
2

3
2

im
l

2
3

3
3

im
l

p − p y − p + p y − p + p y − p + p y w

x

l l l l l l l l

b B

From equation 51, x w can be easily calculated using least squares as:

( ) ( )

−

. (52)

x

w

= B

T

B B

T

b

Figure 3. The projection and 3-D reconstruction process of the 3-D face
model. From two cameras C and C we get a pair of stereo images
through projection. 3-D reconstruction is then applied on each pair of
corresponding points

im

l x to obtain their original 3-D
correspondence x w . The reconstructed 3-D model can then be projected
into an arbitrary virtual camera C to form a virtual view. This is just the
traditional view transformation process. Alternatively, the 3-D model
reconstruction step could be neglected and the virtual view synthesized
directed from the two stereo views. This image-based-rendering idea will be
explored in the next section.

im
r

x and