A synthetic camera model to test calibration procedures

1
A synthetic camera model to test calibration
procedures

• A four step procedure (last slide) based on an
  initial position (LookAt) and 13 parameters
• (?x , ?y ?z ) local Euler rotations
• (dtx dty dtz) local displacement
• (fx fy sh ?1 ?2 cx cy) camera internal
  parameters

2
Initial extrinsic parameters user input
upc
Camera initial extrinsic parameters
atc
oc
upc
oc
atc
The camera must start in a given position (not
too far from the final solution!). The module
must have an initialization procedure.
3
Initial extrinsic parameters first transformation
oc
zw
yw
xw
origin
Notation
system
vector
4
Incremental rotation with Euler angles ?x ?y ?z
z
z
z
qz
y
y
y
qy
qx
x
x
x
for small ?s
where cy cos?y, sx sin?x, etc..
where cy cos?y, sx sin?x, etc..
5
Incremental translation dtx dty dtz
t
dt
t0
zw
yw
xw
6
Transformation from global to local system
next step camera projection
ycd
yc
q
zc
xcd
xc
7
Projection into pixels
where
inclined projections
axis in the middle of the image
yd
xd
projected point written in the coordinate system
(xd,yd) in pixels
center of distortion
8
Taking radial deformation into account
yd
xd
Note that ?1and ?2 are not the same as Tsais k1
and k2. The map shown here is in the inverse
direction.
9
Changing the origin of the image
yd
yim
yd
xd
xd
xim
10
Putting all together(xw, yw, zw)T ?(xc, yc,
zc)T ?(xcd ,ycd )T ?(xd, yd)T ?(xim,yim)T
Given and initial position given by Lat and
(?x, ?y ?z dtx dty dtz fx fy sh ?1 ?2 cx cy)we
can compute xim and yim by
(step 1)
(step 2)
(step 3)
(step 4)