International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004
is possible to establish the position of any object point O in
the En and { system, using simple geometric equations
(sec figure 2).
MR
i
Bx: et
Figure 2. Determination of the position of a point
Xo 7 d: cosa: sind
yo7 d: sina (2)
z97-d':cosa: cosa
Where 9, a are determined as previously shown (1).
In order to determine the previously defined distances for
each pixel of the digital image, a dense digital surface model
(DDSM) can be used. These 3D models are today easily
obtained by laser scanners.
The traditional RGB radiometric data of the image, together
with a “distance matrix” derived from a laser scanner data
set, lcad to a new concept: the “Solid Image".
(2 Bytes/pixel)*
(4 Bytes/pixel)"
BLUE
GREEN (
RED
Tae
PE ER
* J) INTEGER *2: Distances up to 327.27 m
=) REAL*4: Any distances (up to 9999,99 m)
Figure 3. The structure of the Solid Image
A digital image is usually made up of threc matrices where
the fundamental RGB (Red, Green and Blue) radiometric
components are stored.
The distance values corresponding to each pixel are stored in
a supplementary matrix D that has the same size as the RGB
matrices, in terms of lines and columns.
A Solid Image is therefore made up of 4 matrices: R, G, B
and D (see Fig. 3).
[n order to obtain the distance values that have to be stored in
the new matrix, the laser scanner and the photograph should
be made from two taking points close to each other, in order
to reduce the shaded areas, of which it is not possible to
determine the 3D position.
In addition, it is possible to add to the previously described
Solid Image another set of information. Recent laser scanners
are also able to measure the reflectivitv value for cach point
of the “cloud” (in terms of % of reflected laser beam).
This set of information is not yet frequently used in laser data
treatment commercial software, but it should not be neglected
when dealing with research. The reflectivity value is related
to the type of material the object is made up of, an aspect that
could be of fundamental importance in the analysis and
development of 3D models.
These reflectivity values are known, as for the distances. This
set of mformation can be interpolated and stored in a fifth
“reflectivity matrix” A. ;
A Solid Image obtained using such modern laser scanners can
therefore be made up of 5 matrices: R, G, B, D and A.
1.2 Calibration of the image
In order to fill the D and A matrices with correct distance and
reflectivity values, it is first of all necessary to determine the
image orientation (3 rotations + 3 translations) and the image
calibration values (lens distortion, principal distance and
coordinates of the principal point).
This can be achieved by measuring the image coordinates for
a sufficient number of control points. The procedure can be
made fully automatic if a set of high reflectivity markers is
used to determine the control point positions both on the
image and inside the DDSM [Bornaz, Rinaudo, Lingua
2002]. In this case, orientation and calibration parameters of
the image are given in the laser scanner reference system.
1.3 Projection of the point cloud
In order to interpolate the D and A matrices, the first step
consists in projecting each point of the DDSM onto the
image. This operation consists in calculating, for each point
of the DDSM, the corresponding image coordinates £, n.
The mathematical model used to project the point cloud is
that of the collinearity equations (in which the radial
distortion components are added).
n(X = Xu) + (Y- Yo) ns(Z = Ze)
A Xn rie nz -Z,)
n-zntg-c
n(X - X.) r (Y 5% Y) n(Z - Z,)
/
ni T X,) i r4 - E mlz i Zu)
E=& +Af-C
Where: 7;; 7 the elements of the rotation matrix
En = the image coordinates of the point
X, Yo,Zp 7 the object coordinates of the projection
centre
X,Y,Z 7 the object coordinates of the point
c = the focal length
AC, An 7 the distortion components.
The distortion components are modelled by:
AS = ( -&) «*, qo +k, pt +1, qu)
(4)
Am 7 (0 - m) ph sot kso pt)
Where: p= the distance of the pixels from the image centre
ki, ky and k; = the radial distortion coefficients.
Other types of distortion have not been considered.
‘
1.4 Interpolation of the distance and reflectivity matrices
The density of the pixels in the digital image is usually much
higher than the density of the acquired point cloud. For this
reason, when the point cloud is projected onto the digital
image, the distance matrix is not completely filled: the
distance values are only associated to some pixels (this
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