Three-dimensional Model Algorithm of Neared Objects Algorithm using
Videogrammetry
ELOINA COLL, JOSE-CARLOS MARTINEZ, JESUS IRIGOYEN, JOSE HERRAEZ
Department of Geodesic, Cartographic, Photogrammetric Engineering
Polytechnic University of Valencia
Camino de Vera, 46022 – Valencia
SPAIN
Abstract: - In this paper an alternative is presented to the terrestrial photogrammetry or to the laser systems, to
obtain the complete model of near objects in an automated way, only using the part of the corresponding image
on the edge of the object that is wanted to model. Since the edge of the object contains very little information, it
is necessary to have many photogrammetric takings that provide other so many sections, for it has been opted it
to use videogrammetric technicals . The process can define it as a refined sustractive of the constructive model.
This way, each point of the final model of the object, it will come defined by a series of right encircling that they
will locate it in the space, and they will characterize it in precision, without the identification in any case of
homologous points. As a result final the model will be obtained in three-dimensional (VRML) with application
of textures of the studied object.
Key-Words: - Video, Videogrammetry, Scanner 3D, System automation, VRML, Computer vision
1 Introduction
The methodology proposed in this investigation for
the obtaining of the three-dimensional coordinates of
the object, is not based on the well-known techniques
of identification of homologous points, either in a
manual way by means of stereoscopic vision, or
automatic using on in technical of correlation of
images. The principle of the developed method,
consists on the study of the geometry that define all
the edges of the object, in all the images that have
him, to obtain its modeling one.
The problem consists in that a point of the edge
with two coordinates, has to be defined a point of the
model with three coordinates. The problem would be
simple if we have the position of that same point in
two frames (a point in two frames provides two
coordinates ' x' and two coordinates ' y', that is to say,
four data) however like we have proposed a point of
the edge previously it only appears probably in only
one
frame,
therefore
the
stereoscopic
photogrammetry cannot be solved the problem. In
principle the outlined problem is monoscopic.
2 Previous data
The data obtained in the previous phases and that are
needed to model the object are:
1) Parameters of external orientation of all the
images, that is to say, the projection center (X0, Y0,
Z0) and the rotation (w, f, k) of the camera in each
taking point about the trajectory that will belong
together with each one of the obtained images of the
video sequence. Focal distancel and radial distortion
correction, besides other data that define the
geometry of the video sequence.
2) The pixel coordinated (x, y) of the object edges in
each one of the images
With all these data we pretend to obtain in an
automatic way, the three-dimensional model of the
object and their precision. Also, the results are
supplemented with the three-dimensional graphic exit
by means of VRML, of the pattern obtained so much
in format of wires, faces or textures.
Once known these parameters, the object model is
obtained in two phases. In a first step, it is carried out
the extraction of the object in each image of the
videotape sequence, and their edges are detected by
means of the use of diverse technical as the
correlation, filters in the space domain and the
detection of discontinuities of the image (figures 1).
model is also limited to a margin of height or
horizontal sector (figure 3).
Fig. 1. Edge detection of the object in each image
In a second step, a methodology is studied to
model the object (methodology that is presented in
this article), using the projected rays that define each
point of border of each image in the whole video
sequence. Since the data to use belong on the edge of
the object that is observed in each image, in any case
we will have data of homologous points in different
images.
3 Planteamiento del problema
The system of coordinates used to define the threedimensional model of the object will be cylindrical
coordinates.
Is to say, the model will be formed by sectors
that will have a certain resolution (number of sectors
in each horizontal plane and number of horizontal
planes). Each sector will belong to a point of the
surface of the object and it will come defined by an
angle on the axis of the X (Ф), a height on the inferior
platform (H), and a radius (ρ) to the axis Z (figure 2).
Fig. 3. Object resolution
To carry out the object model, initially we have a
cylinder of height H0-H1, with as many sectors for
plane, and so many horizontal planes as shows the
figure 7. therefore, in this case we have 90.000
sectors that will correspond after the object model to
other so many faces on the surface of the object.
Of each sector according to their space position,
we have the coordinates by definition (Ф, H). The
coordinate ρ will be the distance to calculate to locate
the point on the surface of the object and in a
principle it is initialized to a the maximum value as it
can be the radius of the platform.
The algorithm to apply consists on defining the
sectors that are crossed by each projected ray of each
one of the points of the borders of each image,
calculating the minimum distances to the sectors.
4 Problem solution
Initially we have for example 90.000 sectors of
coordinates (Ф, H, ρ) where a initially taking a
maximum value similar to the radius of the platform
(0,5 m).
According to the video taking we will have 1.500
images approximately recovering totally to the
studied object (video of 60 seg. at 25 images per
second).
For each coordinated image Pi(x, y) belonging to a
edge point in the image i [1, 1500] the following
algorithm will be applied:
Fig. 2. Coordinate system used
The number of sectors used for modeling the
object, is specified initially in the software that has
been developed for the later calculations. The object
1) Calculation of the projected ray Ri (x, y) [1] that
unites the projection center with the point of edge
of pixel coordinates (x, and) on the image.
X  X 0 Y  Y0 Z  Z 0


XI
YI
ZI
X I 
 XI 
 
donde  Y I   Rw, , k    YI 
 ZI 
 F 
 
R
Will the three-dimensional model calculated
starting from the points of border of all the images of
the video sequence, come therefore given when
minimizing the coordinate ρ of each one of the
90.000 sectors (according to the example), in a
combined way.
(1) projected ray of the point Pi(x, y)
2) Calculation of the sectors that are intersected for
the projected ray.
a) Intersection in plant: Calculation of the
coordinates Ф of all the sectors intersected
(figure 3)
b)
As exit graph of results it has been opted to use
VRML, to represent the pattern created in three
dimensions with the application of textures. In the
figure 4 one of the original images of the video
sequence appears (left) and the object model one
created from a point of view (right).
θi
θ2
θ1
Ri
(X0 Y0 Z0)
Fig.
3.
Intersection in plant
c) Elevation Intersection. Calculation of the
coordinates H of all the sectors intersected in
plant.
3) Calculation of the distance D to the center of the
cylinder of each one of these sectors. If this distance
is smaller to the coordinate ρ of this sector (initially
equal to 0,5 m), then the value D is assigned to ρ.
θi
θ2
θ1
Fig. 4. Calculation to the coordinate ρ
Fig. 4. Original image and created model
4 Improves of the algorithm
As it has been commented the coordinate previously
ρ is the smallest distance in a projected ray of some
point of image border that intersected to the
corresponding sector. With the purpose of improving
the procedure they have been kept in mind for the
calculation of this coordinate ρ, all the projected rays
that happen to an it distances near (figure 5) and not
only the nearest.
This way, after the study of the statistical ones of
stocking and typical deviation, we redesign the
coordinate ρ of all the sectors. The improvement in
the object model you can appreciate in the figure 6
(in the image of the left the object model appears
original and to the right the object model where this
improvement has been applied)
References:
[1] Guillem Picó, S., Herráez Boquera, J., Restitución
Analítica (método de determinación simultánea
de todos los elementos de orientación), SPUPV91499, 1995.
[2] Clarke, T.A. Cooper M.A.R. & Chen, J. &
Robson, S. Automated 3-D measurement using
multiple CCD camera views. Photogrammetric
Record, Vol. XV, No..86, 1994, pp. 315-322.
[3] Thomas Lobonc Jr., Edward M. Mikhail, Human
Supervised Automated Tools for Digital
Photogrammetric Systems, GIS/LIS Proceedings,
1994, pp. 523-524
[4] Wang Zhizhuo, Principles of photogrammetry
(width remote sensing), Press of Wuhan Techical
University of Surveying and Mapping, 1990.
Fig. 5. Sector defined by next rays
Fig. 6. Improves to the object model.
5 Conclusion
The mathematical model here exposed, it allows
us to obtain the three-dimensional coordinates of the
object, with a contrasted precision and in a simpler
way for the user, turning out to be an alternative to
the methods classic terrestrial photogrammetric that
use conventional photographic cameras, or to the new
and expensive systems of three-dimensional
digitalization by means of laser techniques.
In a simple way it is obtained in an automatic way
the modeling one three-dimensional of small objects,
using a conventional device (video camera).