You are using an outdated browser that does not fully support the intranda viewer.
As a result, some pages may not be displayed correctly.

We recommend you use one of the following browsers:

Full text

The 3rd ISPRS Workshop on Dynamic and Multi-Dimensional GIS & the 10th Annual Conference of CPGIS on Geoinformatics
Chen, Jun

1SPRS, Vol-34, Part 2W2, “Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001
Taravudh TIPDECHO & Xiaoyong CHEN *
Space Technology Applications and Research (STAR) Program
School of Advanced Technologies
Asian Institute of Technology, THAILAND
This paper addressed ways to assess accuracy of integrated data, photograph and laser data. Polynomial function was employed for
this experiment. It was applied to be a relational model between buildings represented in photograph and laser data. The experiment
was undertaken on one group of data with twenty-four control points, which were randomly selected from photograph with their
corresponding laser data. Least square method was applied for finding out the best fit of control points on existing data. Expectation
values were calculated and compared between calculated and referenced data, then ranked from the lowest to highest one. The result
showed expectation value substantially increased, which was closing to one when increasing number ofsample points. And also few of
control points resulted an acceptable accuracy. According to this experiment, it implied that the use of polynomial functions could offer
an effective method to reconstruct 3D building objects from 2D building objects, based on single photograph. Even the accuracy was
not high, it could be adjusted by integrating it with others instruments such as GPS, Laser and etc.
Graphical technologies are increasingly becoming important
topic for computer applications. Those abilities have obviously
been applied in several kinds of application particularly in the
filed of landscape. Creating the graphical 3D representation of
the environment and paint is a common approach now [3]. The
automated reconstruction of 3D models from real environments
is the latest technology with respect to 3D spatial object
reconstruction [5] using the combination between spatial data
and visual data. Modeling from pictures is another way now
particularly in the field of computer graphic based on shading of
objects [2]. They were several available ways to achieve 3D
reconstruction, most of the techniques aim to use
photogrammetric-method based, in terms of image geometry
model, to achieve 3D object reconstruction. Even this technique
rather gave high accurate results when compared with other
techniques; it consumed high complex technology, high picture
resolution, highly accurate algorithms, lots of relative
parameters, etc. There were basic requirements for system that
expert person must provide them. Nowadays the technology has
been changed positively. Some new tools or methodologies
could be applied for this environment. This study aimed to
experiment on polynomial function being applied for 3D-building-
objects reconstruction based on integrated data, a photograph
and its laser data. The accuracy assessment was the main part
of this experiment, in order to be known how much of accuracy
and possibility to apply for 3D reconstruction. Finally the level of
accuracy was released in terms of expectation value (E).
For this studying, polynomial equation was applied for serving
3D reconstruction from single image. Basically the simple
polynomial equation for one variable can be defined as [1]
f(x) = a0 + a1x + a2x 2 + ... + anx n (1)
For two variables, they can be defined as
f(x,y) = aO + a1x + a2y + a3x 2 + a4y 2 +a5xy (2)
, in case of three variable they can be defined as
f(x,y,z) = aO + a1x + a2y + a3z + a4x 2 + a5y 2 +a6z 2 + a7xy+ a8yz
+a9xz+a10x 3 + ally 3 + a12z 3 + a13x 2 y + a14x 2 z +
a15/x + a16/z + a17z 2 x+ a18z 2 y + a19xyz (3)
, from (3) it can be normalized, according to result of testing
shown (in Figure. 1)
f(x,y,z) ~ aO + a1x + a2y + a3z + a4x 2 + 35/+ a6z\4)
Figure 1. Result of testing of normalizing the polynomial
equation from 6 to 20 constant values [tested with 24 sample
points, accuracy measured by expectation value, E].
With the number of control points, the reduction of matrix based
on Least Square theory was applied for this study, in order to
result value of constants and solve polynomial function. [4] as
square matrix. Many given square matrices of matched control
points were selected, then only one matrix being qualified as
group representative with optimum value under the expectation
value (E).
.when U| is original referenced data.
u is mean value of referenced data.
u, A is calculated value of referenced data by
polynomial function.
ST = Z (Uj - u) 2 (5)
SSE = Z (u, - Uj A ) 2 -> Z e 2 (6)
E (expectation) = SU/ST -> 1
The way generating 3D objects from single photograph was how
to reconstruct them with easily and possibly mathematic
function. Polynomial function was a choice for this study. The
following processes were entire details of working.
Find out the best fit of polynomial function on building data
based on least square method by considering whole
building in a picture, that is presented as 3 dimension
* Supported by Visiting Scholar Foundation of Keb Lab. In Wuhan University, P. R. China