GEOMETRIC ERROR ASSESSMENT ON SATELLITE IMAGERY FOR GISANALYSIS
Kyaw Sann OO*, Masataka TAKAGI**
Department of Infrastructure Systems Engineering
Kochi University of Technology
Tosayamada, Kochi, Japan*E-mail: 108007u@gs.kochi-tech.ac.jp**E-mail: takagi.masataka@kochi-tech.ac.jp
ABSTRACT: Imagination of earth-surface’s objects is contaminated with errors by sensor to target
acquisition systems in the satellite remote sensing. Movement of the sensor and displacement of the target
are propagated geometric error on the imagery. Systematic errors could be removed by trajectory model andrigorous sensor model; however, random errors are existed that in which is difficult to remove without
affecting to image geometry. The study introduced geometric error assessment (GEA) on image objects tounderstand the error geometries from the imagery. At first, ground control points (GCP) and check points(CP) are scattered in all direction of the image. Then, errors are generated seeding the GCP location using
Box-Muller method. The method produced simulated GCP contaminated with errors. Random errors aresubtraction from simulated GCP by the true one. The study found that the error of CP is approached to zero
when the CP closed to GCP. The corrected image would be applied for GIS analysis such as
land-use/land-cover mapping and management, disaster risk mapping and management, urbanization
prediction and management, water resource management.
KEYWORDS: Geometric error, GCP, check points, random error
1. INTRODUCTION

error generation processes were applied whenSurveyors and engineers are believes that errors aresimulating GCP and CP. Random values arepropagated in all kind of measurements (Charles D.

generated by Box-Muller method and it provides theGhilani, 2006). The errors could be systematic errors

random values from the standardized Gaussian

or random errors. Systematic errors could be

distribution N(0,1) (Cox et al., 2001). The generated

removed by applying related physical conditions andrandom values are added to the true value of control

correct measurement procedures; however, random

points. By iterating the transformation process witherrors are complex and it is the arduous work togenerated random errors, the geometry of errors wasremove the random errors. Despite the fact thecalculated. The study compares that error geometry

random errors could be the least by understanding

between 3D affine transformation and 3D projective

the geometry of errors and iterating the observationstransformation. The different distributions of GCP(Charles D. Ghilani, 2006). The geometry of random

and CP also demonstrated. The approach of thiserrors was generated from the simulated groundstudy investigated that the geometry and distribution

control points (GCP) and check points (CP). Iteratedof random errors in ALOS PRISM image to the leastof the random errors propagation. The result image

where Ut, Vt

are true values; fu (x, y, z) and fv (x, y,could be used in the processes of location basedz) are transform function for assume u and v.

monitoring and analysis such as land-use/land-cover
mapping and management, disaster risk mapping andmanagement,

urbanization

prediction

2.1 GCPs and Check Points

andmanagement, water resource management.

From sample datasets, ground control points (GCP)
and check points (CP) are visually interpreted asassume control points. They are well distributed

2. Methodology(figure 2) in the sample area. Each control points
There are three datasets used to implement this study. could be recognized in both of target and reference
They are IKONOS image as reference data,image.

elevation data from DSM (RaMSE: Kokusai

kogyo CO., LTD.) data and the target image ofALOS PRISM. In the study, we assumed that thelocation of IKONOS image is true and DSM’s highvalue also acquired based on it.

Figure 2: Location distribution of control points
Figure 1: The general flow of methodology
By inserting coordinates of GCP and PC to theThere four mains steps in the procedure (figureequation 1, a pair new transformation function

1). X and Y values are collected from reference(equation 2 &3) is produce.

IKONOS image and Z values are from the DSM data.
Assume Ui and Vi data are collected from target

For GCP, transformed function can be

ALOS’s PRISM data visually. True values Uj and Vj

Ugcp = fu (x, y, z)

are produced by transform function (equation 1). InVgcp = fv (x, y, z).

(2)other side, generated errors (euj,evj) are added to theassume image control points. The process of errors
contamination was iterated to 20 times.

Ucp = fu (x, y, z)
Vcp = fv (x, y, z).

Ut =fu (x, y, z)
Vt = fv (x, y, z)

For CP, transform function can be

(1)

(3)

The transform function will be changed base on theFor GCP,

method of transformation. Two transformation
methods are applied in this study. Prior to theu’gcp =transformation, random errors intruded true control

v’gcp =

(6)

points (GCP and CP) are generated by adding thetrue values and generated random values.

and for CP,

2.2 Method of random error generation

u’cp =v’cp =(7)

Box-Muller transformation (equation 4) generated apair of independent standard uniformly distributed

The simulated control points are generated using therandom numbers from the standardized Gaussian

equations 7&8. 20 pairs of control points are

distribution N(0,1). Suppose U1 and U2 aresimulated by iterating 20 times. This iteration data

independent random variables that are uniformly

will be the basic requirement for random error

distributed in the interval (0,1); then, X0 and X1 aregeometry investigation.

independent random variables with a normal
distribution of standard deviation 1.

2.3 Method of transformation

X0 =
X1 =

Amount several types of transformation methods, the(4)study selected 3D affine and 3D projective
transformation methods based on effectiveness ofRandom errors were generated using this algorithm.

them.

Let ug and vg are independent random errors withmean of true GCPs of standard deviation 1. The

In general, 3D affine transformation function can be

Box-Muller random variable generator is generated

represented by the equation 8.

random error with specific mean u and v (equation5).

u = ax + by + cz + dug =vg =v =ex + fy + gz + h(8)(5)
And, 3D Projective transformation function can bewhere ug and vg are x, y coordinate of simulated

represented by equation 9.

random error intruded control points; and u andv are true location of the coordinate control

u = (a1x+a2y+a3z+a4)/(b1x+b2y+b3z+1)

points. This generation process was iterated forv = (a5x+a6y+a7z+a8)/(b1x+b2y+b3z+1)(9)

20 times, producing 20 pairs of simulated
control points.

Based on parameter requirements of these functions,
we selected 25 control points including 11 GCP andIf we substitute coordinate of control points to the14 CP scattering in the image. There four types ofequation 5, the random error contaminated control

patternpoints are calculated (equation 6&7).

transformation process to investigate the influent of

distribution(figure3)

areusinginground condition to error geometry.

Ghilani, 2006). By definition, the difference of a true
value and its measured value is an error. Suppose,

Pattern #1

Pattern #2

ε is the error in an observation, y is the measured
value, and μ its true value, thenε = y - μ.

(10)

The equation 10 will yield a new equation, if you
substitute coordinate of control points.

Pattern #3

ε u = Ut ± U’
εv = Vt ± V’

Pattern #4(11)

where Ut, Vt is true value and U’, V’ is simulated
control points.

3. RESULTThere are 20 times of 25 control points (11 GCP and14 check points) were generated with different
Figure 3: Distributions of GCP and CP

distribution patterns. By locating all those error
coordinates, the vectors of error geometry are

In distributions, pattern 1 is well distributed over thecalculated. The vectors are originated in true

image; while others had less scattering. Pattern 2’s

coordinate; then headed the direction trend of errors.

image control points are selected in the non-elevated

After magnified the vectors by 100 times theplain and it is located in the right side of image.

geometries of vector are distinct to the view (figure

When pattern 4 is distributed in the elevated area5). In all four patterns, red dots represent GCP; blue

pattern 3 is distributed diagonally ranging fromdots represent control points; green arrows represent

elevated area through plain with narrow distribution.

3D affine error vectors; and golden errors represent
3D projective error vecotors.

In other hand, there

In other hand, the propagated errors could be

are four distribution patterns are used to input to thecalculated.

two kinds of selected transformation functions (3Daffine and 3D projective transformation).

2.4 Error propagation
In the results of root mean squares error (RMSE),
The computational process into the new values can

the well distributed ground control points (GCP)

be propagated with the errors that were presented in

produced the least RMSE comparing with others

the original direct observations. Therefore, thedistribution patterns. The orientation of highfunctions of the original errors could be containingchanged the vector of errors. The result shows thatas indirectly in next measurements (Charles D.

aggregated ground control points (GCP) contributed

low potential to far check points. Uneven ground

Error Vector on Pattern #3

condition reflected more complex error geometry.
Error Vector on Pattern #1

Error Vector on Pattern #4
Error Vector on Pattern #2

Figure 5: Error vectors of each distribution

As of transformations processes, 3D projective

Hastedt, H., 2006. (2006). Monte-Carlo-Simulationtransformation gives more precision than 3D affine

in close-range photogrammetry, The International

in whatever GCP or CP. Apart from control points

Archives of the Photogrammetry, Remote Sensing

and transformation methods, the study proved thatand Spatial Information Sciences, Vol. 34, Part

the selection and distribution pattern have positively

XXX[CD-ROM].

related with condition for ground elevation.

Richards, J. A., Remote Sensing Digital Image
Analysis, Springer-Verlag, Berlin, 1999.
Russ, John C., The image processing handbook,

4. DISCUSSIONCRC Press, Inc., USA, 1995.
Pattern 1, well distributed control points, had more

Takeshiprecision consistency than others for both ofMasataka TAKAGI, (2006).Extracting Method oftransformation. Pattern 2, GCPs from non-elevatedMudflow Disaster by using Arial Photography,area, precision consistency is high around GCPs

Proceedings

when CPs had low precision. Pattern 3, narrow

Management Systems for Disaster Prevention,

distribution GCPs, high accuracy around GCPs.

JAPAN.

Unexpectedly, 3D affine transformation had more

Masataka TAKAGI, Lecture on Survey 1,section 7, “Vector”.
Masataka TAKAGI, Lecture on Survey 2,section 10, “Transformation”.

potential around CPs. Pattern 4, GCPs from elevatedarea, there are low precision for some GCPs.
The reference IKONOS image may be intrudedoriginal errors. The removal of it will be anothertask.
5. FUTURE WORK
By using VRS-GPS GCPs, the errors of reference
data were minimized to the VRS-GPS standard. The
next step of the study will be worked along theALOS’s PRISM and AVNIR II datasets to get
VRS-GPS

standard

precision.

Then,futurediscussion will be
REFERENCES
Cox, M. G., Dainton, M.P., Harris, P.M. 2001.
Software Specifications for Unvertainty Calculation
and Associated Statistical Analysis, NPL Report
CMSC 10/01.
Ghilani, Charles D., and Paul R. Wolf. 2006.
Addustment Computation: spatial data analysis, 4thed., John Wiley & Sons, Inc., Hoboken, NJ.

MIYATA,ofJong

Hyeok

International

JEONG

Symposium

andon