Image Correlation of Digital SPOT Stereo Images to Update ...

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Image Correlation of Digital SPOT Stereo Images to Update ...

in: Proceedings of the ACSM 57th Annual Convention and ASPRS 63rd Annual Convention, 7-10 April 1997, Seattle Washington, Vol. 3, pp. 600-609

IMAGE CORRELATION OF DIGITAL SPOT STEREO IMAGES TO UPDATE

ELEVATIONS FOR MAPS 1:50,000

Evangelos G Papapanagiotu, PhD Student

Dr. John N Hatzopoulos, director of Remote Sensing Laboratory

Efstratios Papadopoulos, PhD Student

University of the Aegean, Department of Environmental Studies, Mytilene, GREECE

Correlation models used for this project are presented and analysed. Algorithms specialised to adopt the complexity

and the speciality of the Greek terrain are presented. Results are compared with commercial software and show that

improved algorithms could be used to cover a high percentage of the elevations of an area for 1:50,000 scale map revision.

INTRODUCTION

Photogrammetry and photogrammetric techniques have been used in the past for accurate measuring purposes in a

wide field of sciences. The availability of SPOT panchromatic digital imagery and the recent advances in the form of digital

photogrammetric workstations, offer a cost effective method for mapping the earth surface in all three dimensions. In the

field of ground elevation determination from SPOT digital stereo-images, automatic processes unquestionably promise a

faster and less expensive approach. Such processes need to deal with the two main problems.

Spot imagery is more geometrically complicated than aerial photographs. Geometric deformations are mainly caused

by earth rotation and panoramic effects and are common to most space imagery. Additional distortions are caused by the

push-broom scanning HRV sensor which delivers images that do not follow the central perspective since they are formed

line-by-line during the 9.024 second scanning period. In order to apply the collinearity condition and extract ground

elevations, images have to be transformed to frame geometry. This requires the development of a suitable mathematical

model which can effectively rectify both stereo-images taking into account all their systematic and non-systematic

geometric errors. Many such models have been proposed in the past (Konecny et al., 1987; Gugan & Dowman, 1988;

Kratky, 1989a; Haan, 1992; Pattyn, 1992). Generally speaking, they are quite complex and require a full and in depth

understanding of the satellite’s orbiting parameters and the sensor’s scanning behaviour. To simplify the process

polynomial mapping is used for the six orientation parameters of the collinearity condition (Rodriguez et al., 1988;

Angleraud et al., 1992; Zhong, 1992; Chen & Lee, 1993) at the cost for an increased number of ground control points

(GCPs) since the ephemeris data is not used but with no lack in accuracy (0.5 pixel i.e. 5-6 m on the ground, for the GCPs

and 1 pixel i.e. 10-14 m, for the check points - CPs).

Further on, appropriate software need to be developed which can automatically locate corresponding ground points on

the two images of the stereo-pair. This process, also known as matching, tries to match a small portion (reference window)

of one image to an equally sized portion of the second image based on some similarity measures. The matching can be

performed on either previously extracted feature characteristics (feature matching) or pixel intensities (area matching). Both

methods are known to give sub-pixel accuracy under ideal conditions but they are influenced by the underlying satellite

geometric model used and they are very computationally expensive. To reduce the processing time, approximate initial

matched positions can be determined either using previous knowledge of image geometry or using the technique of image

pyramids. To overcame problems of erroneous matches certain criteria can be imposed to the parameters involved during

the matching process or when matching is completed (Trinder et al., 1994; Heipke, 1996).

A new model has been developed at the Remote Sensing Laboratory of the University of the Aegean (RSLUA) for the

automatic determination of ground elevations from digital SPOT stereo-images. A description of the process and the first

results are presented.

KRATKY’S POLYNOMIALS

A different approach to the problem of the SPOT image geometry, was initially presented by V. Kratky (1989b) in the

concept of real-time positioning of SPOT images in analytical stereo-plotters. In this work, among others, two pairs of

mapping polynomials were presented. The polynomials were experimentally derived and they offer direct mapping

functions between the two images (13-term and 11-term polynomials) of the stereo-pair and between one of the images and

the ground (11-term polynomials) as shown below:

x" = F x (x',y',h) = (1 h x' y' h² hx' hy' x'y' x'² y'² x'²y' x'³ hx'²)P x (1)

y" = F y (x',y',h) = (1 h x' y' hx' hy' x'y' x'² y'² x'²y' x'³)P y (2)

X = F X (x',y',h) = (1 h x' y' hx' hy' x'y' x'² y'² hx'² x'³)P X (3)

Y = F Y (x',y',h) = (1 h x' y' hx' hy' x'y' x'² y'² hx'² x'³)P Y (4)


where x', y', x"and y" are the image co-ordinates (left and right image respectively) of a ground point with co-ordinates

X, Y and height h, P x , P y , P X , and P Y are the corresponding vectors of parameters (term coefficients).

The functions F x and F y can effectively perform an image-to-image registration when the height h is known. Similarly

the functions F X and F Y perform an image-to-ground registration for known heights. Both registrations by-pass the

collinearity equation but the results do not lack accuracy. According to Kratky the application of the above polynomials

give a maximum absolute error of 1.1 m for X and 0.4 m for Y for any practical range of elevations. In addition the

application of the above polynomials offer an extremely fast calculation cycle (even faster than that of standard frame

photographs) making them suitable for digital image analysis and processing systems.

Kratky’s polynomials were later validated (Baltsavias & Stallmann, 1992) and it was proven that they are faster,

equally accurate and easier to implement than strict transformations and a very good approximation of the epipolar line

can be derived from them.

THE PROPOSED MODEL

The proposed model adoptes Kratky’s polynomials to perform image-to-image registration (equations 1 and 2) and

image-to-ground registration (equations 3 and 4). The unknown coefficients P x , P y , P X , and P Y can be calculated by least

squares if adequate control data is available (known height, ground and image coordinates of at least 13 points). The imageto-image

polynomials are also used during the matching process for the location of candidate homologous points on the

stereo-pair by varying the height term (h) between a minimum and a maximum value, effectively reducing the search-space

to epipolar points. The selection of the correct candidate homologous point (and its ground height from which it came from)

is made on the basis of its cross-correlation coefficient which is the simpler and faster matching algorithm (Trinder et al.,

1994) and falls in the category of area matching. The image-to-ground polynomials can be used after the matching process

is completed (heights are already known) to deliver ground coordinates of matched points.

In practice, during matching, certain parameters can be adjusted in order to get an increase in computational speed and

reduce false matches. These are summarised below:

• Definition of maximum and minimum possible heights as close as possible to ground’s real heights.

• Definition of a suitable step height between minimum and maximum. Small step values reduce computation speed

(since more candidate points are checked) but increases accuracy.

• Usage of heights of neighbouring pixels (if known) for the redefinition of the possible maximum and minimum

ground height.

• Usage of an appropriate minimum value for the cross-correlation coefficient as a rejection threshold of false

matches.

The model described has some very interesting characteristics compared to other algorithms for the automatic

extraction of ground elevations:

• The image geometry is taken into account during the matching process.

• Ground elevations are obtained during the matching process as a by-product and there is no need for further

processing if only pixel heights are required.

• Reduce of false matches since matching is guided by the geometry (epipolar line) and not the radiometric

intensities.

• Its speed is reduced according to the accuracy required, which is defined by the range of possible elevations and the

height step to be used (in all our

tests we used 20m height step).

TEST RESULTS

In order to test the validity of the

proposed model, a cloud-free SPOT

digital panchromatic stereo-pair was

obtained of Lesvos island - Greece

(Fig. 1). The characteristics of the

individual images of the stereo-pair are

listed in Table 1. For practical purposes

(mainly speed), subsequent tests were

made on a small portion of the overlap

area covering the Southeast part of the

island (referred from here on as test site)

as shown in Fig. 2. The test site was

carefully chosen so as to be

Fig. 1 SPOT stereo-pair of Lesvos island in Greece (the black

box indicates the test site) - ©SPOT Image 1993 CNES


epresentative of the typical greek isle

terrain with its special features such as

coast line, heavy vegetation of olive and

pine trees, high hills etc.

Height data for the test site of the

form of 20 m contour lines were digitised

(accuracy 1-2 m) from corresponding map

sheets of scale 1:5,000 and later (for

testing purposes) transformed in grid

format (729 rows by 901 columns with

cell size of 10 m). The same maps were

used for the extraction of 43 points which

were clearly identifiable in both images

Left Image Characteristic Right Image

11.09.1993 09:30 Date & Time 23.09.1993 08:59

SPOT2 - HRV1-Pan Satellite-HRV-Mode SPOT2 - HRV1-Pan

Az: 162.1° - El: 54.5° Sun Position Az: 154.2° - El: 48.1°

E 22°20'02" - N 39°53'37" Satellite Position E 29°45'20" - N 38°44'05"

3 Shift Along Track 3

L 25.8° Incidence Angle R 22.0°

1Á Pre-Processing Level 1Á

6000 Column and Rows 6000

14,1° Orientation Angle 8,9°

E 26°17'38" - N 39°08'53" Center Location E 26°23'55" - N 39°08'43"

Table 1 Characteristics of SPOT stereo pair

Fig. 2 Stereo-pair of the test site area (south-east part of Lesvos island). Top image

577x837, bottom 605x895 (rows x columns). Maximum elevation 547 m, minimum 0 m,

mean 150 m. Average slope 27%. Ground area about 9x7.3 km. Sea Cover 30%.


and the map. On the basis of a better distribution over the test site, 18 of these points were randomly selected to be used as

GCPs and the rest 25 points were used as CPs. The test site data were processed by both the proposed model and the

OrthoMax.

The coefficients of image-to-image polynomials were found using least squares giving RMS error of 0.21 pixels

(column) and 0.3 pixels (row) for the GCPs. The RMS error for the CPs was 1.06 and 0.99 respectively. For the image-toground

polynomials the errors were 4.89 m (easting) and 5.91 m (northing) for the GCPs. For the CPs RMS errors of 13.32

m and 11.01 m were found. These errors are similar to the ones obtained from the systematic treatment of the image

geometry by other international research work proving that Kratky’s polynomials can be safely used for the fast

rectification of SPOT imagery. At this point it must be noted that the GCP errors obtained by OrthoMax, which uses the

systematic mathematical approach, were 0.48 pixels for column, 0.80 pixels for row and 7.94 m for easting, 7.25 m for

northing compared to those obtained by

the polynomials.

Having the proposed model

transferred in software format, a series of

runs were made testing the various

parameters of the matching process. The

extracted elevations were compared to

the elevations obtained from the digitised

maps. The foundings (summary in Fig.

3) indicate that radiometric enhancement

and suitable elevation rejections can

increase the accuracy of extracted

elevations of about 15-20 m. Increased

correlation window size does not have a

major influence on elevation accuracy.

High correlation coefficients deliver

more accurate elevations but this

criterion by itself is not always enough

for rejecting false matches (coefficients

above 0.9 were not able to ignore all

false matches). It must be noted that

generally speaking the test case c

(elevation processing) delivers elevations

with better accuracy since the increased

RMS error that appears for the lower

coefficients in Fig. 3 comes from erroneous elevation regions (located in hill shadows) that do not have neighbours (to be

successfully rejected). If these regions are removed (population criterion), then the RMS error is about 20 m for all

coefficients, which is the expected accuracy (Trinder et al., 1994) since the terrain is not ideal for matching (forest with

slopes from 0% to 194%, average 27%).

The RMS error obtained from

OrthoMax was just above 37 m

indicating once more the matching

difficulty of the terrain.

As indicated by Fig. 4 and Table 2,

a high percentage of automatically

extracted elevations have an absolute

error between 30 and 10 meters making

the proposed model reaching the

accuracy levels of 1:50,000 scale

mapping (90% of elevations having

absolute error below 10 meters).

Elevation differences above 75 m are

mostly contributed by low values of

cross-correlation coefficients.

Coefficients of 0.8-0.9 deliver not only

most points (over 50%) but with better

accuracy. No point extracted from the

sea (30% of the total overlap area).

Elevation RMS Error (m)

60

50

40

30

20

10

Raw Data

Elevation Processing

Radiometric Processing

Population Criterion

0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95

Cross-Correlation Coeffiecient Thershold (window size 15x15)

Fig. 3 Elevation RMS error against various cross-correlation coefficient thresholds for a)

Raw Data (no processing on images), b) Radiometric Processing (noise removal and edge

enhancement) , c) Elevation Processing (regions with height difference more than 30 m

from their neighbours are removed) and d) Population Criterion (regions with less than

500 extracted elevation points are removed)

15000

7...0

10000

20...10

50...30 Absolute

5000

Elevation

100...75

Difference

0

(m)

600...200

0.6 0.7 0.8 0.9

Cross-Correlation Coefficient (window size 15x15)

Fig. 4 Contribution of cross-correlation coefficients in number of points automatically

extracted for different elevation differences

Number of Points


About 72% of the total land points had

their elevations automatically extracted

compared to 50% of OrthoMax. The

rest 28% of points that could not have

their elevation extracted are points in

hill shadows or in over-lighted areas

(flat limestone areas without

vegetation).

The matching speed was quite high

(28 pixels/sec i.e. total time 4h 50 min)

compared to the platform used (PC

Pentium-75MHz-8MB) and equal to

that of OrthoMax which unquestionably

was running on a faster platform (Sun

Sparc Station 10) and with smaller

window size (7x7).

From the automatically extracted

elevations a DTM in surface format was

produced using a weighted distance

interpolator (Fig. 5). The visual study of

the extracted terrain surface reveals the

smallest (area I) of the two areas that

could not had their elevations extracted

(the other cannot be seen from this view

angle). Area II (south part of DTM) had

an elevation error of about 250 meters

(causing increase in RMS error)

compared to map data but is believed that

the extracted elevations are correct since

the specific area has been used as a

dumping site of the excavation works for

the expansion of Mytilene’s airport

twenty years ago (the maps used were

prior to these works).

Absolute Elevation

Error (m)

Percentage of extracted

Elevations

RMS Error (m)


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