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 Washing**to**n, 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, direc**to**r **of** Remote Sensing Labora**to**ry

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 s**of**tware 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

Pho**to**grammetry and pho**to**grammetric 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

pho**to**grammetric workstations, **of**fer 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, au**to**matic 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 pho**to**graphs. Geometric deformations are mainly caused

by earth rotation and panoramic effects and are common **to** most space imagery. Additional dis**to**rtions 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 in**to** 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 s**of**tware need **to** be developed which can au**to**matically 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 Labora**to**ry **of** the University **of** the Aegean (RSLUA) for the

au**to**matic 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 **of**fer 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 vec**to**rs **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 **of**fer an extremely fast calculation cycle (even faster than that **of** standard frame

pho**to**graphs) 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 image**to**-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 au**to**matic

extraction **of** ground elevations:

• The image geometry is taken in**to** 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 con**to**ur 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

**SPOT**2 - HRV1-Pan Satellite-HRV-Mode **SPOT**2 - 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, bot**to**m 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-**to**ground

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 s**of**tware 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** au**to**matically

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 **to**tal 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 au**to**matically

extracted for different elevation differences

Number **of** Points

About 72% **of** the **to**tal land points had

their elevations au**to**matically 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 limes**to**ne areas without

vegetation).

The matching speed was quite high

(28 pixels/sec i.e. **to**tal 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 au**to**matically extracted

elevations a DTM in surface format was

produced using a weighted distance

interpola**to**r (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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