- Email: [email protected]
Influence of image compression on the in situ stereoscopic reconstruction of a cometary surface for the Rosetta mission
C. R. Acad. Sci. Paris, t. 327, SCrie II b, p. 547-554, Techniques astronomiques/Astronomical techniques (Signal, informatique/Signa/, computers)
1999
Influence of image compression on the in situ stereoscopic reconstruction of a cometary surface for the ROSETTA mission Sylvain TAKERKART,
Philippe LAMY,
Laboratoire
spatiale,
E-mail:
d’astronomie
UPR
Antoine LLEBARIA
CNRS
9019,
(ReCu le 19 f&ier
Abstract.
1998, accept6 aprbs r&ision
8, 13376
Marseille
cedex 12, France
le 14 octobre 1998)
As part of the ROSETTA mission, the surface science package, which will land on the nucleus of the comet 46P/Wirtanen, includes a stereoscopic imaging instrument (;IVA-P. The data volume required by the scientific objectives and the limited capability of the telemetry imposes the use of image-loss compression techniques. We study the influence of the losses due to compression on the three-dimensionnal surface reconstruction. We prove that the best strategy consists in compressing both the left and right images with the same ratio, transmitting them and finally applying on Earth the stereoscopic calculation on the decompressed images. We also prove that the compression ratio imposed by the telemetry (1 :lO) allows a good reconstruction when this strategy is applied. 0 AcadCmie des sciences/Elsevier, Paris
image compression
/ stereoscopy
/ comets
Influence de la compression ste’rkoscopique in situ d’une pour la mission ROSETTA R&urn&
BP
[email protected]
d/image surface
sur la reconstruction come’taire
Dans le cadre de la mission ROSETTA, la sonde de surface qui doit atterrir sur le noyau de la comtte 46P/Wirtanen comporte un instrument imageur ste’rkoscopique CIVA-P. Le volume de don&es requis par les object@ scientifiques et la limitation de la ttWme’trie impose l’utilisation de techniques de compression d’images avec pertes. Nous avons Ptudie’ 1’inJuence des pertes dues ri la compression sur la reconstruction tridimensionnelle de la surjkce. Nous montrons que la meilleure stratkgie consiste 6 cornprimer les images de droite et de gauche ci des taux identiques, 2 les transmettre et jinalement, ir appliquer le calcul ste’re’oscopique sur la Terre & partir des images dkomprime’es. Nous montrons kgalement que le taux de compression impose’ par la te’le’me’trie (I:1 0) permet une bonne reconstruction grkce ci 1‘application de cette stratkgie. 0 Acadkmie des sciences/Elseviel; Paris compression
d’image
/ sttkkoscopie
1 corn&es
Note prCsent6e par Pierre ENCRENAZ. 1287-4620/99/032700547
0 AcadCmie
des sciencesElsevier,
Paris
547
S. Takerkart
Version
et al.
frangaise
abrdghe
La mission ROSETTA de I’ESA est destinee a l’etude in situ de la comete 46P/Wirtanen. Elle est composee d’un orbiteur et d’un atterrisseur qui comporte un ensemble de cameras panoramiques CIVA-P (Lamy, 1996) dont l’une est stereoscopique, ce qui permettra la reconstruction tridimensionnelle du site d’atterrissage. L’important volume de donnees requis par les objectifs scientifiques et la limitation de la telCm&rie impose l’utilisation de techniques de compression d’images avec pertes a des taux d’environ 1: 10. Nous avons done etudit l’influence des pertes dues a la compression sur la qualite de la reconstruction obtenue par stereoscopic. En effet, la faiblesse des capacites de calcul disponibles a bord ne pet-met pas l’implantation de methodes de compression specifiques aux images stereo (Aydinoglu, 1995 ; Woo, 1996). Nous devons done utiliser des methodes de compression d’image classiques et tenter de minimiser les erreurs de reconstruction causees par les pertes. Deux options sont envisageables. Option 1 : le champ de disparite est calcule B bord a partir des images originales, puis cornprime et transmis avec une des deux images. Option 2 : le calcul des disparites est effect& sur la Terre a partir des images transmises avec pertes. Un bon etalonnage du bane stereo et l’application de l’algorithme d&tit par Lamboley et al. (1994) pour le calcul du champ de disparite permet d’obtenir un grand nombre de < 1 pixel (gris clair + intermediaire + fence). Les incertitudes correspondantes sur z sont presentees sur lafigure I. Le but est de maximiser les taux de pixels corrClCs presentant une faible incertitude. Les degradations introduites par l’option 1 sont celles d’une compression avec pertes : pas de changement geometrique (le pourcentage total de <>est le meme que sur &) mais des pertes en precision. A 0,25 et 0,5 bpp (strategies 1 et 2), le pourcentage de <
image
compression
and stereoscopic
reconstruction
traduisent par une diminution du nombre total de <>sur d,,, et le nombre de <>a faible incertitude satisfaisant (qui permettra effectivement une reconstruction de la surface par cette methode) et des resultats independants du type d’image consider&
1. Introduction The international ROSETTA mission led by the European Space Agency is devoted to the in situ study of comet 46P/Wirtanen. Its lander includes an instrument called CIVA-P with a pair of coaxial cameras which will provide three-dimensional stereoscopic reconstruction of the landing area. A full description of this instrument can be found in Lamy et al. (1996). This reconstruction (with a 2 mm resolution near the probe) will contribute to the improvement of our knowledge of the dust mantle of short period comets (Rickman et al., 1990). The purpose of the present note is to study the influence of the losses due to the compression techniques imposed by the low telemetry capability of the lander on the stereoscopic process, and to optimize the strategy of data handling. It is organized as follows. In section 2, we present CIVA-P, its stereoscopic capability and the problems arising from image compression. The algorithms for image compression and disparity calculation are described in section 3 as well as the tests carried out for this study. The test images and their characteristics are introduced in section 4. Finally the results are discussed in section 5. 2. CIVA-P
and its operation
Each camera of CIVA-P is composed of a frame transfer CCD of 1024 * 1024 pixels associated to a wide-angle optics offering a field-of-view of 70”. The images will be initially coded at 10 bits per pixel (bpp) leading to a size of 10 megaoctets per image. In order to adapt the large flow of data to the telemetry available to the instrument, onboard data compression with a mean compression ratio of 1:lO must be applied. The algorithms especially designed for stereocospic images compression (Aydinoglu et al., 1995; Woo and Ortega, 1996) cannot be implemented in this case as they would require too large onboard computing resources. The use of classical image compression algorithms is therefore necessary. The compression ratio of I:10 is such that lossless techniques are inapplicable, and it is imperative to find a solution which minimizes the impact of the compression errors on the stereo reconstruction. Two options are available to us: - option 1: we compute the disparity field onboard from the original left (L) and right (R) images and we compress and transmit one of the original images (either L or R) and the disparity map; - option 2: we compress and transmit both the L and R images and compute the disparity field on Earth from the decompressed L and R images. Our approach to the study, optimization and comparison of these two options consists in developing a method as similar as possible to that which will be used by CIVA-P and to apply it to real images representative of the surface of a cometary nucleus. 549
S. Takerkart
et al.
3. The method We compute the disparity field following the method described by Lamboley et al. (1994). At each pixel for which the calculation of the disparity d is successful, we determine the distance z from the camera via the relationship d =~73/z where f is the focal length of the cameras and B, the distance between their optical axis. The uncertainty in this measurement (caused by the imperfection of the correction of the distortion which leads to an uncertainty in the disparity estimated at Ad, = l/4 pixel) is shown by the solid curve in figure I and given by AZ = Ad,.z2 Ifi. The compression algorithm used in this study has been selected after evaluation of presently available techniques. It performs first a wavelet transformation by the conventional 6/10 filter (Villasenor et al., 1995), then a tree-based quantification adapted from the SPIHT algorithm (Said and Pearlman, 1996) and finally an arithmetic coding. Its implementation has been performed by Langevin and Fomi (1997) on individual image blocks of 128 * 128 pixels compatible with the available onboard memory. Tts performances are close to those of the original SPlHT algorithm. The different tests are performed as follows. First the disparity field is computed from the original L and R images without any compression; this gives the reference field d,,. Then we try several strategies for each option. - Option 1: dref is calculated and compressed onboard the lander. This calculation generates an array of real numbers coded in 32 bits which we first transform to an array of integers coded at 10 bpp before applying the compression. Three different compression ratios are considered corresponding to 0.25 bpp (strategy l), 0.5 bpp (strategy 2) and 1 bpp (strategy 3). The latter case corresponds to the mean compression of the L and R images and is taken as a maximum value since we do not want the size of the compressed disparity field to exceed that of a compressed image. Following decompression, the inverse transformation from integers to real numbers with the original dynamic is performed so that the resulting map can be compared to dref - Option 2: we compress the L and R images in different ways and apply the disparity calculation on the decompressed images: strategy 4 consists in using the same compression ratio on both L and R (1: 10.67 hereafter abbreviated to 1: 10); strategy 5 uses different compression ratios on L (1: 16) and on R (1:8), and strategy 6 is the opposite of the latter (1:s for L and 1:16 for R). Note that the volume of data taken by the two images remains constant for these strategies since 1 I+1 2*im= 8 16’
1 pixel,’ /
I’
l/2
pixel.!
I’
,’ , ,’
:’ .’
Figure 1. Uncertainty on the determination distance AZ versus the distance z for different the uncertainty on the disparity.
of the values of
Figure 1. Incertitude sur la me.wre de la distance AZ en ,fonction de la distance z pour diffbrentes valeurs de [‘incertitude sur la disparit6.
10 Distance
550
20 z (m)
Image compression
Figure Figure
Figure Figure
2. Left
2. Image
4. Disparity 4. Champ
image
de gauche
of stereo
pair #13.
de la paire
field resulting
from
Figure
ste’rcfo no 13.
option
de disparite’ obtenu (.~tra6kgie 2).
Figure
I (strategy
avec l’option
2). I
Figure
and stereoscopic
3. Original 3. Champ
5. Disparity
Figure
5. Champ
disparity
de disparite’
field resulting
reconstruction
field original
from option
de disparite’ obtenu (strat&ie 6).
(&). (d,,).
2 (strategy
avec l’option
6). 2
Figures 2 to 5 illustrate this process by presenting an original left image figure 2), the original disparity field dref figure 3) and the disparity fields resulting from option 1, strategy 2 @gure 4) and from option 2, strategy 6 yigure 5). 4. The test images The Groupement d’ktude en robotique mobile spatiale (GEROMS) of the Centre national d’ktudes spatiales (Toulouse) has built a special terrain in order to test its planetary rovers. One of its sections was found adequate to represent a cometary surface. As the CIVA-P experiment has not yet been built, we used a stereo camera from the GEROMS kindly made available to us by M. Lamboley. The two identical camera heads include a CCD detector of 382 * 282 pixels of 23 * 23 microns and a wide-angle objective (f= 5.84 mm, field of view: 70”). The base B between the cameras is 200 mm. All images were coded at 10 bpp. The stereo camera was set up at 800 mm above the ground and its optical axis was tilted down by 20”. 551
S. Takerkart
et al.
We have selected five stereo pairs of images (among the 25 available) as best representatives of very different situations in terms of stereoscopic reconstruction. They are described in table 1. Table I. Description of the chosen test images. Tableau I. Description
des images de tests stlectionnkes.
Pair #
Description of the scene
5 10 13 14 25
Inclined ground covered by small rocks Flat ground of gravel; one rock in the center of the field View on a rock belt The same rock belt from further away Flat ground with rocks of various sizes
5. The results The ultimate accuracy of the determination of the distance (the range) is controlled by the uncertainty affecting the disparity. We have already seen in section 3 that the optical distortion is a first source of uncertainty estimated at Ad, = l/4 pixel. The compression constitutes a second source of uncertainty Ad, which can be estimated by comparing the actual disparity to the reference one: Ad,= Id,,-dl. W e note that the two options 1 and 2 will not introduce the same uncertainty since the compression takes place after (option 1) and before (option 2) the calculation of the disparity. In order to calculate conveniently the total uncertainty resulting from both distortion and compression, we assume that these two sources are independent and follow a gaussian law so that we can write Ad,,, = dm and finally Aztot = Ad,,.z2 f@. For each stereo pair, the bar charts on&are 6 present the percentages of “correlated pixels” for each strategy. Except for dref, the uncertainties are always larger than l/4 pixel and the figures give the percentages of “correlated pixels” corresponding to uncertainties lower than l/2 pixel (light grey bars), lower than 1 pixel (light + medium greys) and larger than 1 pixel (light + medium + dark greys). The corresponding uncertainties affecting the range z are plotted injgure 1. Let us now examine these results having in mind that our goal is to find the strategy which minimizes the errors on the reconstruction, i.e., which maximizes the number of “correlated pixels” with the lowest uncertainty (l/2 pixel). Option 1 leads to degradations expected from “lossy” compressions. The percentages of “correlated pixels” are the same for the three strategies 1, 2 and 3 as for the reference (there are no geometric changes in the disparity map). There is just a loss in accuracy which decreases as the bit rate increases @gure 4). Option 1 at low bit rates is clearly unacceptable as the percentages of “correlated pixels” do not exceed 28 % at 0.25 bpp and 41.4 % at 0.5 bpp. Moreover its efficiency depends strongly upon the type of images. When the ground is flat, the disparity field is easily compressed since it is smooth and continuous. This explains the good results on the stereo pairs #lO and #25. When the ground is rough (e.g., when rocks are present), discontinuities appear on the disparity map and its compression gives bad results: the highest percentage at 1 bpp for l/2 pixel on the stereo pairs #5, #12 and #14 is 32.7 %. Options 2 leads to degradations of a different type which could not be simply predicted. There is a global loss in the total percentages of correlated pixels as best illustrated by the black holes in j@re 5 together with a loss in accuracy as well. We further note that the use of symmetrical compression ratios is preferable. Indeed, the percentages of correlated pixels at all accuracies are higher by about 5 % in strategy 4 than in strategies 5 or 6. Let us finally discuss the best strategy for each option, strategy 3 for option 1 and strategy 4 for option 2, by comparing the percentages of correlated pixels at l/2 pixel to the reference. For strategy 4, the degradation is almost constant as the difference ranges from 17.2 % to 24 YC&pending upon the 552
Image compression
Stereo ---_”
__ . ..-
6 r^--.
. .._._ - .
0
. ..^..-
. .
20
30
40
stereo
pair
Figure
60
70
60
--
~-20
30
40 pair
0
10
50
20
30
40
Stereo
pair
Q’
..-_.. 3!21
60
70
80
..-
tip-.+..
50
60
70
80
#14
~_---..
62,Sj
/
0
P5 72.5
r __
a
Figure
50
-.10
. -.--~ ^” .
t13
-”
Stereo
Q
X25 72,9j
6 L----.-.a-_--.
~-------~-
____0
pair
Qt-
- ---.-xGl
-~---___ 10
v--Q _---~~--
Stereo
Cl0
reconstruction
-..
QfY-
c
pair
and stereoscopic
10
20
6. Performances 6. Performances
30
40
50
on the test images sur les images
60
70
of the disparity calculation different strategies.
de test du calm1 de dispariti di$e’rentes strat&gies.
(in percentage (en pourcentages
of “correlated de CCpixels
pixels”) corr&s
for the #) pour
les
images. The performance of strategy 3 depends upon the nature of the images, superior to those of strategy 4 for the simple images (e.g., pairs #IO and #25, with a gain of up to 10.4 %), but clearly inferior for the complex images (pairs #5, #13 and #14, with losses up to 23.5 %). As the nature of the 553
S. Takerkart
et al.
cometary surface is unknown, we recommend adopting a strategy independent of the type of images, namely strategy 4, stressing further that the gain possibly offered by strategy 3 for certain types of images remains small (less than 10.4 %). 6. Conclusion
The recommended strategy (4) allows one to obtain a satisfactory percentage of “correlated pixels” with an acceptable uncertainty. This means that, despite the losses due to compression, the threedimensional reconstruction of the landing site will be possible using stereoscopic techniques. We however emphasize that these results are purely statistical; indeed we will not have access to d,,, and consequently, we shall not know the locations of the pixels for which the disparity is known with an uncertainty of l/2 pixel. The result could however be ascertained by comparison with those of photoclinometry techniques (shape from shading) which will also be implemented on CIVA-P. References Aydinoglu H., Kossentini F., Hayes M. H., 1995. Region-based stereo image coding, International Conference on Image Processing, Washington D.C. Lamboley M., Rastel L., Fouvet G., 1994. Navigation autonome Marsokhod: chaine de traitement d’images, Internal CNES Document, private communication. Lamy P., Bibring J.P., Nguyen-Trong N., Soufflot A., Boit J.L., Dohlen K., 1998. The panoramic camera for the Champollion and Roland cometary surface science packages, Adv. Space Res., vol. 21, No. 11, 1581-1588. Langevin Y., Fomi O., 1997. Algorithme de compression en ondelettes adapt& aux experiences spatiales embarqutes (images et cubes-images spectra). Internal Document Institut d’Astrophysique Spatiale, private communication. Rickman H., Fernandez J.A., Gustafson, B.A.S.. 1990. Formation of stable dust mantles on short period comet nuclei, Astron. Astrophys., vol. 237, 524-53.5. Said A., Pearlman W.A., 1996. A new fast and efficient code based on set partitioning in hierarchical trees, IEEE Trans. Circuits Syst. Video Tech.. vol. 6, 243-250. Villasenor J.D., Belner B., Liao J., 1995. Wavelet filter evaluation for image compression, IEEE Trans. Image Processing, vol. 4, 1053-1060. Woo W., Orlega A., 1996. Stereo image compression with disparity compensation using MRF model, SPIE Proc. VCIP’96, vol. 27, 28841,
554
1999
Influence of image compression on the in situ stereoscopic reconstruction of a cometary surface for the ROSETTA mission Sylvain TAKERKART,
Philippe LAMY,
Laboratoire
spatiale,
E-mail:
d’astronomie
UPR
Antoine LLEBARIA
CNRS
9019,
(ReCu le 19 f&ier
Abstract.
1998, accept6 aprbs r&ision
8, 13376
Marseille
cedex 12, France
le 14 octobre 1998)
As part of the ROSETTA mission, the surface science package, which will land on the nucleus of the comet 46P/Wirtanen, includes a stereoscopic imaging instrument (;IVA-P. The data volume required by the scientific objectives and the limited capability of the telemetry imposes the use of image-loss compression techniques. We study the influence of the losses due to compression on the three-dimensionnal surface reconstruction. We prove that the best strategy consists in compressing both the left and right images with the same ratio, transmitting them and finally applying on Earth the stereoscopic calculation on the decompressed images. We also prove that the compression ratio imposed by the telemetry (1 :lO) allows a good reconstruction when this strategy is applied. 0 AcadCmie des sciences/Elsevier, Paris
image compression
/ stereoscopy
/ comets
Influence de la compression ste’rkoscopique in situ d’une pour la mission ROSETTA R&urn&
BP
[email protected]
d/image surface
sur la reconstruction come’taire
Dans le cadre de la mission ROSETTA, la sonde de surface qui doit atterrir sur le noyau de la comtte 46P/Wirtanen comporte un instrument imageur ste’rkoscopique CIVA-P. Le volume de don&es requis par les object@ scientifiques et la limitation de la ttWme’trie impose l’utilisation de techniques de compression d’images avec pertes. Nous avons Ptudie’ 1’inJuence des pertes dues ri la compression sur la reconstruction tridimensionnelle de la surjkce. Nous montrons que la meilleure stratkgie consiste 6 cornprimer les images de droite et de gauche ci des taux identiques, 2 les transmettre et jinalement, ir appliquer le calcul ste’re’oscopique sur la Terre & partir des images dkomprime’es. Nous montrons kgalement que le taux de compression impose’ par la te’le’me’trie (I:1 0) permet une bonne reconstruction grkce ci 1‘application de cette stratkgie. 0 Acadkmie des sciences/Elseviel; Paris compression
d’image
/ sttkkoscopie
1 corn&es
Note prCsent6e par Pierre ENCRENAZ. 1287-4620/99/032700547
0 AcadCmie
des sciencesElsevier,
Paris
547
S. Takerkart
Version
et al.
frangaise
abrdghe
La mission ROSETTA de I’ESA est destinee a l’etude in situ de la comete 46P/Wirtanen. Elle est composee d’un orbiteur et d’un atterrisseur qui comporte un ensemble de cameras panoramiques CIVA-P (Lamy, 1996) dont l’une est stereoscopique, ce qui permettra la reconstruction tridimensionnelle du site d’atterrissage. L’important volume de donnees requis par les objectifs scientifiques et la limitation de la telCm&rie impose l’utilisation de techniques de compression d’images avec pertes a des taux d’environ 1: 10. Nous avons done etudit l’influence des pertes dues a la compression sur la qualite de la reconstruction obtenue par stereoscopic. En effet, la faiblesse des capacites de calcul disponibles a bord ne pet-met pas l’implantation de methodes de compression specifiques aux images stereo (Aydinoglu, 1995 ; Woo, 1996). Nous devons done utiliser des methodes de compression d’image classiques et tenter de minimiser les erreurs de reconstruction causees par les pertes. Deux options sont envisageables. Option 1 : le champ de disparite est calcule B bord a partir des images originales, puis cornprime et transmis avec une des deux images. Option 2 : le calcul des disparites est effect& sur la Terre a partir des images transmises avec pertes. Un bon etalonnage du bane stereo et l’application de l’algorithme d&tit par Lamboley et al. (1994) pour le calcul du champ de disparite permet d’obtenir un grand nombre de <
image
compression
and stereoscopic
reconstruction
traduisent par une diminution du nombre total de <
1. Introduction The international ROSETTA mission led by the European Space Agency is devoted to the in situ study of comet 46P/Wirtanen. Its lander includes an instrument called CIVA-P with a pair of coaxial cameras which will provide three-dimensional stereoscopic reconstruction of the landing area. A full description of this instrument can be found in Lamy et al. (1996). This reconstruction (with a 2 mm resolution near the probe) will contribute to the improvement of our knowledge of the dust mantle of short period comets (Rickman et al., 1990). The purpose of the present note is to study the influence of the losses due to the compression techniques imposed by the low telemetry capability of the lander on the stereoscopic process, and to optimize the strategy of data handling. It is organized as follows. In section 2, we present CIVA-P, its stereoscopic capability and the problems arising from image compression. The algorithms for image compression and disparity calculation are described in section 3 as well as the tests carried out for this study. The test images and their characteristics are introduced in section 4. Finally the results are discussed in section 5. 2. CIVA-P
and its operation
Each camera of CIVA-P is composed of a frame transfer CCD of 1024 * 1024 pixels associated to a wide-angle optics offering a field-of-view of 70”. The images will be initially coded at 10 bits per pixel (bpp) leading to a size of 10 megaoctets per image. In order to adapt the large flow of data to the telemetry available to the instrument, onboard data compression with a mean compression ratio of 1:lO must be applied. The algorithms especially designed for stereocospic images compression (Aydinoglu et al., 1995; Woo and Ortega, 1996) cannot be implemented in this case as they would require too large onboard computing resources. The use of classical image compression algorithms is therefore necessary. The compression ratio of I:10 is such that lossless techniques are inapplicable, and it is imperative to find a solution which minimizes the impact of the compression errors on the stereo reconstruction. Two options are available to us: - option 1: we compute the disparity field onboard from the original left (L) and right (R) images and we compress and transmit one of the original images (either L or R) and the disparity map; - option 2: we compress and transmit both the L and R images and compute the disparity field on Earth from the decompressed L and R images. Our approach to the study, optimization and comparison of these two options consists in developing a method as similar as possible to that which will be used by CIVA-P and to apply it to real images representative of the surface of a cometary nucleus. 549
S. Takerkart
et al.
3. The method We compute the disparity field following the method described by Lamboley et al. (1994). At each pixel for which the calculation of the disparity d is successful, we determine the distance z from the camera via the relationship d =~73/z where f is the focal length of the cameras and B, the distance between their optical axis. The uncertainty in this measurement (caused by the imperfection of the correction of the distortion which leads to an uncertainty in the disparity estimated at Ad, = l/4 pixel) is shown by the solid curve in figure I and given by AZ = Ad,.z2 Ifi. The compression algorithm used in this study has been selected after evaluation of presently available techniques. It performs first a wavelet transformation by the conventional 6/10 filter (Villasenor et al., 1995), then a tree-based quantification adapted from the SPIHT algorithm (Said and Pearlman, 1996) and finally an arithmetic coding. Its implementation has been performed by Langevin and Fomi (1997) on individual image blocks of 128 * 128 pixels compatible with the available onboard memory. Tts performances are close to those of the original SPlHT algorithm. The different tests are performed as follows. First the disparity field is computed from the original L and R images without any compression; this gives the reference field d,,. Then we try several strategies for each option. - Option 1: dref is calculated and compressed onboard the lander. This calculation generates an array of real numbers coded in 32 bits which we first transform to an array of integers coded at 10 bpp before applying the compression. Three different compression ratios are considered corresponding to 0.25 bpp (strategy l), 0.5 bpp (strategy 2) and 1 bpp (strategy 3). The latter case corresponds to the mean compression of the L and R images and is taken as a maximum value since we do not want the size of the compressed disparity field to exceed that of a compressed image. Following decompression, the inverse transformation from integers to real numbers with the original dynamic is performed so that the resulting map can be compared to dref - Option 2: we compress the L and R images in different ways and apply the disparity calculation on the decompressed images: strategy 4 consists in using the same compression ratio on both L and R (1: 10.67 hereafter abbreviated to 1: 10); strategy 5 uses different compression ratios on L (1: 16) and on R (1:8), and strategy 6 is the opposite of the latter (1:s for L and 1:16 for R). Note that the volume of data taken by the two images remains constant for these strategies since 1 I+1 2*im= 8 16’
1 pixel,’ /
I’
l/2
pixel.!
I’
,’ , ,’
:’ .’
Figure 1. Uncertainty on the determination distance AZ versus the distance z for different the uncertainty on the disparity.
of the values of
Figure 1. Incertitude sur la me.wre de la distance AZ en ,fonction de la distance z pour diffbrentes valeurs de [‘incertitude sur la disparit6.
10 Distance
550
20 z (m)
Image compression
Figure Figure
Figure Figure
2. Left
2. Image
4. Disparity 4. Champ
image
de gauche
of stereo
pair #13.
de la paire
field resulting
from
Figure
ste’rcfo no 13.
option
de disparite’ obtenu (.~tra6kgie 2).
Figure
I (strategy
avec l’option
2). I
Figure
and stereoscopic
3. Original 3. Champ
5. Disparity
Figure
5. Champ
disparity
de disparite’
field resulting
reconstruction
field original
from option
de disparite’ obtenu (strat&ie 6).
(&). (d,,).
2 (strategy
avec l’option
6). 2
Figures 2 to 5 illustrate this process by presenting an original left image figure 2), the original disparity field dref figure 3) and the disparity fields resulting from option 1, strategy 2 @gure 4) and from option 2, strategy 6 yigure 5). 4. The test images The Groupement d’ktude en robotique mobile spatiale (GEROMS) of the Centre national d’ktudes spatiales (Toulouse) has built a special terrain in order to test its planetary rovers. One of its sections was found adequate to represent a cometary surface. As the CIVA-P experiment has not yet been built, we used a stereo camera from the GEROMS kindly made available to us by M. Lamboley. The two identical camera heads include a CCD detector of 382 * 282 pixels of 23 * 23 microns and a wide-angle objective (f= 5.84 mm, field of view: 70”). The base B between the cameras is 200 mm. All images were coded at 10 bpp. The stereo camera was set up at 800 mm above the ground and its optical axis was tilted down by 20”. 551
S. Takerkart
et al.
We have selected five stereo pairs of images (among the 25 available) as best representatives of very different situations in terms of stereoscopic reconstruction. They are described in table 1. Table I. Description of the chosen test images. Tableau I. Description
des images de tests stlectionnkes.
Pair #
Description of the scene
5 10 13 14 25
Inclined ground covered by small rocks Flat ground of gravel; one rock in the center of the field View on a rock belt The same rock belt from further away Flat ground with rocks of various sizes
5. The results The ultimate accuracy of the determination of the distance (the range) is controlled by the uncertainty affecting the disparity. We have already seen in section 3 that the optical distortion is a first source of uncertainty estimated at Ad, = l/4 pixel. The compression constitutes a second source of uncertainty Ad, which can be estimated by comparing the actual disparity to the reference one: Ad,= Id,,-dl. W e note that the two options 1 and 2 will not introduce the same uncertainty since the compression takes place after (option 1) and before (option 2) the calculation of the disparity. In order to calculate conveniently the total uncertainty resulting from both distortion and compression, we assume that these two sources are independent and follow a gaussian law so that we can write Ad,,, = dm and finally Aztot = Ad,,.z2 f@. For each stereo pair, the bar charts on&are 6 present the percentages of “correlated pixels” for each strategy. Except for dref, the uncertainties are always larger than l/4 pixel and the figures give the percentages of “correlated pixels” corresponding to uncertainties lower than l/2 pixel (light grey bars), lower than 1 pixel (light + medium greys) and larger than 1 pixel (light + medium + dark greys). The corresponding uncertainties affecting the range z are plotted injgure 1. Let us now examine these results having in mind that our goal is to find the strategy which minimizes the errors on the reconstruction, i.e., which maximizes the number of “correlated pixels” with the lowest uncertainty (l/2 pixel). Option 1 leads to degradations expected from “lossy” compressions. The percentages of “correlated pixels” are the same for the three strategies 1, 2 and 3 as for the reference (there are no geometric changes in the disparity map). There is just a loss in accuracy which decreases as the bit rate increases @gure 4). Option 1 at low bit rates is clearly unacceptable as the percentages of “correlated pixels” do not exceed 28 % at 0.25 bpp and 41.4 % at 0.5 bpp. Moreover its efficiency depends strongly upon the type of images. When the ground is flat, the disparity field is easily compressed since it is smooth and continuous. This explains the good results on the stereo pairs #lO and #25. When the ground is rough (e.g., when rocks are present), discontinuities appear on the disparity map and its compression gives bad results: the highest percentage at 1 bpp for l/2 pixel on the stereo pairs #5, #12 and #14 is 32.7 %. Options 2 leads to degradations of a different type which could not be simply predicted. There is a global loss in the total percentages of correlated pixels as best illustrated by the black holes in j@re 5 together with a loss in accuracy as well. We further note that the use of symmetrical compression ratios is preferable. Indeed, the percentages of correlated pixels at all accuracies are higher by about 5 % in strategy 4 than in strategies 5 or 6. Let us finally discuss the best strategy for each option, strategy 3 for option 1 and strategy 4 for option 2, by comparing the percentages of correlated pixels at l/2 pixel to the reference. For strategy 4, the degradation is almost constant as the difference ranges from 17.2 % to 24 YC&pending upon the 552
Image compression
Stereo ---_”
__ . ..-
6 r^--.
. .._._ - .
0
. ..^..-
. .
20
30
40
stereo
pair
Figure
60
70
60
--
~-20
30
40 pair
0
10
50
20
30
40
Stereo
pair
Q’
..-_.. 3!21
60
70
80
..-
tip-.+..
50
60
70
80
#14
~_---..
62,Sj
/
0
P5 72.5
r __
a
Figure
50
-.10
. -.--~ ^” .
t13
-”
Stereo
Q
X25 72,9j
6 L----.-.a-_--.
~-------~-
____0
pair
Qt-
- ---.-xGl
-~---___ 10
v--Q _---~~--
Stereo
Cl0
reconstruction
-..
QfY-
c
pair
and stereoscopic
10
20
6. Performances 6. Performances
30
40
50
on the test images sur les images
60
70
of the disparity calculation different strategies.
de test du calm1 de dispariti di$e’rentes strat&gies.
(in percentage (en pourcentages
of “correlated de CCpixels
pixels”) corr&s
for the #) pour
les
images. The performance of strategy 3 depends upon the nature of the images, superior to those of strategy 4 for the simple images (e.g., pairs #IO and #25, with a gain of up to 10.4 %), but clearly inferior for the complex images (pairs #5, #13 and #14, with losses up to 23.5 %). As the nature of the 553
S. Takerkart
et al.
cometary surface is unknown, we recommend adopting a strategy independent of the type of images, namely strategy 4, stressing further that the gain possibly offered by strategy 3 for certain types of images remains small (less than 10.4 %). 6. Conclusion
The recommended strategy (4) allows one to obtain a satisfactory percentage of “correlated pixels” with an acceptable uncertainty. This means that, despite the losses due to compression, the threedimensional reconstruction of the landing site will be possible using stereoscopic techniques. We however emphasize that these results are purely statistical; indeed we will not have access to d,,, and consequently, we shall not know the locations of the pixels for which the disparity is known with an uncertainty of l/2 pixel. The result could however be ascertained by comparison with those of photoclinometry techniques (shape from shading) which will also be implemented on CIVA-P. References Aydinoglu H., Kossentini F., Hayes M. H., 1995. Region-based stereo image coding, International Conference on Image Processing, Washington D.C. Lamboley M., Rastel L., Fouvet G., 1994. Navigation autonome Marsokhod: chaine de traitement d’images, Internal CNES Document, private communication. Lamy P., Bibring J.P., Nguyen-Trong N., Soufflot A., Boit J.L., Dohlen K., 1998. The panoramic camera for the Champollion and Roland cometary surface science packages, Adv. Space Res., vol. 21, No. 11, 1581-1588. Langevin Y., Fomi O., 1997. Algorithme de compression en ondelettes adapt& aux experiences spatiales embarqutes (images et cubes-images spectra). Internal Document Institut d’Astrophysique Spatiale, private communication. Rickman H., Fernandez J.A., Gustafson, B.A.S.. 1990. Formation of stable dust mantles on short period comet nuclei, Astron. Astrophys., vol. 237, 524-53.5. Said A., Pearlman W.A., 1996. A new fast and efficient code based on set partitioning in hierarchical trees, IEEE Trans. Circuits Syst. Video Tech.. vol. 6, 243-250. Villasenor J.D., Belner B., Liao J., 1995. Wavelet filter evaluation for image compression, IEEE Trans. Image Processing, vol. 4, 1053-1060. Woo W., Orlega A., 1996. Stereo image compression with disparity compensation using MRF model, SPIE Proc. VCIP’96, vol. 27, 28841,
554