1 Introduction

Using metaballs tomodeling and animate
clouds from satellite
imagesYoshinori Dobashi1 ,Tomoyuki Nishita2 ,Hideo Yamashita3 ,Tsuyoshi Okita1
1 Hiroshima City University, Faculty of Information

Sciences, 3-4-1 Ozukahigashi, Asaminami-ku,
Hiroshima, 731-3194, Japan
E-mail: {doba, okita}@im.hiroshima-cu.ac.jp
2 The University of Tokyo, Department of Information
Science, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033,
Japan
E-mail: nis@is.s.u-tokyo.ac.jp
3 Hiroshima University, Faculty of Engineering, 1-4-1
Kagamiyama, Higashi-Hiroshima, 739-8527, Japan
E-mail: yama@eml.hiroshima-u.ac.jp

We propose modeling that uses metaballs tocreate realistic clouds from satellite images.
The method is intended for space flight simulators, visualization of the weather information, and simulation of surveys of the earth.
The density distribution inside the clouds isdefined by a set of metaballs. The parameters(center positions, radii, and density values)
are automatically determined so that the synthesized image is similar to the satellite image. We also propose an animation method
for clouds generated by a sequence of satellite images taken at a given interval. We give
several examples of clouds generated fromsatellite images of typhoons passing throughJapan.
Key words: Clouds – Image-based modeling – Satellite image – Metaballs
Correspondence to: Y. Dobashi

The Visual Computer (1999) 15:471–482
c Springer-Verlag 1999

The simulation of natural phenomena, such as water, smokes, fire, and clouds, has often been attempted in computer graphics (Klassen [12]; Kaneda
et al. [11]; Stam and Fiume [23]; Max [15]; Stamand Fiume [24]; Nishita et al. [19]; Foster andMetaxas [5]). Clouds play an important role in theimages of outdoor scenes, the earth viewed fromouter space, and the visualization of weather information. This paper proposes a method for modelinglarge-scale clouds viewed from space, such as thosein a typhoon. Many methods have been developed
for modeling clouds, and they can be classified into
two groups.
Methods in the first group create clouds by procedural modeling. Voss [26] and Musgrave [16] create
realistic clouds with fractals. Gardner [6] has produced realistic images of clouds by using Fourier
synthesis. However, this does not create a true threedimensional geometric model. Ebert and Parent [3]have used solid texture to generate clouds in threedimensional space. Ebert [2] has also developed
a method combining metaballs and a noise function
to model clouds. Sakas [20] has modeled clouds byusing spectral synthesis, and Nishita et al. [19] create clouds by generating metaballs using the ideaof fractals. Using these methods to create clouds
that the user pictures in the mind is, however, very
difficult since many parameters have to be specified by trial and error. Stam and Fiume [22] havedeveloped a simple method for modeling clouds.
In their method, a user specifies density values atseveral points in three-dimensional space. Then thedensity distribution of the clouds is obtained by interpolating the specified density values. Although
this method can create realistic clouds, it is impractical for creating large-scale clouds viewed fromspace. Methods for modeling a set of clusters ofclouds have also been developed. Ebert et al. [4] create realistic images of typhoons by the proceduralapproach. Nishita and Nakamae [19] have modeled clouds to generate realistic images of the earth
viewed from space. In both these methods, however, clouds are simply modeled by applying twodimensional fractals. The color and shape of clouds
change depending on both the viewpoint and the position of the sun. These methods cannot simulate
such effects.
Methods classified in the second group model clouds
by simulating the physical process of the clouds
forming (Kajiya and Herzen [9]; Stam and Fiume [23, 24]). In these methods, however, there is of-

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Y. Dobashi et al.: Using metaballs to modeling and animate clouds from satellite images

ten a high computational cost for simulating clouds
over the earth.
To address this problem, we propose a new method
for modeling three-dimensional clouds based ona satellite image. In recent years, many methods ofimage-based rendering and/or modeling have beendeveloped in computer graphics (Terzopoulos andWitkin [25]; Debevec et al. [1]; Gortler et al. [7];Levoy and Hanrahan [14]; Seitz and Dyer [21];Horry et al. [8]). The proposed method makes use of
the image-based approach to generate clouds. Lee etal. [13] also use satellite images to generate clouds
in order to visualize weather information. However,they use polygons to model them, resulting in poorlooking clouds. In the proposed method, the density
distribution of clouds is represented by using metaballs. Parameters of metaballs (center positions, effective radii, and density values) are determined automatically so that a synthesized image of the clouds
coincides with the satellite image. With the satellite
image, the proposed method makes use of the factthat the color of clouds can be calculated by integrating the scattered light due to particles in them. In thismethod, clouds with a shape and color similar to real
clouds can be automatically generated. Moreover,this paper also proposes an animation method forclouds generated by a sequence of satellite images.
Note that our method does not reconstruct the exact
three-dimensional shape of clouds in the satellite image. The goal of our method is to generate realistic
clouds as easily as possible, so that they can be used
for TV films and so on. In order to demonstrate theusefulness of the method, we apply it to animationsof the visualization of weather information and theearth viewed from space.
In the following sections, the basic idea of modeling clouds is described in Sect. 2. Next, in Sect. 3,
the details of the modeling method are discussed.
In Sect. 4, the method for animating the generated
clouds is proposed. In Sect. 5, several examples are
given. Finally, in Sect. 6, conclusions and future
work are discussed.

2 The basic idea of modeling clouds
from a satellite image
Various representations can be used for modelingclouds. Examples are: voxels (Kajiya and Herzen [9]),procedural functions (Ebert et al. [4]; Ebert [1]), andmetaballs (or blobs) (Stam and Fiume [24]; Nishita

et al. [19]). With metaballs, clouds can easily be animated by moving their centers. Therefore, we use
metaballs to model them as shown in Fig. 1.
A density value at a point P in the cloud is given by
the following equation.
ρ(P) ≈NX

q j f(r j , R j )

(1)

j=1

where N is the number of metaballs, q j the density
at the center of a metaball j, f the field function,
and R j the radius of the metaball. Further, r j is the
distance between the point P and the center position of a metaball, C j ; that is, r j = |P − C j |. We
use the field function proposed by (Wyvill and Trotman [27]). That is to say,  
4 r j 6 17 r j 4+f(r j , R j ) = −
9 Rj
9 Rj
 2
22 r j−+1,
9 Rj
when r j ≤ R j , otherwise 0.
Determining parameters of the metaballs is equivalent to solving an inverse problem of determining thedensity distribution inside the clouds so that an image of synthesized clouds is similar to a satellite image. The problem is, however, very complicated andhard to solve. Therefore, we assume that the multiple
scattering can be neglected. Furthermore, for modeling clouds, the attenuation of light due to cloud particles is approximated by a constant. Despite theseassumptions, there is no unique solution to the problem. Therefore, the parameters of the metaballs areheuristically determined as follows. First, each pixelof the satellite image is classified as part of either
a cloud region or a background region. To do this,the satellite image is converted to monotone. Thenpixels with intensities higher than a specified threshold are identified as clouds. Next, one metaball isadded at the pixel with the maximum intensity inthe cloud region. After that, its radius and density at
the center are optimized and the approximated image is calculated from the clouds modeled by metaballs. Then a new metaball is added if the error between the satellite image and the approximated image is greater than a specified threshold. These processes are repeated until the error is less than thethreshold.
The overview of the proposed method is as follows.

Y. Dobashi et al.: Using metaballs to modeling and animate clouds from satellite images473

1. Classify the pixels in the satellite image into either
cloud regions or background regions.
2. Generate a metaball at the pixel with the maximum intensity in the cloud regions of the satellite
image.
3. Optimize the radius and the density value at thecenter of the metaball.
4. Calculate the approximated image using the clouds
modeled by metaballs.
5. If the error between the satellite image and the approximated image is less than a specified threshold,stop. Otherwise, go to step 6 after calculating the image of difference between the satellite image and theapproximated image.
6. Go to step 3 after generating a metaball at the pixel
with the maximum intensity in the cloud regions of
the image of difference.
In the following sections, details of the method are
discussed.
Fig. 1. Geometry of clouds

3 Modeling clouds with metaballs
In this section, the method for determining the parameters is proposed after we describe the method
for calculating the error between the satellite image
and the image synthesized by using clouds modeledby metaballs.

Ii (λ) = Ib (λ) exp(−τ(L ab , λ)) + Isun (λ)β(φ, λ)ZPb
ρ(t) exp(−τ(t, λ) − τ(s, λ))dt ,

×

(3)

Pa

3.1 Calculating the error between thesatellite image and synthesized image
The parameters of the metaballs are determined sothat the mean square error between the satellite image and the synthesized image is minimized; that is:
1 X (true)(I− Ii )2 → min ,M i=1 i
M

Err =

(2)

where M is the number of pixels in the satellite image, and Ii(true) and Ii are the intensity of the satellite
image and the intensity of the synthesized image at
pixel i, respectively. In the following, the calculation
method of Err is described.
As shown in Fig. 1, let the density be ρ(t) at a point
P at distance t from the viewpoint Pv . Then theintensity Ii is calculated by the following equation(Kaneda et al. [10]).

where Ib is the background color; λ, the wave length;
L ab , the distance from Pa to Pb ; β(φ, λ), the phasefunction of the cloud particles; φ, the phase angle between the viewing ray and the sun direction; Isun , theintensity of the sunlight outside the atmosphere; andτ(L ab , λ) is the optical length from Pa to Pb . The optical length is obtained by integrating the density of
the cloud particles from Pa to Pb . Similarly, τ(t, λ)is the optical length from Pa to P; and τ(s, λ), from
Pc to P (see Fig. 1). Although s is a function of t,
we denote it as s instead of s(t) for simplification.
By putting Eq. 1 into Eq. 3, the following equation is
obtained.
Ii (λ) = Ib (λ) exp(−τ(L ab , τ)) + Isun(λ)β(φ, λ)ZPb  XN×
q j f j (r j , R j )
Pa

j=1


× exp(−τ(t, λ) − τ(s, λ)) dt ,

(4)

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Y. Dobashi et al.: Using metaballs to modeling and animate clouds from satellite images

whereτ(t, λ) = c

Zt X
N
0

q j f j (r j , R j )dt ,

(5)

j=1

and c is the extinction coefficient. Since it is difficult to determine the parameters of metaballs so thatthe intensity of the satellite image coincides with theintensity calculated by Eq. 4, it is approximated asfollows. First, the wavelength is neglected since scattering of light due to cloud particles obeys Mie scattering, and the spectrum of scattering is not much influenced. Therefore, the satellite image is converted
to a monotone one and the phase function β(φ, λ)depends only on φ. Second, the attenuation terms
exp(−τ(L ab , λ)) and exp(−τ(t, λ) − τ(s, λ)) in Eq. 4
are approximated as constants κ1 and κ2 . Note thatthese approximations are only for modeling clouds.
Then, the following equation is obtained.
Ii = Ib κ1 + Isunβ(φ)κ2

ZPb X
N
Pa

= Ib κ1 + Isunβ(φ)κ2

q j f(r j , R j )dt

the intensity after adding it. Then,

j=1

N
X

q j F(r j , R j ) ,Ii(new) = Ii(old) + Isun β(φ)κ2 qk F(rk , Rk ) .
(6)

j=1

,(i = 1, . . . , M)
where
out

ZP j
F(r j , R j ) =f(r j , R j )dt ,Fig. 2. Determination of center of metaballs

(7)

P in
j

and P jin and P jout the intersection point of the viewing
ray with the metaball j. F is the integrated function of the field function f and can be calculated
analytically (Nishita and Nakamae [17]). To obtain
the background intensity Ib a satellite image without
clouds is required. We obtain this image by assembling the background regions of a set of satellite images by hand. The threshold to decide whether pixels
belong in cloud regions or background regions is experimentally determined. Then, the intensity Ii of thesynthesized image can be calculated by Eq. 6. Thiscan be calculated incrementally every time a newmetaball is added. Let us assume that Ii(old) is the intensity before adding the metaball k and that Ii(new) is(8)

The second term in Eq. 8 is evaluated at the pixels
through which the viewing rays intersect the metaball k. Therefore, Ii can be calculated with a small
computation cost, resulting in faster optimization
processes for the parameters.
Using Ii obtained by this method, the error Err between the satellite image and the synthesized image
is calculated. Metaballs are added repeatedly until
the error is less than a specified tolerance.

3.2 Determining the center of a metaball
When the number of metaballs becomes large, thecomputation for generating images takes a long time.
Therefore, the number of metaballs should be as
small as possible. Depending on the position of thecenter of each metaball, the number of metaballschanges for representing the clouds within the tolerance. The integrated function F of the field function f has a peak value at r j = 0, and it decreases
gradually as r j increases, finally becoming zero atr j = R j . The number of metaballs tends to be small
when the center position is chosen where the function F fits the intensity distribution of the satellite

Y. Dobashi et al.: Using metaballs to modeling and animate clouds from satellite images

475

Fig. 3. Optimization steps for the density and radius

image. The reason for this is that the intensity distribution of cloud images is smooth and the distribution
around the pixel with the maximum intensity is considered similar to the distribution of the function F.
Therefore, the center position is determined on theviewing ray through the pixel with the maximum
intensity. In order to determine the center positionin three-dimensional space, a base plane is virtually
generated (see Fig. 2). In our system, the base planeis set parallel to the image plane. Although generation works well in most cases, the user can also
specify it manually. The center point of the metaball is set to the intersection point of the viewing raywith the base plane. After the metaballs have beenplaced at the intersection point, the intersection pointof the viewing ray with the metaballs is calculated,
and the center is set to the nearest point as shownin Fig. 2. After one metaball is generated, the image of the difference is calculated. Then it is used for
determining the center of the next metaball in order
to avoid the same pixel being chosen for the center point.

3.3 Optimization of the radius and density
at the center
The basic idea for calculating radius Rk and density qk at the center of the metaball k is to search
for the optimal values by changing them little by little. Figure 3 shows the process for determining theradius and density. In Fig. 3, the base plane is parallel to the image plane, and the dotted curve indicates the function F(rk , Rk ). For this search, theupper limit R∗ for the radius is specified by theuser.
The radius Rk and the density qk are determined
to minimize the difference of intensity between thesynthesized image and the satellite image at pixels inside the radius of the metaball. In Fig. 3, theshaded areas indicate the difference. First, an initial radius and density are set to δ and (Ii(true) −κ1 Ib )/(Isun β(φ)κ2 F(0, δ)), respectively (Fig. 3a). In
other words, the radius and the density are initialized so that the intensity due to the metaball at the476

Y. Dobashi et al.: Using metaballs to modeling and animate clouds from satellite images

Fig. 4. Calculation of flow vectors

pixel is equal to that of the satellite image. Next,
the density is fixed, and the optimal radius that minimizes the error is calculated by incrementing theradius by d (Fig. 3b). Then, after making the density smaller by w, the optimal radius is searched
for again (Fig. 3c). By making the density smaller,
the radius can be larger, hence one metaball cancover a larger area. This results in reducing the number of metaballs. This process is repeated until the
optimal radius and density are found (Fig. 3d). In
this paper, d is set to the size of one pixel andw is specified by the user. Note that a metaball
is deleted if the density becomes zero during thesearch.

line segments, and intermediate images are generated from the correspondence between these featurepoints or line segments. However, this method is
not applicable to the animation of clouds. Clouds
in one image move according to the flow of theatmosphere, resulting in the clouds in the next image. Therefore, their movement cannot be expressedjust by interpolating the feature points. To create realistic cloud motion, we assume each metaball can be classified as one of the following threecases.
Case 1. Clouds move from one place to another.
Case 2. Clouds disappear while moving.
Case 3. Clouds appear while moving.

4 Animation of clouds
In this section, an method for animating clouds
is proposed. First, clouds are modeled from satellite images taken at a certain interval. Then they
are animated by interpolating the parameters of themetaballs.
In traditional morphing techniques, meshes are used
for correspondence between images. Recently, moresophisticated methods have been developed: the user
specifies the features of images by using points or

Although the flow analysis of the atmosphere is required for obtaining the exact movement of clouds
taking these cases into account, this computation is
too expensive. Thus, in the proposed method, theuser inputs the flow as Bézier curves by observing
a sequence of satellite images. Figure 4a shows anexample of flow curves specified by the user. With
the aid of such flowcurves, metaballs are classified
as one of the three cases, and clouds are animatedby changing their center positions, densities, andradii.

Y. Dobashi et al.: Using metaballs to modeling and animate clouds from satellite images

477

4.1 Classification of metaballs using flow
curvesLet us denote the metaballs generated from satellite image A (recorded at time t A ) as M A,i (i =1, . . . , n A ), and the metaballs generated from satellite image B (recorded at t B ) as M B, j ( j =1, . . . , n B ).
n A and n B are numbers of metaballs M A,i and M B, j ,respectively. First, to get correspondence between
M A,i and M B, j , we move metaballs M A,i using theflow curves. The method for this is described in thenext section. Then, M A,i is associated with M B, j if
M B, j is the closest, the distance between M A,i and
M B, j is less than a specified threshold, and M B, j has
not yet been associated with any other metaballs. After this process, each metaball is classified as one of
the three cases. Metaball M A,i is classified as case 1
if there the corresponding metaball M B, j exists; otherwise it is classified as case 2. The metaball M B, j
is classified as case 3 if none of M A,i corresponds
to it. The density qi and the radius Ri of each metaball at time t (t A < t < t B ) are calculated as follows.
The densities, radii, and center positions of case 1
metaballs are linearly interpolated by using the corresponding metaballs. For case 2, the densities arelinearly faded out, and for case 3, they are faded in.
For both these cases, the center positions are determined by a method described in the next section.

4.2 Moving metaballs with flow curves
Each metaball moves toward a flow vector v calculated at its center with the use of the flow curves(Fig. 4b). First, the minimum distance dk and closest point Pk from the center point to each Bézier
curve are calculated. If the distance dk is less thana specified distance D, the Bézier curve affects the
movement of the metaball. Then tangent vector vk at
the closest point is calculated. The flow vector v atthe point is defined as thePweighted sum of the tangent vectors; that is, v = nk=1 wk vk . n is the numberof Bézier curves inside the domain of influence. The
weight wk is calculated as follows. First, the contribution ratio ak is calculated by:
dk 2(dk ≤ D) .
(9)
ak = 1.0 − D
0.0(dk > D)
Then the weight wk is calculated by normalizing ak ;that is,Fig. 5. Clouds generated from a satellite image. a A satellite
image. b Clouds modeled by metaballs. c Clouds viewed fromdifferent viewpoint

wk = ak /

n
X

aj .

(10)

j=1

The amount of movement in time step ∆t is ∆tv.

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Y. Dobashi et al.: Using metaballs to modeling and animate clouds from satellite images

Fig. 6. Examples of animation of clouds

5 Examples
Figure 5 shows examples of clouds using satellite
images viewed from space. Figure 5a is an infrared

image of a typhoon taken from the meteorological satellite “Himawari”. Figure 5b shows clouds
modeled by metaballs. By comparing Fig. 5a with
Fig. 5b, it can be seen that the proposed method

Y. Dobashi et al.: Using metaballs to modeling and animate clouds from satellite images

479

Fig. 7. Examples of the visualization of weather information

can generate clouds similar to those in satellite
images. Figure 5c shows the same clouds froma different viewpoint. Since clouds are modeled inthree-dimensional space, they are seen from different viewpoints, and shadows are cast on Japan. To
generate Fig. 5b and c, the color of the clouds is
calculated by taking into account the single scattering of light by using Eq. 4. The infrared image used here is available on the internet (Several sites provide satellite images, for example,
http://www.jwa.go.jp/gms.html). This image wasrecorded at 21:00 on 16 September 1995.
In this example, the number of metaballs is 9534
and the calculation time for generating them is
15 s on a Silicon Graphics Indigo 2 Maximum Impact (195 MHz MIPS R10000). The calculation

time for generating Fig. 5b is 9.5 min on the samemachine.
Figure 6 shows an example of clouds animated by the
proposed method as it is described in Sect. 4. Figure 6a and f were rendered by using clouds generated
from satellite images and Fig. 6b–e, by interpolatingthem. The satellite image corresponding to Fig. 6a
was recorded 3 h before the satellite image of Fig. 6f,
which is the same as Fig. 5b. As shown in this example, the proposed method can realize the smooth andnatural transition of clouds.
Next, Figs. 7 and 8 show images from two animations of the proposed method, entitled Weather
Report and The Earth II. For both these animations,
13 satellite images were used to generate clouds and
900 images were produced by using the method de-

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Y. Dobashi et al.: Using metaballs to modeling and animate clouds from satellite images

Fig. 8. Examples of the earth viewed from spacescribed in Sect. 4. Figure 7 is for visualizing weather
information. In this animation, the movement ofa typhoon passing across Japan is visualized. Figure 7 shows that the proposed method can generaterealistic clouds even if the viewpoint is varied.
Figure 8 shows examples of the animation of theearth viewed from space. In this animation, the position of the sun changes. The color of the earth iscalculated by taking into account the effect of thescattering of both sunlight and sky light due to theatmosphere with the method developed by Nishita
and Nakamae [17]. In Fig. 8a, the sun is behind theviewer, turning the color of the clouds red. In Figs. 8band c, the sun is above the clouds. Finally, in Fig. 8d,the sun is hidden behind the earth. These examples
show that optical effects can be simulated when 3D

clouds are generated. These effects cannot be simulated just by mapping the satellite image as textures.

6 Conclusions
A method that uses metaballs for modeling clouds inthree-dimensional space from a single satellite image has been proposed. By making use of a satellite
image of real clouds, the proposed method can generate clouds with authentic shapes and colors. We
have also proposed an animation method for clouds
modeled by metaballs. With the proposed method,
three-dimensional clouds are generated, and they canbe viewed from arbitrary directions. The color of theclouds can be calculated by simulating the optical

Y. Dobashi et al.: Using metaballs to modeling and animate clouds from satellite images

effects. Furthermore, the animated clouds are generated from a series of satellite images, and shapes ofclouds at each frame are obtained by interpolating
them.
There are several future projects:
1. In order to increase realism by adding various
plausible fine features, some kind of turbulencemodel, such as the one used by Stam and Fiume [22]or Ebert [1] should be included.
2. To model clouds more accurately, methods for theestimation of the height of clouds from satellite images (Lee et al. [13]) should be incorporated.
3. Extending the proposed method to generate clouds
from photographs taken from the ground will be useful for modeling clouds such as cumulonimbi.
Acknowledgements. The authors thank the reviewers for their constructive criticism and positive comments.

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YOSHINORI D OBASHI has
been a Research Assistant at the
Department of Information Science, Hiroshima City University,
Hiroshima, Japan since 1997. Hereceived his BE, ME, and PhD in
Electrical Engineering from Hiroshima University, Hiroshima,
Japan in 1992, 1994, and 1997,
respectively. His research interests include global illumination
volume rendering, and animation. He is a member of Information Processing Society of Japan.

T OMOYUKI N ISHITA has
been a Professor in the Department of Information Science atUniversity of Tokyo, Japan since1988. He taught at Fukuyama
University from 1979 to 1998.
His research interests center incomputer graphics, including
lighting models, hidden-surface
removal, and antialiasing. He received his BE, ME, and PhD
in Engineering in 1971, 1973,
and 1985, respectively, from Hiroshima University. He is oneof the pioneers of the radiosity
method.

T SUYOSHI O KITA has beena Professor at the Department
of Information Science, Hiroshima City University, Hiroshima, Japan since 1995. He
taught at Yamaguchi University
from 1978 to 1995. His researchinterests center on the system
identification. He received his
ME from Tohoku University,
Japan, in 1964. He is a member of the Institute of ElectricalEngineers of Japan and the Society of Instrument and Control
Engineers.

H IDEO YAMASHITA has
been a Professor at the Department of Electrical Engineering, Hiroshima University,
Hiroshima, Japan since 1992.
He received his BE and ME
in Electrical Engineering from
Hiroshima University, in 1964
and 1968, respectively, and a
PhD in Electrical Engineeringfrom Waseda University Tokyo,
Japan, in 1977. His interests
include electric and magnetic
fields analysis of electric machinery by finite element analysis and visualization of 3D magnetic fields by computer
graphics. He is a member of the Institute of Electrical Engineersof Japan, the IEEE, and the ACM.