VIEWPOINT QUALITY AND GLOBAL SCENE EXPLORATION

STRATEGIES

Dmitry Sokolov, Dimitri Plemenos and Karim Tamine

XLIM Laboratory UMR CNRS 6172, University of Limoges

83 rue d’Isle, 87000 Limoges, France

Keywords:

Scene understanding, automatic virtual camera, good point of view.

Abstract:

Virtual worlds exploration techniques are used in a wide variety of domains — from graph drawing to robot

motion. This paper is dedicated to virtual world exploration techniques which have to help a human being

to understand a 3D scene. An improved method of a viewpoint quality estimation is presented in the paper,

together with a new method for an automatic 3D scene exploration, based on a virtual camera. The automatic

exploration method is related to off-line exploration and is made in two steps. In the ﬁrst step, a set of “good”

viewpoints is computed. The second step uses this set of points of view to compute a camera path around the

scene.

1 INTRODUCTION

One of the reasons for rapid development of com-

puter science was introduction of human-friendly in-

terfaces, which have made computers easy to use and

learn. The increasing exposure of the general pub-

lic to technology means that their expectations of dis-

play techniques have changed. The increasing spread

of the internet has changed expectations of how and

when people are to access information. As a con-

sequence, a lot of problems raised. One of them

is automatic exploration of a virtual world. Dur-

ing last years, people pay essentially more attention

to this problem. They realized the necessity of fast

and accurate techniques for better exploration and

clear understanding of various virtual worlds. A lot

of projects use results of intelligent camera place-

ment researches, from the “virtual cinematographer”

(He et al., 1996) to motion strategies (Marchand and

Courty, 2000).

Quality of a view direction is a rather intuitive term

and, due to its inaccuracy, it is not easy to precise for

a selected scene, which viewpoints are “good” and

which are not. Over the last decades, many meth-

ods were proposed to evaluate qualities of view di-

rections for a given scene and to choose the best one.

All of them are based on the fact that the best view-

point gives to the user maximum amount of informa-

tion about a scene. And again, an imprecise term “in-

formation” is met.

The proposed viewpoint evaluation methods could

be divided into two groups, characterized by the na-

ture of input information:

1. Low-level methods, which consider only quantity

of visible surfaces;

2. Middle-level methods, which take into account

geometry of visible surfaces.

In this paper, a new group of high-level methods, op-

erating with the visibility of scene objects is intro-

duced.

The rest of the paper is organized as follows: sec-

tion 2 gives a brief description of previous works. A

new method of viewpoint quality estimation is de-

scribed in section 3. A comparison of methods is

given in section 4. A new method of global scene

exploration is presented in section 5. Examples of the

new technique application are given in section 6. Fi-

nally, section 7 concludes our work and points out di-

rections of future work.

2 PREVIOUS WORK

2.1 Low-level Methods of Viewpoint

Quality Evaluation

This group of strategies is the most numerous one.

Among these methods, one can point at the Kamada

and Kawai (Kamada and Kawai, 1988) approach.

They have proposed to minimize the angle between

184

Sokolov D., Plemenos D. and Tamine K. (2006).

VIEWPOINT QUALITY AND GLOBAL SCENE EXPLORATION STRATEGIES.

In Proceedings of the First International Conference on Computer Graphics Theory and Applications, pages 184-191

DOI: 10.5220/0001350101840191

Copyright

c

SciTePress

a direction of view and the normal of the considered

plane for a single face, or to minimize the maximum

angle deviation for all the faces of a complex scene.

In (Plemenos and Benayada, 1996) Plemenos and

Benayada have proposed a heuristic that extends the

deﬁnition given by Kamada and Kawai. The heuris-

tic considers a viewpoint to be good if it minimizes

the maximum angle deviation between a direction of

view and normals to the faces and gives a high amount

of details. The viewpoint quality according to (Ple-

menos and Benayada, 1996) can be computed by the

following formula:

C(p)=

n

i=1

[

P

i

(p)

P

i

(p)+1

]

n

+

n

i=1

P

i

(p)

r

, (1)

where:

1. C(p) is the viewpoint quality for the given view-

point p,

2. P

i

(p) is the number of pixels corresponding to the

polygon number i in the image obtained from the

viewpoint p,

3. r is the total number of pixels of the image (resolu-

tion of the image),

4. n is the total number of polygons in the scene.

5. [a] means the ceiling function, i.e the smallest inte-

ger number a

c

∈ N : a

c

≥ a.

In (Vazquez et al., 2001) Vazquez et al. have pro-

vided an information theory-based method, that can

be classiﬁed as low-level method. To select a good

viewpoint they propose to maximize the following

function they have called a “viewpoint entropy”:

I(p)=

N

f

i=0

A

i

A

t

· log

2

A

t

A

i

, (2)

where:

1. p is the viewpoint,

2. N

f

is the number of faces of the scene,

3. A

i

is the projected area of the face number i,

4. A

0

is the projected area of background in open

scenes,

5. A

t

is the total area of the projection.

2.2 Middle-level methods

Directly or implicitly, all the methods from the low-

level group use only two global parameters as input:

1. Quantity of visible surfaces (projected area,

amount of voxels, angle between direction of sight

and normal to a face),

2. Number of visible faces.

In other words, all of them consider a viewpoint qual-

ity as a sum of qualities of separate faces, but don’t

take into account how a polygon is connected to the

adjacent ones.

The number of visible faces is a quite weak cri-

terion for viewpoint quality estimation. For exam-

ple, if we consider a very simple scene that consists

of one square (ﬁgure 1(a)), then equation 2 gives us

I(p)=0for a viewpoint p lying on the perpendicular

to the square’s center. If we subdivide the square (ﬁg-

ure 1(b)), topology of the scene does not change, but

I(p) grows.

(a) (b) (c)

Figure 1: Three scenes represent the same square (a),but

subdivided into 4 parts (b) and 8 parts (c). Equation 2 gives

us I(p)=0for (a), I(p)=log4for (b) and I(p)=log8

for (c).

Thus, the methods using a number of faces to eval-

uate a viewpoint quality, depend on initial scene sub-

division. Using the projected area of a face as a cri-

terion of quality, the dependence appears also if we

don’t use an additive metric, i.e., the sum of areas.

Recently Sokolov and Plemenos (Sokolov and Ple-

menos, 2005) have proposed to consider the total cur-

vature of visible surfaces as an amount of information

appropriate to a viewpoint:

I(p)=

v∈V (p)

2π −

φ

i

∈φ(v)

φ

i

·

f∈F (p)

P (f ), (3)

where:

1. F (p) is the set of faces visible from p,

2. P (f) is the projected area of the face f ,

3. V (p) is the set of visible vertices of the scene,

4. φ(v) is the set of angles adjacent to the vertex v.

The proposed heuristic is invariant to any subdivi-

sion of a scene keeping the same topology. Indeed, if

we subdivide a ﬂat face to several ones, then all the

edges and vertices inside the face are to be discarded

due to zero angles.

An important property of this viewpoint quality de-

ﬁnition is the possibility to extend it, using the total

integral curvature

Ω

|K|dA, into the class of contin-

uous surfaces, such as NURBS etc., more and more

usable nowadays.

VIEWPOINT QUALITY AND GLOBAL SCENE EXPLORATION STRATEGIES

185

3 A NEW HIGH-LEVEL METHOD

Now let us suppose that, having a complex scene,

there exists some proper (in human perception) divi-

sion of a scene into a set of objects. Figure 2 shows

us an example of such a scene. These objects are: the

computer case, the display, the mouse, the mouse pad,

two cables, the keyboard and several groups of keys.

Figure 2: The scene is subdivided into a set of objects. The

display is almost completely hidden by the case, but we

could clearly recognize it.

Only 20% of the display surface is visible, but it

does not embarrass its recognition. Thus, we could

conclude that if there exists a proper subdivision of a

scene into a set of objects, the visibility of the objects

could bring more information than just the visibility

of the faces, and this leads us to the third group of

methods — the high-level class.

The requirement of a scene division into objects

does not limit the area of the method application.

There are many ways to get it. First of all, complex

scenes often consist of non-adjacent simple primi-

tives, and this leads to the ﬁrst disjunction of a scene.

Otherwise, if a scene (or some parts of a scene) is

represented by a huge mesh, it could be decomposed.

The domain of the surface decomposition is well-

studied and there are a lot of methods giving excel-

lent results. One can point at results of Zuckerberger

et al. (Zuckerberger et al., 2002) and Chazelle et al.

(Chazelle et al., 1995).

The method could be used also in declarative mod-

elling. In this case, the decomposition could be pro-

vided by a modeler directly, or it can be combined

with the information extracted from a scene geome-

try.

An accurate deﬁnition of the new heuristic is given

further. Let us suppose that for each object ω of a

scene Ω importance q(ω):Ω→ R

+

is speciﬁed.

We would like to generalize the method and do not

want to be limited by a strict deﬁnition of the impor-

tance function, because it could be done in different

ways, especially, if some additional knowledge about

a scene is supplied. For example, if the method is in-

corporated into some dedicated declarative modeler,

the importance of an object could be assigned in de-

pendence on its functionality. Moreover, after the ﬁrst

exploration the importances could be rearranged in a

different manner to see various parts of a scene more

precisely than during the previous exploration.

If no additional information is provided and the

user takes into account scene geometry only, then the

size of object bounding box could be considered as

the importance function:

q(ω) = max

u,v∈V

ω

|u

x

− v

x

| + max

u,v∈V

ω

|u

y

− v

y

| +

+ max

u,v∈V

ω

|u

z

− v

z

|,

where V

ω

is the set of vertices of the object ω.

It is also necessary to introduce a parameter charac-

terizing the predictability of an object: ρ

ω

:Ω→ R

+

.

In other words, the parameter determines the quantity

of object surface to be observed in order to well un-

derstand what the object looks like. If an object is

well-predictable, then the user can recognize it even

if he sees its small part. The bad predictability forces

the user to observe attentively all the surface.

We propose to consider the function f (t)=

ρ

ω

+1

ρ

ω

+t

t

as the measure of observation quality for an object,

where 0 ≤ t ≤ 1 is the explored fraction of the object

(for example, the area of the observed surface divided

by the total area of the object surface). Refer to ﬁg-

ure 3 for an illustration. If the percentage t for the

object ω is equal to zero (the user has not seen the

object at all), then f(t) is zero (the user cannot recog-

nize the object). If all the surface of the object ω is

observed, then f(t) is 1, the observation is complete.

If nothing is known about a scene except its geo-

metrical representation, then in order to observe it,

the parameter ρ could be taken as rather small value,

for example, ρ

ω

≡ 0.1∀ω ∈ Ω. In such a case even

exploration of a part of an object gives a good com-

prehension.

Now let us suppose that there exists some addi-

tional knowledge, for example, a virtual museum is

considered. Then for all the paintings the parameter

could be taken equal to 1000 and, for all the walls,

chairs, doors equal to 0.1. Now, in order to get a good

comprehension of a painting, one should observe all

its surface, but only a small part of door or wall is

necessary to recognize them.

Let us consider a viewpoint p. For scene objects it

gives a set of values Θ(p)={0 ≤ θ

p,ω

≤ 1,ω ∈ Ω},

where θ

p,ω

is the fraction of visible area for the object

ω from the viewpoint p. θ

p,ω

=0if the object is not

GRAPP 2006 - COMPUTER GRAPHICS THEORY AND APPLICATIONS

186

t

comprehension

quality

Figure 3: The behavior of the function f (t)=

ρ+1

ρ+t

· t for

two values of the parameter ρ. (a) ρ =0.1, even a part of

an object provides a good knowledge. (b) ρ = 1000, the

user should see all the object to get a good knowledge.

visible and θ

p,ω

=1if one can see all its surface from

the viewpoint p.

The fraction θ

p,ω

=0may be computed in various

ways. The simplest one is to divide the area of the

visible surface by the total area of an object. A bit

more complicated way is inherited from the middle-

level method (see equation 3). If we divide the curva-

ture of the visible surface by the total curvature of an

object, we obtain the fraction equal to 0 if an object is

not visible at all and equal to 1 if we could see all its

surface.

Thus, we propose to evaluate a viewpoint quality

as a sum of scene object importances with respect to

their visibility:

Q(p)=

ω∈Ω

q(ω) ·

ρ

ω

+1

ρ

ω

+ θ

p,ω

θ

p,ω

. (4)

4 AN EXAMPLE OF APPLYING

THE NEW TECHNIQUE

In this section, the computer model, that we have met

before, is considered more precisely. Figures 4 and

5 show the results of applying two techniques from

the middle and the high level classes. For the new

method no additional information is provided, so, the

bounding box sizes are taken as the importance func-

tion q(ω) and ρ

ω

≡ 0.1∀ω ∈ Ω.

The best viewpoints, chosen with the two methods,

are quite close (the picture is shown at ﬁgure 6), but

there are signiﬁcant differences in the estimation of

other view directions.

Compare ﬁgure 2, showing the scene from the

viewpoint number 10, and ﬁgure 6, showing it from

the best viewpoint. It is clear that the viewpoint 10 is

less attractive, but it still gives a good representation

30

35

25

40

20

45

15

50

10

55

5

60

0

65

95

70

90

75

85

80

(a) The second-class

method.

30

35

25

40

20

45

15

50

10

55

5

60

0

65

95

70

90

75

85

80

(b) The new high-level

method.

Figure 4: The qualities for 100 viewpoints equally distanced

from the center of the model. The best viewpoint is shown

by the black sector.

0 10 20 30 40 50 60 70 80 90

0

0

.1

0

.2

0

.3

0

.4

0

.5

0

.6

0

.7

0

.8

0

.9

1

(a) The second-class

method.

0 10 20 30 40 50 60 70 80 90

0

0

.1

0

.2

0

.3

0

.4

0

.5

0

.6

0

.7

0

.8

0

.9

1

(b) The new high-level

method.

Figure 5: The plain graphs of the qualities for 100 view-

points around the scene (see ﬁgure 4).

Figure 6: The best viewpoint for the computer model.

of the scene. The function on ﬁgure 5(b) decreases

smoothly in this region, while ﬁgure 5(a) shows a

drastic fall. At the viewpoint 17 the function from

ﬁgure 5(b) grows, because a back side of the display

and a part of the keyboard are visible simultaneously.

Then it decreases again because the case covers the

keyboard. The new method also shows a better qual-

ity than the old one from the back side of the scene.

From each viewpoint some parts of the mouse or of

VIEWPOINT QUALITY AND GLOBAL SCENE EXPLORATION STRATEGIES

187

the keyboard are visible, so the estimation should not

be so small as at ﬁgure 4(a).

5 EXPLORING A SCENE

The viewpoint quality estimation is only the ﬁrst step

in the domain of the scene understanding. In order

to help a user to get a good knowledge of a scene,

methods, allowing to choose a best viewpoint (or a

set of viewpoints), should be proposed. Dynamic ex-

ploration methods could be very helpful too, since a

set of static images is often not sufﬁcient for under-

standing of complex scenes.

There are two classes of methods for virtual world

exploration. The ﬁrst one is the global exploration

class, where the camera remains outside the explored

world (see ﬁgure 10). The second class is the local

exploration. In this class the camera moves inside

a scene and becomes a part of the scene. Local ex-

ploration may be useful and even necessary in some

cases, but only global exploration could give the user

a general knowledge on a scene. In this section we

are mainly concerned with global exploration of ﬁxed

unchanging virtual worlds. But it should be said that

interesting results have been obtained with local ex-

ploration techniques in some works.

There are few works dedicated to the problem of

virtual world exploration. Based on the deﬁnition of

good viewpoint (Plemenos and Benayada, 1996), Bar-

ral et al. in (Barral et al., 2000b) present an incre-

mental method for automatic exploration of objects

or scenes. The technique does a global exploration of

a scene, i.e. it creates a “movie” with a camera, whose

trajectory lies on a sphere, surrounding the scene.

Marchand and Courty in (Marchand and Courty,

2000) have presented the general framework that al-

lows an automatic control of a camera in dynamic en-

vironment. The method is based on image-based con-

trol approach.

V

´

azquez et al. in (Vazquez et al., 2001) present

a measure, the viewpoint entropy, based on Shan-

non’s entropy. Then they propose the extension of the

method given by Barral et al. in (Barral et al., 2000a).

In this section a non-incremental method of global

scene exploration is presented. Since we would like

to explore the exterior of a scene, it is reasonable to

restrict the space of feasible viewpoints to a surround-

ing sphere. Moreover, a viewpoint quality is quite

smooth function, so the sphere could be easily dis-

cretized. Thus, the scene is placed in the center of the

sphere, whose discrete surface represents all possible

points of view.

Having the viewpoint quality criterion and a

rapid algorithm for visibility computations (refer to

(Sokolov and Plemenos, 2005)), we are ready to

choose good views. The main idea of the method is

to ﬁnd a set of viewpoints, giving a good represen-

tation of a scene, and then to connect the viewpoints

by curves in order to get a simple path on the sur-

face of the sphere — trajectory of the camera. The

views should be as good as possible and the number

of views should not be too great. These criteria are

satisﬁed with a greedy search scheme. Let us give a

more strict formulation.

Let us suppose that two sets are given for a scene:

a set of faces F = {f

i

, 1 ≤ i ≤ n

f

} and a set of

vertices V = {v

j

, 1 ≤ j ≤ n

v

}. The scene dis-

junction into a set of objects is supplied: Ω=

{ω

k

, 1 ≤ k ≤ n

ω

}, V =

n

ω

k=1

ω

i

, k = l ⇒ ω

l

ω

k

=

∅. For each viewpoint s of the discrete sphere S the

set of visible vertices V (s) ⊆ V is given.

Let us denote the curvature in a vertex v ∈ V as

C(v) and the total curvature of a mesh V

1

⊆ V as

C(V

1

)=

v∈V

1

C(v). We suppose that all objects in Ω

have non-zero curvatures.

In addition to equation 4, let us introduce the qual-

ity of a set of viewpoints:

Q(S

1

⊆ S)=

ω∈Ω

q(ω) ·

ρ

ω

+1

ρ

ω

+ θ

S

1

,ω

θ

S

1

,ω

,

where θ

S

1

,ω

=

C(V (S

1

) ω)

C(ω)

, V (S

1

)=

s∈S

1

V (s).

Since the camera remains outside the scene and al-

ways points to the center of the sphere, there is no

need to deﬁne the view angle.

A set of viewpoints, giving a good scene represen-

tation, could be obtained by a greedy search. The

greediness means choosing the best viewpoint at each

step of the algorithm. More strictly: having given a

threshold 0 ≤ τ ≤ 1, one should ﬁnd a set of view-

points M

k

⊆ S such as

Q(M

k

)

Q(S)

≥ τ . At the be-

ginning M

0

= ∅, each step i of the algorithm adds

to the set the best viewpoint s

i

: Q(M

i−1

{s

i

})=

max

s∈S

Q(M

i−1

{s}), M

i

= M

i−1

{s

i

}.

Figure 7 shows the amount of acquired information

in dependence on the number of algorithm steps. It is

easy to see that often only few viewpoints are neces-

sary to get a good knowledge of a scene.

The next question is: if the camera has to move

from one viewpoint to another, what path on the

sphere is to be chosen? A naive answer is to con-

nect the viewpoints with a geodesic line, the shortest

one. This preserves the camera from brusque changes

of trajectory during traversal from one point to an-

other and gives the shortest solution, but acute angles

still could appear in control points of trajectory. Such

connection does not guarantee that the path consists

of good viewpoints. This drawback is serious, and, in

GRAPP 2006 - COMPUTER GRAPHICS THEORY AND APPLICATIONS

188

1 2 3 4 5

Computer

Sphere

Teapot

Average

6 7

0

0

.1

0

.2

0

.3

0

.4

0

.5

0

.6

0

.7

0

.8

0

.9

1

Figure 7: The amount of acquired information in depen-

dence of number of viewpoints selected by greedy search

for the Utah teapot model (ﬁgure 11), the sphere with im-

posed objects (ﬁgure 12) and the computer model (ﬁgure 6).

order to avoid it, we have to introduce additional costs

and discounts.

The main idea is to make the distances vary in-

versely to the viewpoint qualities. It means the aug-

mentation of path’s length if it contains bad view-

points and the reduction of the length otherwise. For

example, it can be done in the following way: if two

vertices s

1

and s

2

are adjacent in a sphere tessellation,

then the new distance between s

1

and s

2

is calculated

with the formula:

ˆ

d

s

1

,s

2

= || s

1

− s

2

|| · c

q

(s

1

,s

2

), (5)

where || s

1

− s

2

|| is the Euclidean distance between

points s

1

and s

2

and c

q

(s

1

,s

2

)=1−

Q(s

1

)+Q(s

2

)

2 max

s∈S

Q(s)

is

the discount that forces the camera to pass via “good”

viewpoints.

Figure 8: The reason to change the metric. The circles rep-

resent viewpoints: larger circles denote better viewpoints.

The solid line shows the geodesic line between viewpoints

A and B, the dashed line shows the shortest path according

to the new metric.

This empiric formula augments distances near

“bad” viewpoints and reduces near “good” ones. The

reason is shown at ﬁgure 8. Figure 9 gives an ex-

ample. It is easy to see that the camera trajectory pre-

sented at ﬁgure 9(b) brings to a user more information

than the shortest one.

Now, having deﬁned the metric and having found

the set of viewpoints, we would like to determine a

trajectory of the camera. It is not hard to construct a

complete graph of distances G =(M

k

,E), where the

(a) Shortest line connecting

two viewpoints.

(b) Shortest line with re-

spect to the viewpoint qual-

ities.

Figure 9: The trajectories between two selected points on

the surface of the surrounding sphere.

weight of an arc (v

1

,v

2

) ∈ E is equal to the metric

between the viewpoints v

1

and v

2

(equation 5).

Now the trajectory could be computed as the short-

est Hamiltonian path (or circuit, if we would like to

return the camera to initial point). The problem is also

known as the travelling salesman problem (TSP). Un-

fortunately, the TSP problem is NP-complete even if

we require that the cost function satisﬁes the triangle

inequality. But there exist good approximation algo-

rithms to solve the problem. Moreover, often |M

k

| is

rather small (see ﬁgure 7), and the problem in such

a case could be solved even by the brute-force algo-

rithm in real-time.

6 EXPLORATION EXAMPLES

Figures 10 and 11 show camera trajectories for the

Utah teapot model. The ﬁrst one is obtained by ap-

plying the incremental technique with the viewpoint

entropy as the quality heuristic, and the second one is

obtained by our method.

Both of them show 100% of the surface of the

teapot model. The new method could give brusque

changes of the trajectory, and the old one is free of

this disadvantage. A simple way to smooth the trajec-

tory is to construct a NURBS curve. Control points

for the curve are to be taken from the approximation

of the minimal set of viewpoints, and its order is to

be deﬁned by solving the TSP task. The new tech-

nique gives signiﬁcantly shorter trajectories, and this

advantage is very important.

One more example of the new method application

is shown at ﬁgure 12. This model is very good for

exploration technique tests, it represents six objects

imposed into the sphere with holes, and the explorer

should not miss them.

VIEWPOINT QUALITY AND GLOBAL SCENE EXPLORATION STRATEGIES

189

1

2

3

4

Figure 10: The exploration trajectory for the Utah teapot

model. The trajectory is computed by the incremental

method using the viewpoint entropy as the quality heuris-

tic. Images are taken consequently from the “movie”, ﬁrst

one is the best viewpoint.

1

2

3

4

Figure 11: The exploration trajectory for the Utah teapot

model, obtained with the new technique. Images are taken

consequently from the “movie”. Black knots are the control

points of the trajectory, i.e. an approximation of the mini-

mal set of viewpoints sufﬁcient to see all the surface of the

teapot model.

7 CONCLUSIONS AND FUTURE

WORKS

In this paper a new criterion of viewpoint quality eval-

uation is presented. The criterion introduces a new

level of a scene comprehension methods, so-called

1

2

3

4

Figure 12: The exploration trajectory for the sphere with

several embedded objects. Images are taken consequently

from the “movie”, black knots are the control points of the

trajectory.

high-level methods.

A new non-incremental method of global scene ex-

ploration is also presented.

In the future we shall investigate, what kinds of ad-

ditional knowledge can be efﬁciently used in scene

exploration. For example, if we have a room with

paintings, it is more reasonable to pay more attention

to the objects of art than to walls and chairs.

It would be interesting to develop automatic meth-

ods of scene exploration allowing interaction with the

user, where the user can point at parts of a scene he

would like to explore in details.

ACKNOWLEDGMENTS

The authors would like to express their gratitude to-

wards the European Community and the Limousin

Region for their ﬁnancial support of the present work.

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