Journal of Virtual Reality and Broadcasting, Volume 3(2006), no. 12

High level methods for scene exploration

Dmitry Sokolov, Dimitri PlemenosXLIM Laboratory UMR CNRS 6172, University of Limoges

83 rue d’Isle, 87000 Limoges, Francesokolov@msi.unilim.fr, plemenos@unilim.fr

Abstract

Virtual worlds exploration techniques are used in awide variety of domains — from graph drawing to ro-bot motion. This paper is dedicated to virtual worldexploration techniques which have to help a human be-ing to understand a 3D scene. An improved method ofviewpoint quality estimation is presented in the paper,together with a new off-line method for automatic 3Dscene exploration, based on a virtual camera. The au-tomatic exploration method is working in two steps. Inthe first step, a set of “good” viewpoints is computed.The second step uses this set of points of view to com-pute a camera path around the scene. Finally, we de-fine a notion of semantic distance between objects ofthe scene to improve the approach.

Keywords: Scene understanding, automatic virtualcamera, good point of view.

1 Introduction

One of the reasons for rapid development of computerscience was the introduction of human-friendly inter-faces, which have made computers easy to use andlearn. The increasing exposure of the general public

Digital Peer Publishing LicenceAny party may pass on this Work by electronicmeans and make it available for download underthe terms and conditions of the current versionof the Digital Peer Publishing Licence (DPPL).The text of the licence may be accessed andretrieved via Internet athttp://www.dipp.nrw.de/ .First presented at the International ConferenceGRAPP 2006, extended and revisedfor JVRB

to technology means that their expectations of displaytechniques have changed. The increasing spread of theinternet has changed expectations of how and whenpeople are to access information. As a consequence,a lot of problems arose. One of them is the automaticexploration of a virtual world. In recent years, peoplepay essentially more attention to this problem. Theyrealized the necessity of fast and accurate techniquesfor better exploration and clear understanding of var-ious virtual worlds. A lot of projects use results ofintelligent camera placement research, from the “vir-tual cinematographer” [HCS96] to motion strategies[MC00].

In Computer Graphics a lot of efforts are focusedon improving quality and realism of renders, but rarelyone focuses on the interaction and modeling. Indeed,usually, the user must choose viewpointshimself tobetter inspect and even to understand what a scenelooks like. The goal of this work was the developingof new techniques for automatic exploration of virtualworlds.

Quality of a view direction is a rather intuitive termand, due to its inaccuracy, it is not easy to precisefor a selected scene, which viewpoints are “good” andwhich are not. Over the last decades, many methodswere proposed to evaluate quality of view directionsfor a given scene and to choose the best one. Allof them are based on the fact that the best viewpointgives the user maximum amount of information abouta scene. And again, an imprecise term “information”is met.

This paper is organized as follows: section2 gives abrief description of previous works. A new method ofviewpoint quality estimation is described in section3.A new method of global scene exploration is presentedin section4. Section5 shows how Artificial Intelli-gence techniques could be used in the domain of au-tomatic exploration. Finally, section6 concludes ourwork and points out directions of future work.

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2 State of the art

As we have mentioned above, due to advances in infor-mation technologies, the importance of crafting bestviews has grown. The key-role in the domain of au-tomatic explorations belongs to estimating viewpointquality procedure, so, we start with reviewing ad-vances in this domain.

2.1 Viewpoint quality and camera placement

A number of papers have addressed the problem of au-tomatically selecting a viewpoint that maximally elu-cidate the most important features of an object.

The first works on visual scene understanding werepublished at the end of the years 80s. Kamada andKawai [KK88] have proposed a fast method to com-pute a point of view, which minimizes the number ofdegenerated edges of a scene (refer to figure1). Theyconsider a viewing direction to be good if parallel linesegments lie in a projection as far away from eachother as possible. Intuitively, the viewer should be asorthogonal to every face of the 3D object as possible.As this is hard to realize, they suggest to minimize themaximum angle deviation (over all the faces) betweena normal to the face and the line of the viewer’s sight.

(a) (b)

Figure 1: View (b) is better than(a), because it doesnot contain degenerated faces.

The technique is interesting for small wire-framemodels, but it is not very useful for more realisticscenes. Since this technique does not take into accountwhich parts of the scene are visible, a big element ofthe scene may hide all the rest in the final image. Ple-menos and Benayada [PB96] have proposed a heuris-tic that extends the definition given by Kamada andKawai. The heuristic considers a viewpoint to be goodif it gives a high amount of details in addition to theminimization of the deviation. Thus, the function isthe percentage of visible polygons plus the percentageof used screen area.

Stoev and Straßer in [SS02] consider a different ap-proach that is more suitable to viewing terrains, in

which most surface normals in the scene are similar,and visible scene depth should be maximized.

Sbert et al. [SFR+02] introduced an informationtheory-based approach to estimate the quality of aviewpoint. To select a good viewpoint they proposeto maximize the so called “viewpoint entropy”. Thefunction is the Shannon’s entropy, where projected ar-eas of faces are taken as a discrete random variable.Thus, the maximum entropy is obtained when a cer-tain point can see all the faces with the same relativeprojected area. By optimizing the value of entropy inimages, Sbert et al. try to capture the maximum num-ber of faces under the best possible orientation.

Recently Chang Ha Lee et al. [LVJ05] have in-troduced the idea of mesh saliency as a measure ofregional importance for graphics meshes. They de-fine mesh saliency in a scale-dependent manner us-ing a center-surround operator on Gaussian-weightedmean curvatures. The human-perception-inspired im-portance measure computed by the mesh saliency op-erator gives more pleasing results in comparison withpurely geometric measures of shape, such as curva-ture.

Blanz et al. [BTB99] have conducted user studiesto determine the factors that influence the preferredviews for 3D objects. They conclude that selection ofa preferred view is the result of complex interactionsbetween task, object geometry, and object familiarity.

2.2 Dynamic exploration

A single good point of view is generally not enoughfor complex scenes, and even a list of good viewpointsdoes not allow the user to understand a scene, as fre-quent changes of viewpoint may confuse him (her).To avoid this problem, dynamic exploration methodswere proposed.

Barral et al. and Dorme [BDP00, Dor01] proposed amethod, where a virtual camera moves in real time onthe surface of a sphere surrounding the virtual world.The scene is being examined in incremental mannerduring the observation. In order to avoid fast returnsof the camera to the starting position, the importanceof a viewpoint is made inversely proportional to thedistance along the camera path from the starting to thecurrent position.

Vazquez and Sbert [VS03] propose an automaticmethod of indoor scene exploration with limited de-grees of freedom (in order to simulate a human walk-through). The method is based on the viewpoint en-

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tropy.In [MC00, VFSH02] image-based techniques are

used to control the camera motions in a changing vir-tual world. The problem faced in the paper is the adap-tation of the camera behavior to the changes of theworld.

For more details, a state of the art paper on vir-tual world global exploration techniques is avail-able [PS06].

3 A new high-level method

Although the above methods of viewpoint quality es-timation allow to obtain interesting results, they arelow-level methods, as they use inadequate “vocab-ularies”. Let us consider an example. The scan-ning process at 300 dpi resolution produces about 9megapixels per A4 page. However, nobody uses el-ementary pixel configuration to describe content andstructure of this page. Instead, people apply Opti-cal Character Recognition methods and represent con-tent by characters and structural markup. ComputerGraphics suffers from weak representation of 3D data.Development of proper “vocabularies” for a new gen-eration of meta-data, able to characterize content andstructure of multimedia documents, is a key-feature forcategorization, indexing, searching, dissemination andaccess. It would be a grand challenge if a completesemantic 3D model could be used instead of projec-tion in lower dimensions (image, text, animations) orstructureless collection of polygons.

Thus, while these low-level methods work good inestimating viewpoint quality of a single object, theyoften fail in complex scenes. In this section the firsthigh-levelmethod is presented. The main idea of themethod is to pass to higher level of perception in or-der to improve the notion of viewpoint quality. Letus suppose that, having a complex scene, there existssome proper division of the scene into a set of objects.Figure2 presents an example of such a scene, wherethe subdivision into a set of objects is shown by dif-ferent colors. These objects are: the computer case,the display, the mouse, the mouse pad, two cables, thekeyboard and several groups of keys.

Only 20% of the display surface is visible, but itdoes not embarrass its recognition because, if we arefamiliar with the object, we couldpredict what doesit look like. Thus, we conclude that if there exists aproper subdivision of a scene into a set of objects, thevisibility of the objects could bring more information

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.

than just the visibility of the faces, and this leads us tothe new level of abstraction.

This method of viewpoint quality estimation makesthe first few steps in the direction of semantic descrip-tion of a 3D scene. Note that developing innovativeways to represent a scene originates a lot of problemssuch as conversion of already existing scenes to newformat. However, the requirement of a scene divi-sion into a set of objects does not limit the area ofthe method application. There are many ways to getit. First of all, complex scenes often consist of non-adjacent simple primitives, and this leads to the firstdisjunction of a scene. Otherwise, if a scene (or someparts of a scene) is represented by a huge mesh, itcould be decomposed. The domain of the surface de-composition is well-studied and there are a lot of meth-ods giving excellent results. One can point at resultsof Zuckerberger et al. [ZTS02] and Chazelle et al.[CDST95].

The method we propose is also useful in declara-tive modelling by hierarchical decomposition (refer to[Ple95] for the main principles). In such a case, the de-composition could be provided by a modeler directly,or it can be combined with the information extractedfrom the scene geometry.

The main idea is to define howpertinenteach ob-ject is and how well it ispredictable. Then for anyviewpoint we can determine visible parts of the scene.With this information given we can calculate how welleach object is observed. The total viewpoint quality

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consists of the sum of observation qualities for eachobject.

An accurate definition of the new heuristic is givenfurther. Let us suppose that for each objectω of asceneΩ its importanceq(ω) : Ω → R+ is specified.

We would like to generalize the method and do notwant to be limited by a strict definition of the impor-tance function, because it could be done in differentways, especially, if some additional knowledge abouta 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 firstexploration the importances could be rearranged in adifferent manner to see various parts of a scene moreprecisely than during the previous exploration.

If no additional information is provided and the usertakes into account scene geometry only, then the sizeof object bounding box could be considered as the im-portance function:

q(ω) = maxu,v∈Vω

|ux − vx|+ maxu,v∈Vω

|uy − vy|++ max

u,v∈Vω

|uz − vz|,

whereVω is the set of vertices of the objectω.It is also necessary to introduce a parameter charac-

terizing thepredictability(or familiarity) of an object:ρω : Ω → R+. In other words, the parameter deter-mines the quantity of object surface to be observed inorder to well understand what the object looks like. Ifan object is well-predictable, then the user can recog-nize it even if he sees a small part of it. Bad pre-dictability forces the user to observe attentively all thesurface.

The ρω parameter sense could be also interpretedin a different manner. Even if an object is well-predictable (for example, it is a famous painting), theparameterρω could be chosen as for an object withbad predictability. This choice forces the camera toobserve all the painting.

We propose to consider the functionf(t) = ρω+1ρω+t t

as the measure of observation quality for an objectwith predictabilityρω, where0 ≤ t ≤ 1 is the ex-plored fraction of the object (for example, the area ofthe observed surface divided by the total area of theobject surface). Refer to figure3 for an illustration. Ifthe percentaget for the objectω is equal to zero (theuser has not seen the object at all), thenf(t) is zero(the user cannot recognize the object). If all the sur-face of the objectω is observed, thenf(t) is 1, the

t

comprehensionquality

Figure 3:The behavior of the functionf(t) = ρ+1ρ+t · t

for two values of the parameterρ. (a) ρ = 0.1, evena part of an object provides a good knowledge.(b)ρ = 1000, the user should see all the object to get agood knowledge.

observation is complete.

If nothing is known about a scene except its geo-metrical representation, then one may suppose thatthe scene does not contain extraordinary (very rough)topology. Then the parameterρ could be taken asrather small value, for example,ρω ≡ 0.1∀ω ∈ Ω.In such a case even exploration of a part of an objectgives a good comprehension.

Now let us suppose that there exists some additionalknowledge, for example, a virtual museum is consid-ered. Then for all the paintings the parameter could betaken equal to 1000 and, for all the walls, chairs, doorsequal to 0.1. Now, in order to get a good comprehen-sion of a painting, one should observe all its surface,but only a small part of door or wall is necessary torecognize them.

Let us consider a viewpointp. For scene objects thispoint gives a set of valuesΘ(p) = 0 ≤ θp,ω ≤ 1, ω ∈Ω, whereθp,ω is the fraction of visible area for theobjectω from the viewpointp. θp,ω = 0 if the objectis not visible andθp,ω = 1 if one can see all its surfacefrom the viewpointp.

The fractionθp,ω may be computed in various ways.The simplest one is to divide the area of thevisiblesurface by thetotal area of an object. Another wayis to divide the curvature of the visible surface by thetotal curvature of the object. In both cases, we obtainthe fraction equal to 0 if an object is not visible at alland equal to 1 if we could see all its surface.

Thus, we propose to evaluate the viewpoint qualityas the sum of scene objectimportanceswith respect to

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theirvisibility andpredictability:

Q(p) =∑

ω∈Ω

q(ω) · ρω + 1ρω + θp,ω

θp,ω. (1)

Figure 4 shows the behaviour of two viewpointquality heuristics. The mean curvature is taken as thefirst one, while the high-level heuristic, proposed inthis section, is taken as another one. For the high-levelmethod no additional information is provided, so, thebounding box sizes are taken as the importance func-tion q(ω) andρω ≡ 0.1∀ω ∈ Ω.

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(b) The high-level heuristic

Figure 4:The qualities for 100 viewpoints equally dis-tanced from the center of the model. The best viewdirections are indicated by the black sectors.(a) Meancurvature;(b) the high-level heuristic.

The best viewpoints, chosen by the two methods,are quite close (the picture is shown in figure5), butthere are significant differences in the estimation ofother view directions.

Let us compare figure2, showing the scene from theviewpoint number 10, and figure5, showing it from thebest viewpoint. It is clear that the viewpoint 10 is lessattractive, but it still gives a good representation of thescene. The function on figure4(b)decreases smoothlyin this region, while figure4(a)shows a drastic fall. Atthe viewpoint 17 the function from figure4(b) grows,because the back side of the display and a part of thekeyboard are visible simultaneously. Then it decreasesagain because the case covers the keyboard. The high-level method also shows a better quality than the low-level one from the back side of the scene. From eachviewpoint some parts of the mouse or of the keyboard

Figure 5:The best viewpoint for the computer model.

are visible, so the estimation should not be as small asat figure4(a).

4 Exploring a scene

4.1 Introduction

The viewpoint quality estimation is only the first stepin the domain of scene understanding. In order tohelp a user to get a good knowledge of a scene, meth-ods, allowing to choose the best viewpoint (or a setof viewpoints), should be proposed. Dynamic explo-ration methods could be very helpful too, since a set ofstatic images is often not sufficient for understandingof complex scenes.

There are two classes of methods for virtual worldexploration. The first one is theglobal explorationclass, where the camera remains outside the exploredworld. The second class is thelocal exploration one.In this class the camera moves inside a scene and be-comes a part of the scene. Local exploration maybe useful and even necessary in some cases, but onlyglobal exploration could give the user a general knowl-edge on a scene. In order to simplify the presentation,we present a method of global exploration of fixed un-changing virtual worlds. The method can be adaptedto perform local explorations. The only difficulty isthe collisions detection. It can be solved introducingdisplacement maps for the camera.

Thus, let us suppose that a scene is placed in the cen-ter of the sphere, whose discrete surface represents allpossible points of view. Having the viewpoint quality

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criterion and a rapid algorithm for visibility computa-tions (refer to [SP05]), we are ready to choose goodviews. The main idea of the method is to find a setof viewpoints, giving a good representation of a scene,and then to connect the viewpoints by curves in orderto get a simple path on the surface of the sphere, thetrajectory of the camera.

As the viewpoint quality measure we use equa-tion (1). The heuristic is very flexible and gives goodresults even (and especially) for complex scenes. Theviewpoints should be as good as possible (provideas much information as possible) and the number ofviewpoints should not be very great. These criteria aresatisfied with a greedy search scheme. Firs of all, wedefine the quality of a set of viewpoints. Then, startingfrom the best viewpoint, at each step we find the bestviewpoint for the unexplored part of the scene. The al-gorithm stoppes when the quality of the set surpassesthe desirable level of the comprehension.

4.2 Observation quality for a set of views

Let us suppose that the sceneΩ consists of separatedmeshesω1, . . . , ωnΩ. The sets of verticesV and

viewpointsP are provided.V =nΩ⋃k=1

ωi, k 6= l ⇒ωl

⋂ωk = ∅. For each viewpointp of the discrete

sphereP the set of visible verticesV (p) ⊆ V is given.Now let us extend the definition given by equa-

tion (1) and define the quality of a set of views (pho-tos). Let us suppose we have selected a set of view-points P1 from the all possible camera positionsP .Each objectω of the scene may be visible from multi-ple viewpoints, so it is necessary to determine its visi-ble partθP1,ω.

Let us denote the curvature in a vertexv ∈ V asC(v) and the total curvature of a meshV1 ⊆ V asC(V1) =

∑v∈V1

C(v). Then for a given objectω its visi-

ble fractionθP1,ω equals to the curvature of visible partdivided by the total curvature of the object’s surface.Therefore,θP1,ω = C(V (P1)

Tω)

C(ω) , V (P1) =⋃

p∈P1

V (p).

Of course, we suppose here that all the objects inΩhave non-zero curvatures.

Once we have determined which parts of every ob-ject are visible from our set of viewpointsP1, the qual-ity equation remains the same:

Qα(P1 ⊆ P ) =∑

ω∈Ω

q(ω) · ρω + 1ρω + θP1,ω

θP1,ω.

As we have mentioned before, a set of views, givinga good representation of a scene, could be obtainedby a greedy search. The greediness means choosing abest viewpoint at each step of the algorithm. Startingfrom the best viewpoint, at each step we find the bestviewpoint for the unexplored part of the scene. Thealgorithm stoppes when the quality of the set surpassesthe desirable level of the comprehension.

More strictly: having given a threshold0 ≤ τ ≤ 1(the desirable level of the comprehension), one shouldfind a set of viewpointsMk ⊆ P such asQ(Mk)

Q(P ) ≥ τ .HereQ(Mk) means observation quality for the set ofviewpointsMk, andQ(P ) is the observation qualityfor the set of all possible viewpoints.

At the beginningM0 = ∅, each stepi of the al-gorithm adds to the set the best viewpi. Mi =Mi−1

⋃ pi:

Q(Mi−1

⋃pi

)= max

p∈PQ(Mi−1

⋃p).

4.3 Dynamic exploration

The next question is: if there are two viewpoints andthe camera has to move from one to another, whichpath is to be chosen? A naive answer is to connect theviewpoints with the shortest path (geodesic line). Butit does not guarantee that the path consists of goodviewpoints. Let us consider factors influencing thequality of a film.

We suppose that the resulting distance function isthe superposition of different costs and discounts. Firstof all, one must take into account the cost of movingcm the camera from one point to another (proportionalto the Euclidian distance). The cost of camera turnsmay be discarded as the camera moves are restrictedto the sphere.

Now let us introduce the discountcq that forcesthe camera to pass via “good” viewpoints. The mainidea is to make the distances vary inversely to theviewpoint qualities. For example, it can be done inthe following way: if two viewpointsp1 and p2 areadjacent in a sphere tessellation, then the new dis-tance betweenp1 and p2 is calculated with the for-mula: cq(p1, p2) = 1 − Q(p1)+Q(p2)

2maxp∈P

Q(p) . This empiric

formula augments displacement costs between “bad”viewpoints and reduces near “good” ones.

Thus, the resulting distance function between twoadjacent viewpoints is:

dp1,p2 = cm(p1, p2) + cq(p1, p2). (2)

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Figures6 and 7 illustrate the idea. It is easy tosee that the camera trajectory presented at figure7(b)brings to a user more information than the shortest one.

Figure 6: The reason to change the metric. The cir-cles represent viewpoints: larger circles denote betterviewpoints. The solid line shows the geodesic line be-tween viewpoints A and B, the dashed line shows theshortest path according to the new metric. It is clearthat sometimes it would be better to increase the lengthof the walk-trough in order to better inspect certainplaces.

(a) Shortest line connectingtwo viewpoints.

(b) Shortest line with respectto the viewpoint qualities.

Figure 7:The trajectories between two selected pointson the surface of the surrounding sphere.

Now, having defined the metric and having foundthe set of viewpoints, we would like to determine atrajectory of the camera. It is not hard to construct acomplete graph of distancesG = (Mk, E), where theweight of an arc(v1, v2) ∈ E is equal to the metricbetween the viewpointsv1 andv2 (equation (2)).

Now the trajectory could be computed as the short-est Hamiltonian path (or circuit, if we would like toreturn the camera to initial point). The problem is alsoknown as thetravelling salesman problem(TSP). Un-fortunately, the TSP problem is NP-complete even ifwe require that the cost function satisfies the triangleinequality. But there exist good approximation algo-rithms to solve the problem. Moreover, often|Mk| israther small, and the problem in such a case could besolved even by the brute-force algorithm in real-time.

Now we can compute a broken line as the cameratrajectory. However, brusque change of direction invertices of the line may be disattracting. The simplesolution is to calculate a spline with the line verticesas control points.

4.4 Exploration examples

Figures8 and9 show camera trajectories for the Utahteapot model. The first one is obtained by applyingthe incremental technique with the viewpoint entropyas the quality heuristic, and the second one is obtainedby our method.

Figure 8: The exploration trajectory for the Utahteapot model. The trajectory is computed by the in-cremental method using the viewpoint entropy as thequality heuristic. Images are taken consequently fromthe “movie”. The first one is the best viewpoint.

Both of them show 100% of the surface of the teapotmodel. The new method could give brusque changesof the trajectory, and the old one is free of this disad-vantage. A simple way to smooth the trajectory is toconstruct a NURBS curve. Control points for the curveare to be taken from the approximation of the mini-mal set of viewpoints, and its order is to be defined bysolving the TSP task. The new technique gives signif-icantly shorter trajectories, and this advantage is veryimportant.

The next example of the new method application isshown at figure10. This model is very good for testingexploration techniques, it represents six objects im-posed into holes on the sphere, and the explorer should

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Figure 9: The exploration trajectory for the Utahteapot model, obtained with the new technique. Im-ages are taken consequently from the “movie”. Blackknots are the control points of the trajectory, i.e. anapproximation of the minimal set of viewpoints suffi-cient to see all the surface of the teapot model.

not miss them. None of the previously proposed meth-ods can properly observe this model. All of them, hav-ing found an embedded object, are confused in choos-ing the next direction of movement. This happens be-cause of missing information about unexplored areas.On the contrary, the new method operates with the an-alytic visibility, allowing to determine where some un-explored areas rest.

5 Semantic distance

As we have mentioned above, it would be very helpfulif a semantic 3D model could be used instead of struc-tureless collection of polygons. Let us consider an ex-ample (see figure11). Figure11(a)shows a scene withtwo churches. There are three manually fixed view-points. The dashed line is the trajectory, obtained bythe above method of exploration, adapted to indoor ex-plorations. The exploration is started at the viewpoint1. It is easy to see that the camera turns aside fromthe big church in the viewpoint 2 and then reverts backagain. The trajectory is very short and smooth, but theexploration is confusing for the user.

Figure11(b)shows another trajectory, where the ex-ploration starts in the viewpoint 1, passes via 3 and

Figure 10: The exploration trajectory for the spherewith several embedded objects. Images are taken con-sequently from the “movie”, black knots are the con-trol points of the trajectory.

(a)

(b)

Figure 11:Two different trajectories.(a) During tra-versal from the point 1 to 3 the camera turns aside fromthe big church and then reverts back again.(b) Thecamera turns aside from the big church only when itsexploration is complete.

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terminates in the point 2. The camera turns aside fromthe big church only when its exploration is complete.Despite the increased length of the trajectory, the ex-ploration is more clear.

Thus, we postulate that the above method of auto-matic exploration could be improved by regroupingthe control frames in dependence onrelativenessofinformation they show. In other words, if two framesshow the same object, they are to be consequent in thefinal animation.

The relativeness (or semantic distance) can bedefined in many ways. For example, Foo et al.in [FGRT92] define a semantic distance in concep-tual graphs based on Sowa’s definition. Zhong et al.in [ZZLY02] propose an algorithm to measure the sim-ilarity between two conceptual graphs.

In our work we use semantic networks. An ex-ample of such a network is given at figure12. The

painting sculpture

Monet V an Gogh Da V inci unknown

RenaissanceImpressionism

School

Mp vGp1 vGp2 dVsdVp Unks

Figure 12:The semantic network example for a virtualmuseum. Importances of relationships are denoted bythickness of lines.

figure shows a semantic network for a small vir-tual museum, which contains paintings by Van Gogh(vGp1, vGp2), Monet (Mp), Da Vinci (dVp) andtwo sculptures by Da Vinci (dVs) and unknown sculp-tor (Unks). Importances of relationships are denotedby thickness of lines. Thus, the information thatMp

is created by Claude Monet is more important than theinformation thatMp is a painting.

In order to measure semantic distance between twoobjectss andt, we transform the semantic network toan undirected flow networkG = (C, EC). EdgesECcorrespond to relationships between conceptsC of thesemantic network, capacitiesb(i, j) > 0 ∀(i, j) ∈ ECare to be set according to the relationship importances.

s and t are the source and the sink with unboundedsupply and demand, respectively. Let us denote thecapacity of anxy-cut (x, y ∈ C) ascut(x, y) and thecapacity ofxy-mincut asmin cut(x, y). Then the se-mantic distance can be defined as follows:

D(s, t) =1

min cut(s, t). (3)

For continuity reasons we defineD(x, x) ≡ 0 ∀x ∈C. It is easy to see that equation (3) defines a metricD : C × C −→ R+.

Now, having defined the semantic distance betweentwo objects, we can introduce the semantic distancebetween two “photos”. More strictly, if one “photo”shows a set of objectsA ⊆ C and another shows aset of objectsB ⊆ C, one can define the similaritydistance between the sets as follows:

D(A,B) =

∑(ai,bj)∈A×B

D(ai, bj)

|A| · |B| .

The distance between sets is also a metric.Now let us show how the metric could be used in

scene exploration. In the previous section we haveconstructed a complete weighted graphG. We rede-fine the travelling cost between two “photos” as thelength of the shortest path (equation (2)) between themplus the semantic distance between the “photos”.

Figure13(a)presents the shortest exploration trajec-tory for a small virtual museum we presented above.The corresponding semantic network is shown in fig-ure 12. The exploration starts from the Van Goghpainting (vGp1), then comes Da Vinci paintingdVp,Monet (Mp) etc. The exploration terminates after vis-iting the second painting of Van Gogh (vGp2).

It is clear that the order is not good. For example,it is better to observe creations of one author conse-quently. A trajectory, obtained with respect to the se-mantic network is shown at figure13(b). The cam-era starts with two paintings by Van Gogh (vGp1,vGp2), continues with Monet (Mp), then shows thepainting by Da Vinci (dVp), passes to the sculptureby Da Vinci (dVs) and terminates with the sculptureby unknown author (Unks).

It is easy to see that the second trajectory is morelogical than the first one. The trajectory does not inter-rupt exploration of items by the same author and thecamera passes to the renaissance items only when allthe impressionists paintings are explored.

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Journal of Virtual Reality and Broadcasting, Volume 3(2006), no. 12

vGp1

dVp

Mp

vGp2

Unks

dVs

(a)

vGp1

dVp

Mp

vGp2

Unks

dVs

(b)

Figure 13: The virtual museum exploration trajecto-ries. (a) The shortest trajectory.(b) The shortest tra-jectory with respect to the semantic network shown atfigure12.

6 Conclusion and future work

In this paper a new high-level approach to evaluateviewpoint quality is presented. A non-incrementalmethod of global scene exploration is demonstrated.It allows a camera to navigate around a model untilmost of interesting reachable places are visited. Themethod runs in real-time. In distinction from [Dor01],it guarantees that all interesting places in a scene willbe observed. The techniques, presented in this paper,may be generalized in order to be used in local explo-ration too. In order to make the generalization, it isnecessary to solve the camera-objects collision prob-lem. Figure14 shows our preliminary results in thedomain of local exploration.

Figure 14: Free navigating in 3D: the resulting trajec-tory is shown from two points of view: from the sideand from the top. The hidden part of the trajectory isshown in the white dashed line.

A new measure of similarity between objects is alsointroduced in this paper. It is useful when some addi-tional knowledge of scene structure could be provided.This measure, so called semantic distance, evaluatesrelationships in the scene to improve the explorationmethod.

Semantic networks promise to be a rich area forfurther research. We are currently defining similaritymeasure between objects, but it should be possible toextend the definitions taking into account user pref-erences. It will also be an interesting exercise to usemachine learning techniques to take into account im-plicit user preferences. Different people have differenttastes, and artificial intelligence techniques could helpto handle some uncertainties. Probably, it would bepossible to create for each user a database of prefer-ences to improve exploration of further scenes.

7 Acknowledgements

The authors would like to express their gratitude to-wards the European Community and the Limousin Re-gion for their financial support of the present work.

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CitationDmitry Sokolov and Dimitri Plemenos,High levelmethods for scene exploration,Journal of VirtualReality and Broadcasting, 3(2006), no. 12,August 2007, urn:nbn:de:0009-6-11144,ISSN 1860-2037.

urn:nbn:de:0009-6-11144, ISSN 1860-2037