From geometric to semantic human body models

12 Pages·2006·0.74 MB·English

ARTICLE IN PRESS
Computers&Graphics30(2006)185–196
www.elsevier.com/locate/cag
From geometric to semantic human body models
(cid:1)
M. Mortara, G. Patane´ , M. Spagnuolo
IstitutodiMatematicaApplicataeTecnologieInformatiche,ConsiglioNazionaledelleRicerche,Genova,Italy
Abstract
The paper introduces a framework for the automatic extraction and annotation of anthropometric features from
humanbodymodels.Theframeworkisbasedontheconstructionofastructuralmodelofthebody,builtuponamulti-
scale segmentation into main bodies (e.g., torso) and limb features (e.g., fingers, legs, arms). The decomposition is
independentofthebodyposture,itisstabletonoise,andnaturallyfollowstheshapeandextentofthelimbfeaturesof
thebody.Thestructuraldescriptionofthehumanbodyisturnedintoasemanticdescriptionbyusingasetofrulesand
measuresrelatedtothefeaturesandbyreasoningtheirconfiguration.Resultsareshownbothforscannedbodymodels
andvirtual humans,and applicationsare discussed inrelation to several tasks ofthe animationprocess.
r2006Elsevier Ltd. Allrights reserved.
Keywords:Shapeanalysis;Shapereasoning;Semanticsofshapes;Humanbodyanalysis;3Dsurfacescandata
1. Introduction study and analyse the shape of the human body in
digital contexts. Due to the advances of scanning
The automatic recognition of features in free-form technology,it hasbeenpossible to carry outoneof the
shapes is a challenging issue, especially when the largest anthropometric survey within the CAESAR
semantics underlying the feature definition is related to project [1] which has made available a set of data of
an intrinsically not formalized context. This is the case over 10000 individuals in digital form. Traditional
offeaturesofthehumanbody:neck,legs,thigh,elbow, anthropometric practices largely rely on the knowledge
and many other terms which identify relevant body oftheexpertperformingthemanualmeasuringofsizes
parts,refertoportionsofthebodyshapewhichcannot and shapes, using tapes and calipers, and on the use of
be precisely coded or identified by a mathematical different postures to get a precise evaluation of the
formulation. Also, some of the body features are various anthropometric parameters. Body size measur-
composition of other features: a leg is defined by the ing tools are generally limited to 1D information
shin, the calf, the thigh, its articulation depends on the while the new 3D body scanning technology provides
knee and by the ankle and hip which connect it to capabilities such as segmental volumes and surface
thebody.Atthesametime,inthelastdecadeweassisted areas [1], and may support a more reliable and surely
to a growing interest in computer-aided methods to less expensive way to measure shapes. The potential
impact of 3D surface anthropometry is therefore very
(cid:1) highinfieldsrelatedtoergonomics,clothandprosthetic
Correspondingauthor.Tel.:[phone];
design,obesity studies,and manymore[2].
fax:[phone].
E-mail addresses: [email protected] (M. Mortara), Human body models, being either scanned or
[email protected](G.Patane´),[email protected] modelled,areofhighinterestfortheanimationindustry
(M.Spagnuolo). as well. A modelling system based on human features
0097-8493/$-seefrontmatterr2006ElsevierLtd.Allrightsreserved.
doi:10.1016/j.cag.2006.01.024
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186 M.Mortaraetal./Computers&Graphics30(2006)185–196
would greatly improve several steps of the animation the graph usedto code the human body and itsuse for
pipeline. A human body is usually animated by extracting and computing relevant anthropometric
associatingaso-calledcontrolskeletontothe3Dshape, measures are described; in Section 5, the use of the
which is a connected set of segments corresponding to framework is discussed in relation to the input data
limbsandjoints,thatis,thepointswheretheconnected characteristics and applications. Finally, conclusions
limbs may move. Unfortunately, both the skeleton and futurework are drawn.
extraction and the establishment of the correspondence
between the geometry and the skeleton can be strongly
time-consuming. Some commercial software packages 2. Previous work
include tools for skeleton-based animation, like Maya
and 3D Studio MAX. Nonetheless, the creation of a Theparadigmofshapesegmentationhasbeenlargely
controlskeletonmayrequireseveralhoursofwork,and studied in the literature, both for generic and specific
theusermustpossessafairdegreeofproficiencywitha application contexts as well as for discrete and
package to obtain even a rudimentary motion. A continuousshaperepresentationschemes.Inthespecific
decomposition of the human body into relevant contextofhumanbody,thesegmentationhasbeenoften
features would therefore contribute to speed up these addressed in parallel with the automatic location of
applications. landmarks.Thefirstattemptsweredevisedforworking
In this context, we present the results of a new onthepointcloudsresultingfromthescanningsessions.
frameworkforautomaticallyannotatingahumanbody The work presented in [5] approaches the problem of
model with information related to the body features. recognizing relevant body parts as an aid to the
The annotation and reasoning about the features are optimizationofthebodymeasuresthemselves.3Dbody
supported by the segmentation of the human body scanners acquire data along horizontal slices and the
models into geometric features, by the creation of a qualityoftheresultingmeasurementobviouslydepends
skeletonwhichencodesthefeatureattachmentrelations, on physical limitations of the scanning device and the
and by a measuring scheme which allows to attach body posture. If the body is scanned using a natural
quantitative descriptorsto eachpart. The segmentation standingposition, indeed,the armswillgenerally touch
approach is based on the multi-scale method called the torso and in this area it is impossible to distinguish
Plumber, developed for segmenting a surface into pointsonthearmfrompointsonthetorso.Tosolvethis
generalized cones and cylinders [3,4]. Plumber defines problem, the method proposed in [5] is aimed at the
thebasicdecompositionofthebodymodelintotubular- detection of sharp variations of the contour shape,
like parts and main body, usually corresponding to the which are usedto trimthe arm dataand toreconstruct
torsointhecontextofhumanbodymodels.Thesurface the missing torso data. The method does not have a
patchcorrespondingtothetorsoisfurthersegmentedin general validity, as it depends on the specific posture,
ordertoextractsymmetryregionsandareasofinfluence and the segmentation provides a quitepoor description
ofthe variousattachmentsof jointsto thetorso. Based of the body features.
on this geometric segmentation, a semantic model is Themethoddescribed in[6]andrefinedin [7]adopts
built as an annotated shape-graph where each node an approach based on the alignment of a stick figure,
corresponds to a relevant feature represented by its representingtheabstractskeletalstructureofabodyina
centreline skeleton and a set of cross-sections. Reason- standard pose, to the raw data. The stick figure is
ing can be performed on the shape-graph to deduce composed of six linear segments, which are aligned to
furthermeasuresandidentifycompoundoffeatures,as thescandataunderusercontrol.Thismethodprovides
well as to classify body models using standard anthro- the segmentation and also the computation of the
pometricrules. featurecentrelines,butitsuffersofthesamedependence
The main characteristics of the method proposed are onthebodypostureasthemethodpreviouslydescribed.
the ability to produce a semantically consistent shape- The segmentation indeed uses information of the
graph of human body models independently of their horizontal scanning contours, and it produces a space-
posture, and the automatic association of skeletal lines based andnota shape-based decomposition.
to body limbs together with cross-sections and size The analysis of horizontal slices has been more
parameters. Due to the properties of the Plumber recentlyusedin[8]withinaframeworkwhichsegments
method,thesegmentationisstablewithrespecttonoise rawdataaccordingtotheirmembershiptoabodypart,
in themodel. reconstructs the shape of the body parts, and attaches
Thepaperisorganizedasfollows:first,previouswork themtogetherinordertobuildthefullbodyreconstruc-
onthecharacterizationofthehumanbodyisreviewedin tion. Again, the segmentation is functional to the
Section 2; the segmentation approach underlying the reconstruction and the boundary of the body parts is
presented framework is briefly described in Section 3, horizontal, as it is computed relying on the horizontal
andthereadercanfindfulldetailsin[3,4];inSection4, scanning slices.
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M.Mortaraetal./Computers&Graphics30(2006)185–196 187
The advantages of defining the segmentation directly
onthebodysurfaceinsteadofonthespaceoccupiedby
the body has been introduced in [9], where the body is
segmented using concepts of Morse theory. A topolo-
gicalgraphwhichcodestheevolutionofthelevelsetsof
real-valued mapping functions is used to segment the
bodyshape.Terminalandbranchingnodesofthegraph
correspond to critical values of the mapping function,
which is chosen as the integral geodesic distance. The
graph connectivity is used to segment the shape into
parts which representthe relevant features of the body.
Astheauthorspointout,oneofthemainadvantagesof
the method is to provide a posture independent
segmentationof the shape.
3. Multi-scalegeometric shapesegmentation
Theproposeddecompositionofthehumanbodyand
its semantic annotation rely upon a general shape
segmentation method called Plumber, developed by the
authors and fully described in [3,4]. For the sake of
clarity, we summarize here the main aspects of the
segmentation, while details can be found in the cited
references.
Fig. 1. (a) Evolution of the intersection curves between the
The Plumber approach to shape decomposition is
input surface and a set of spheres with the same centre and
aimed at the extraction of tubular features of a 3D
increasing radii, (b) classification of blend, sharp and planar
surface represented by a triangle mesh. The Plumber
vertices,(c)tubularfeaturesclassifiedascylindersandcones.
algorithm segments a surface into connected compo-
nents that are either body parts or elongated features,
regionswhicharethenusedtocomputethefirstreliable
thatis,handle-likeandprotrusion-likefeatures,together
tubesection,calledthemedialloop.Thisloopisensured
withtheirconcavecounterparts,i.e.narrowtunnelsand
to be around each candidate tube and works as a
wells. The recognition is based on the classification of
generatorofthefeature.Then,themedialloopismoved
vertices according to geometric and morphological
inbothdirectionsontheshape,byusingspheresplaced
descriptors evaluated on neighbourhoods of increasing
not on the surface but at the barycentre of the medial
size. The set of neighbourhoods associated to each
loop iteratively and until the tube is completely swept.
vertex is defined by a set of spheres, centred at the
Thestopcriteriaoftheiterativeprocedurearediscussed
vertex,andwhoseradiirepresentthescaleatwhich the
inSection3.3.Thetubedetectionworksinamulti-scale
shapeisanalysed.Thenumberofconnectedcomponents
setting, starting with the extraction of small tubes first.
of the intersection curve between each sphere and the
Assuming that the shape is represented by a mesh
surface gives a first qualitative characterization of
triangleMandthatweareusingasetoflevelsofdetail
theshapeina3Dneighbourhoodofeachvertex.Then,
frg,thestepsoftheextractionprocedurearepresentedin
the evolution of the length ratio of these components
thefollowing paragraphs.
withrespectto the radiusof the spheres canbeused to
refinetheclassificationanddetectspecificfeatures,such
assharpprotrusionsorwells,mountsordips,blendsor 3.1. Vertex classification
branching parts. For example, for a thin limb, the
intersection will be simply connected for a small radius For each vertex v2M and scale r, we consider the
anditwillrapidlysplitintotwocomponentsastheradii surface region containing v and delimited by the
increase. For a point on the tip of a limb, the intersection between M and the sphere Sðv;rÞ of centre
intersection will remain connected, but the ratio of its vand radiusr;letgbethe boundaryof thisregion and
lengthtotheradiusofthespherewillbedecreasing.See let us discard all other regions of intersection between
Fig. 1 foranexample of theprocess. the sphere and the mesh that might occur but do not
Plumberspecializesthisapproachtothedetectionand contain v (see Fig. 1(a)). If g has only one connected
extraction of tubular features. At the first step, seed component (see Fig. 1(b)), then the surface around v is
verticesarelocatedandclusteredtoformcandidateseed equivalent to a disc and its curvature at scale r is
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188 M.Mortaraetal./Computers&Graphics30(2006)185–196
approximatedbythenon-negativeratioG ðvÞ:¼l =r[10],
r g
wherel isthelengthofg.Furthermore,visclassifiedas
g
planar if GrðvÞ(cid:1)a, sharp if GrðvÞoa, and blend if
G ðvÞ4a, where a isa giventhreshold.
r
Let us now suppose that g has two connected
components, and in this case the vertices are labelled
aslimb.Thevertexvatscalerisclassifiedascylindrical
whentheratiobetweenthemaximalandminimallength
ofg andg doesnotexceedagiventhreshold(cid:1),thatis,
1 2
l (cid:1)(cid:1)l ; otherwise, it is labelled as conical (see Fig.
g1 g2
1(c)).Ifghasthreeormoreconnectedcomponents,visa
branching and we do not consider other geometric
descriptors.
The set of radii is automatically set by uniformly
samplingtheintervalbetweentheminimumedgelength
and the diagonal of the bounding box of M. These
parameters,aswellasthoseonesusedfortheclassifica-
tionofthevertices(i.e.,a:¼2p,(cid:1):¼2),canbeselectedby
theuserifanaprioriinformationontheinputshapeis
available or if he/she is searching for some specific
configurations(e.g.,verticeswhosesharpestangleisless
thanagivenvalue).Thechoiceofaand(cid:1)canobviously
take into account a specific application context, as
detailed in Section4.
Fig. 2. (a) Selection of a level of detail r, (b) classification of
3.2. Shapesegmentation
vertices,(c)identificationofaseedlimbregion,(d)medialloop,
(e) iterations, (f) extraction and abstraction of the tubular
The vertex classification is used for defining a shape featureasaskeletallineandasetofcontours.
segmentation into connected components which are
either tubular features (i.e., regions which can be respect to the scale at which they were found. The
described as generalized cones or cylinders) or body connected components of the shape which are not
parts (i.e., regions which connect tubular features). To classifiedastubularfeaturesdefinethebodypartsofthe
this end, we proceed in the following steps: we select a inputsurface.InSection4,anextensionandrefinement
level of detail rand we identify seedlimb-regions as the of the Plumber segmentation for body parts will be
maximal edge-connected regions of limb-vertices with presented.
respecttoadepth-firstsearch(seeFig.2(a–c)).Then,we
computethemedialloopofeachseedlimb-regionwhich
representsthegeneratorofthefeature,anditisusedfor
itsexpansionuntilastopcriteriaissatisfied.InFig.2(d), 3.3. Shape segmentationproperties
themedialloopistheboundaryofthedarkregion,while
the growing phase is shown in (e). Then, we iterate the Thedescribedsegmentationmethodisrobusttonoise
processon Mbyconsidering thenextlevel of detail. andindependentofthevertexsamplingandconnectivity
Theradius,orscale,ofthesphereinfluencestwosteps regularity (see Fig. 3). In fact, the computation of the
of the tube recognition process: once for the morpho- intersection curves among M and the selected set of
logicalanalysis,tolocatethelimbverticesandcandidate spheres uses the connectivity structure only for the
tuberegions,andonceforthetubegrowingphase.The computationofg,whiletheclassificationofavertexpas
stop condition of the tube sweeping phase is decided belongingtoatubeatscaler(i.e.,kp(cid:2)ck2pr,withcas
eitherbyathresholdonthevariationoftheintersection centre of the current sphere) relies only on the set of
length,bytheendingofthetubularfeatureitself,orby vertices. The curvature evaluation on the real scan
thesplittingofthetubeatabranchingsite.Ifthetubular modelshowninFig.4isperformedatthreeradii;atthe
featureends,thetubeiscalledcapanditwillhaveonly smallest radius, the segmentation presents many tiny
oneboundary,asitisshapedasageneralizedcone.The regions, mainly composed by one vertex only, and due
extraction of tubes adopts a fine-to-coarse strategy, tothenoiseinthedata.Atlargerscales,theinfluenceof
markingtrianglesasvisitedwhilethetubegrowssothat noiseonthecurvaturecomputationandtubeextraction
they are not taken into account at the following steps. becomesnegligible;infact,theintersectionbetweenthe
Attheendofthewholeprocess,tubesarelabelledwith sphere and the mesh is computed exactly and it is not
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Fig. 3. Shape decomposition when the geometry of the input
surfaceis(a)coarse,(b)smooth,and(c)affectedbynoise.
affected by the underlying mesh quality. Timings are
reported inTable 1. Fig. 4. Main step and robustness to noise of the Plumber
segmentation on a scan model consisting of 13790 vertices;
timingsaregiveninTable1.
3.4. Performanceof thealgorithm
The time complexity required by the tube extraction
depends on the following stages: curvature evaluation, Table1
medial loop computation, and tube growing. In the Timings (in seconds) of the Plumber segmentation shown in
worst case (i.e., when almost all the vertices fall inside Fig.4
the sphere), the curvature analysis at each vertex takes
Task R¼1 R¼5 R¼8
OðnÞ-time, with n number of vertices; therefore, the
complexity for the whole model is Oðn2Þ. Even if the Tailor(s) 11 51 61
average case is less complex and depends on the radius Medialloop(s) – 21 50
size, this is the slowest phase of the workflow. The Tubeconstruction(s) – 3 3
medial loop computation uses Dijkstra’s algorithm and
takesOðm2 logmÞ-timeforeachseedlimbregion,where
m is its number of vertices. The tube growing phase,
the domain. Since the input model represents a human
whichactuallyconstructsthetubularstructures,islinear
body, either virtual or scanned, its relevant tubular
inthenumberoftrianglesbelongingtotubes.Oncethe
features will identify arms, legs, neck, and fingers. The
finalsegmentationisbuilt,theshape-graphisevaluated
torso and its symmetries are also important data in the
in linear timewithrespect tothe number of patches.
anthropometrydomain.Ingeneral,Plumberwillnotfind
directly these features, but some of their parts. For
instance,ahandwillbesegmentedintofivesmalltubes,
4. Thesemantic bodymodel possibly with their associated caps, all of them being
attached to the same body part. Reasoning on the
Inthissection,wedescribehowtoextractthesemantic relative sizes of the features and on the attachment
content, which is implicit in the digital model, from the relations among them makes possible to recognize and
geometry,thestructure,andtheknowledgepertainingto automaticallymeasuresemanticallyrelevantpartsofthe
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190 M.Mortaraetal./Computers&Graphics30(2006)185–196
human body. To this end, let us explain how the
segmentation obtained using Plumber is coded as a
shape-graph, and then we will show how different
descriptorscanbeassociatedtotheshape-graphinorder
toproduceasemanticbodymodel.
4.1. Centrelines oftubular features
Each tubular feature T, extracted at scale r, either
conical or cylindrical is abstracted by a skeletal line Fig. 5. Voronoi-like regions of the body primitives shown in
defined by joining the barycentres b of the intersection Figs.9and15,respectively.
i
curvesg betweenTandthesetofspheresusedtosweep
i
the tube. Since the shape and position of the tubular
feature could be arbitrarily complex, the intersection
curvesaregooddescriptorsforthecross-sectionsofthe
tubealongthecentreline.Atthesametime,positioning
the centrelines at the barycentres of the intersection
curvesallowsustofollowtheextentofthefeatureatthe
resolution that the application requires. It is important
to notice that, from the point of view of the measures
that will be introduced later on, all tubular parts are
representedwithanumberofintersectionsthatdepends
only on the scale and size of the feature, thus ensuring
consistencyoftheclassificationamongdifferentpartsof
the body.
Fig. 6. Surface segmentation of the bi-torus into a body
primitiveandtwotubularfeaturesanditsshape-graph.
4.2. Refinementof the bodyparts
4.3. Coding thefeatures inanadjacency graph
While conical and cylindrical tubular features have a
specific shape, body parts can be arbitrary shaped. It
The surface decomposition and the skeletal lines of
mightbeinterestingtofurther segmenteachofthemin
tubularfeaturesarecodedinaconnectivitygraphwhich
order to identify symmetries in their shape and define
represents the spatial arrangement of the tubular
theinfluenceareasoftheattachedfeaturesforsupport-
features onto bodies. The shape-graph nodes are the
ing the localization ofjoints (see Section5).
extracted primitive shapes, while the arcs code the
Let us consider a body primitive B with kX3
adjacencyrelationsamongthem(seeFig.6).Ingeneral,
boundary components g, i¼1;...;k; in order to
i each arc between two adjacent nodes falls into one of
determine the area of influence of each boundary, a
these cases: cylinder–body, cylinder–cylinder, and con-
reasonableapproachistoclustertheverticesofBwhich
ical–cylinder. The cylinder–body or cylinder–cylinder
areclosertothesameboundarycomponentwithrespect
adjacency is called H-junction (i.e., handle-junction) if
tothegeodesicdistance.Insteadofusingthisapproach,
bothboundariesofthecylinderlayonthesamebody,or
whichistimeconsumingandsensibletotheconnectivity
cylinder; in this case, the arc induces a loop and the
regularity of B, we use a parameterization of the body
cylinderlocatesahandleontheinputmodel.Inthecase
part on a planar domain O isomorphic to B and with
ofhumanbodies,thismighthappenif,forexample,the
respect to one of its boundary components, using the
hand touches the leg or the torso. Finally, if only one
approach presented in [11]. If j:B!O is such a
boundary of the cylinder belongs to the cylinder–body,
parameterization,avertexp2Bcanbeassociatedwith,
the adjacency iscalled aT-junction.
i.e.clusteredwith respectto,the boundaryg suchthat
s
kp%(cid:2)pr ðp%Þk ¼ min fkp%(cid:2)pr ðp%Þk g,
bs 2 j¼1;...;k bj 2
wherepr istheorthogonalprojectionontotheconvex 4.4. Semantic descriptors andreasoning
bj
curveb:¼jðgÞ,andp%:¼jðpÞ.Therefore,theuseofthe
j j
geodesic metric on B has been replaced by the While the adjacency relations in the graph define the
evaluation of the Euclidean distance on the parameter- structure of the human body with respect to the
izationdomain.Atthisstage,regionswiththesamearea decomposition, the geometry of the features are
reflecta symmetry ofthe patch(see Fig. 5). furthercharacterizedbythefollowingdescriptors.Each
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cylindricalnodeisuniquelylabelledinthegraphanditis designedvirtualhumanwheretheshapeofthebodypart
storedwith: can emphasize joints for artistic reasons, like in the
examplegivenin Fig. 9(a,b).
(cid:3) Thekneesectionsmaybesosmalltoberecognizedas
the scale rat which the tubehasbeen found;
(cid:3) candidate tubes at the same scale as the wrist and the
the set of its approximated cross-sections (i.e.,
ankle, respectively. This produces two tubes for each
sphere–tubeintersections) andthe averageradius;
(cid:3) limbtogrow,andwheretheymeet,eachonestops.This
thesetofitscentrelinepoints(i.e.,barycentresofthe
situation is handled by checking if the last computed
sphere–tubeintersections);
(cid:3)
the orientation of each segment of the centreline
(turning);
(cid:3)
the centreline axis length and the approximated
volume.
Eachconicalnodeisstoredwiththesameattributesas
tubes, except the radius of the average cross-section
whichisreplacedbytheradiusofitsbasissection;inthis
casealsothemaximumoftheGaussiancurvatureinthe
region is stored. Each node of type body is stored with
the number of its boundary components, its approx-
imate volume,andits refinedsegmentation.
Basedonthestructuralandgeometricinformation,it
ispossibletoreasononthesemanticaspectsofthebody
model.Firstofall,thereisastrongrelationbetweenthe
scale r at which the feature is found and the minimum
sectionsizeofthetubeitrepresents.Asphereofradiusr
willlabelaslimballtheverticeslyingonatubularpart
whose section has a maximum diameter less than r=2
(seeFig.7).Therefore,runningPlumberfromsmallerto
largerscales,weexpecttorecognizeatfirstfingers,then
arms, legs, and eventually the neck. Note that what is
importantfortheidentificationofatubeistheminimum
Fig.8. Firstrow:inputmodelsofvirtualhumansindifferent
sectionsizetostartthegrowing:wristsarefoundfirstas postures. Second row: cylindrical features are depicted in
candidate tubes, and then the tube growing constructs yellow;conicandbodyfeaturesareshowninblue.Themodel
allthearms;thesameforlegsthatareidentifiedstarting consists of 5775 vertices and the algorithm takes 18s for the
fromtheankles,andsoon.Forthisreason,theneckis curvatureanalysisand2sfortheotherphases.
likely to be the last tube found; its section is usually
larger thanthatof the ankle(see Fig. 8).
Thearmsandlegsmightbefoundasthecomposition
of two tubes: this case happens rarely, and usually for
Fig.7. Thesphereofradiusrcentredintheyellowvertexhas
two intersection curves if the maximum diameter of the tube Fig.9. (a)Twoseedregionsforeachlegarefoundatthesame
sectionislessthanr=2(blackline),andonlyoneifitisgreater scale:thekneeandtheankle.(b)Resultofthetubegrowingon
than r=2 (blue line). The red line represents the limit value the seed regions in (a). (c,d) Result obtained by joining the
ofr=2. adjacenttubesinasingletube.
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192 M.Mortaraetal./Computers&Graphics30(2006)185–196
tube section lies completely on another tube; the two semantic tubular feature, while tube properties, such as
tubes are kept separately but a link is included in the length and section size, will be computed as they were
shape-graph to underline that they form a single two singletubular features(see Fig. 9(c,d)).
The scale attribute together with the tube length, the
informationaboutthesectionsize,andtheshape-graph
makeitpossibletoclassifyeachtubeasarm,leg,finger,
or neck; this step is currently under development but it
has already been validated by results shown in Fig. 10
and Table 2. All the three parameters are needed
because of the many possible types of result. It may
happen that the neck is too short and wide to be
recognized, and the same may happen for fingers.
It is quite frequent, indeed, to identify only some
of the fingers, usually missing the thumb which is
the thickest and shortest. If at least some of the
fingers are recognized, we are able to identify the arms
throughtheshape-graph,andconsequentlyalltheother
limbs.
Wecannotbecompletelyconfidentonthetubelength
either: for fat humans, legs intersect before the hip (see
Fig. 11(a,b)) and the corresponding tubes are shorter,
comparable with the arm length. This may also be
causedbytheposture,asithappensforthesittingman
in Fig. 11(c), where only the foreleg can be recognized.
Fig.10. Firstrow:semanticbodymodelofthevirtualhumans As shown in Fig. 12, fatness represents the major
showninFig.8.Secondrow:identifiersofthefeatures,whose problem,sincePlumber doesnotclassifyastubeslimbs
shapeparametersarereportedinTable2. that are tooshort withrespectto theirthickness.
Table2
ShapeparametersofthefeaturesdetectedinexamplesofFig.10:thefirstrowcorrespondstoexamples(a)and(b),andthesecondrow
toexamples(c)and(d);thefirstcolumncontainsthefeatureidentifier,thesecondthetubelength,thethirdtheaturningvalue,and
finally,thefourththeaveragesectionlength,asdefinedinSection4
N. Tubelength Max.a Aver.sect.length N. Tubelength Max.a Aver.sect.length
2 7.07 (cid:2)0.94 4.94 2 5.27 (cid:2)0.95 5.21
3 5.50 (cid:2)0.93 3.63 3 5.51 (cid:2)0.93 3.61
4 5.51 (cid:2)0.95 3.39 4 5.52 (cid:2)0.95 3.39
5 7.07 (cid:2)0.94 4.94 5 3.65 (cid:2)0.94 4.16
6 5.47 (cid:2)0.95 4.02 6 7.13 (cid:2)0.93 4.76
7 5.50 (cid:2)0.95 3.40 7 5.48 (cid:2)0.93 4.08
8 39.91 (cid:2)0.91 23.26 8 5.47 (cid:2)0.93 3.95
9 39.95 (cid:2)0.95 23.17 9 42.91 (cid:2)0.39 26.60
10 17.84 (cid:2)0.94 67.34 10 39.58 (cid:2)0.61 23.73
11 82.17 (cid:2)0.43 39.22 11 17.61 (cid:2)0.92 67.65
12 93.14 (cid:2)0.79 43.98 12 91.30 (cid:2)0.74 43.86
13 74.86 (cid:2)0.73 36.97
2 5.30 (cid:2)0.95 5.22 2 7.15 (cid:2)0.94 4.95
3 5.56 (cid:2)0.96 3.21 3 3.63 (cid:2)0.96 4.64
4 5.55 (cid:2)0.94 3.33 4 5.57 (cid:2)0.94 3.26
5 5.30 (cid:2)0.96 5.25 5 7.15 (cid:2)0.94 4.95
6 3.61 (cid:2)0.96 4.71 6 3.63 (cid:2)0.92 4.69
7 5.55 (cid:2)0.94 3.28 7 5.57 (cid:2)0.94 3.27
8 39.87 (cid:2)0.69 23.60 8 40.30 (cid:2)0.97 23.28
9 48.23 (cid:2)0.76 28.21 9 40.07 (cid:2)0.72 23.46
10 17.70 (cid:2)0.96 69.48 10 18.03 (cid:2)0.95 69.23
11 92.23 (cid:2)0.92 44.29 11 89.31 (cid:2)0.50 42.53
12 89.61 (cid:2)0.10 41.99 12 96.30 (cid:2)0.53 44.07
ARTICLE IN PRESS
M.Mortaraetal./Computers&Graphics30(2006)185–196 193
formedbyabandbcdiscriminatesbetweenanacuteand
anobtuseangle(aturninggreaterorsmallerthanp)but
2
do not distinguish a ‘‘right’’ from a ‘‘left’’ turning with
respect to a fixed coordinate system. Since the cosine
function is bounded, each turning value belongs to the
range ½(cid:2)1;1(cid:4) and it can be directly used for comparing
virtual humans in different postures. On the contrary,
tubelength,section,andvolumedependoneachmodel
measure unit; then, before running the morphological
analysis the surface models must be normalized.1 For
thetripleða;b;pÞ,letu:¼ða(cid:2)pÞ,v:¼ðb(cid:2)pÞ,andabethe
turning value at p computed as previously described.
Whenða;b;pÞlieonastraightline,uandvformatpan
Fig. 11. (a) Seed regions identified by Plumber on a fat man angle of p corresponding to a null turning; when this
model. Note the low joint between the legs. (b) Identified angle is 2p, i.e. a(cid:5)b, a maximum turning occurs in p
tubularfeatures.Tubesrepresentingthelegsstopincorrespon- (seeTable 2).
dence of the joint and the length of arms and legs becomes ComparingthevaluesinTable3obtainedforvirtual
similar.(c)Thesamemaninasittingposture,witharmslying
and real body models, some further conclusions can be
onthebody.Armswillnotberecognizedastubes,andlegsstop
drawn on the efficacy of the descriptors. For virtual
whentheseatisintersected.
humans, the turning value quite nicely discriminates
betweendifferentposturesandforrealbodymodelswe
mayseethatthedifferentsizesofthebodyisreflectedby
thechanges in the cross-section size.
Finally, approximating each tube with truncated
cones of circular bases, each having the same length of
the corresponding tube cross-section, enables to calcu-
lateanapproximationofthefeaturevolumeasthesum
of the volumes of each building part. Then, the ratio
volume/lengthgivesahintonthehumanlimbfatness,in
analogy with the body mass index (weight/length, see
Fig. 13), and the ratio volume/length discriminates
between two individuals of same limb thickness but
differentheight(see Fig. 14andTable3).
5. Discussion
Our approach subdivides the model into limbs and
Fig.12. Tubesidentifiedat(a)thefirstand(b)secondscales.
body.Thescales(i.e.,theradiusofthespheresusedfor
the characterization and tube growing phases) can be
automaticallytunedonhumananatomicmeasuressuch
The axis inclination gives us a precious information
asapproximatedsectionoffingers,wrist,forearm,arm,
about the body posture. In the context of virtual
ankle,calf,thigh,neck.Then,thegeometricattributesof
humans, we can exploit the fact that limbs are rigid
the recovered tube sections and axis can give informa-
exceptatthejoints;therefore,thetubeaxiswillbenearly
tion about the characteristics of the human model; for
straight, except in a few points, which identify the
instance,theapproximatedvolumeoflimbswithrespect
torsion in the articulation sites. Note that a tube may
totheirlengthmaygivetheamountoffatness/thinness.
haveatmostthreearticulations:forinstance,alegmay
The neck will be recognized as a tube only if it is thin
comprehend the ankle, knee, and hip joints. Again, the
and long, and the same applies to fingers. Also, the
shape-graphisusedtodiscriminateeachjoint,givingan
‘‘outward’’orderingtoeachtube,fromitsattachmentto
thebodytowardsthetipoftheprotrusion.Wecompute 1GiventwotrianglemeshesM1andM2,wenormalizethem
by applyinga uniformscalingon their verticesin such away
the turning a at each node p of the tube axis of T as
thatthenewsurfacesbelongtotheunitcubewhilemaintaining
a:¼cos(cid:2)1ðhu;vi=ðkukkvkÞÞ where u and v are the vectors theirrelativeproportions,thatis,wenormalizetheverticeswith
coofnsTecutwivheichpoisnhtasrealopn.gFTor, tehaechcostirnipeleofðath;be;caÞngolef rjes¼pe1c;t2t;o3gt,hke¼con1;s2ta,natnCd:¼pðjmÞ tahxefcjt1h;cc2ogmwpitohncekn:t¼omfapxp.i2MkfpðijÞ;
i i
ARTICLE IN PRESS
194 M.Mortaraetal./Computers&Graphics30(2006)185–196
Table3
ShapeparametersoftubularandconicalfeaturesrelatedtotheexamplesinFig.14
N. Tubelength Max.a Maxsec.length Minsec.length Aver.sect.length
2 51.13 43.04 47.42 15.51 26.58
3 53.97 42.31 50.26 16.02 28.29
5 66.63 80.21 56.58 23.29 39.67
6 85.88 111.84 56.25 16.08 35.97
7 16.70 (cid:2)33.07 23.88 23.29 23.58
8 23.66 52.77 81.88 55.69 65.33
2 40.99 34.99 39.96 17.65 27.62
3 39.45 36.08 44.24 16.63 28.48
4 66.72 63.43 56.55 22.27 39.63
5 62.75 63.85 53.25 23.08 38.02
6 11.09 16.54 17.65 11.37 14.51
7 17.74 53.49 83.56 58.29 69.27
Fig.13. Analysisofthethinnessandfatnessbasedontheratiobetweenthevolume,size,andlengthofeachbodyfeature.
Inthecaseofascanningprocess,themodelislikelyto
consist of a huge amountof points. The morphological
characterization which represents the first step of the
tube recognition on such dense surfaces is indeed more
precise. On the other hand, the mesh produced by the
triangulator associated to the scanner device usually
produces meshes with holes (e.g., due to occlusions
which might occur in correspondence of armpits), or
tendstojoinpatchesofsurfaceswhichareseparatedbut
very close in space (e.g., the base of fingers or of the
thighs). It is also true that usually human body scans
havebeenacquiredinastandardposture,whichseesthe
human in a standing position, with legs and arms
straight and completely stretched, and closed fists. In
Fig.14. Shapesegmentation;parametersarereportedinTable3.
this case, it is not possible to get fingers as tubular
features.Weusedmodelscapturedfromrealhumansto
approximatedvolumeoftheremainingbodycomponent prove therobustness ofour algorithmto managehuge,
canbecheckedin this direction. noisy, orcorrupted models.
In the proposed approach, we made no assumptions Inthecaseofthegenerationofthevirtualhumanby
onthemethodusedtoproducethehumanbodymodel, the modelling act of a digital artist, the mesh quality is
which can be either an acquisition or a modelling very different: it obviously consists of much less points
process. Differences in the results depend, however, on and the surface is smoother. Generally, fine details
the typeofinputmodel. are not provided and the computed morphological