GeneratingPointCloudfromMeasurementsandShapesBasedon ...downloads.hindawi.com/journals/cin/2019/1353601.pdf · θ 2πj−1/n, and nis the dimension of the slice vectors. Onepointisdistributedtothejth

Research ArticleGenerating Point Cloud fromMeasurements and Shapes Based onConvolutional Neural Network An Application for Building 3DHuman Model

Mau Tung Nguyen12 Thanh Vu Dang 3 Minh Kieu Tran Thi1 and Pham The Bao 3

1University of Science and Technology School of TextilemdashLeather and Fashion Ho Chi Minh City Vietnam2Industrial University of Ho Chi Minh City Ho Chi Minh City Vietnam3Sai Gon University Ho Chi Minh City Vietnam

Correspondence should be addressed to Pham e Bao ptbao2005gmailcom

Received 25 February 2019 Revised 20 June 2019 Accepted 1 August 2019 Published 2 September 2019

Academic Editor Fabio Solari

Copyright copy 2019 Mau Tung Nguyen et al is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

It has been widely known that 3D shape models are comprehensively parameterized using point cloud and meshes e pointcloud particularly is much simpler to handle compared with meshes and it also contains the shape information of a 3D model Inthis paper we would like to introduce our new method to generating the 3D point cloud from a set of crucial measurements andshapes of importance positions In order to find the correspondence between shapes and measurements we introduced a methodof representing 3D data called slice structure A Neural Networks-based hierarchical learning model is presented to be compatiblewith the data representation Primary slices are generated by matching the measurements set before the whole point cloud tunedby Convolutional Neural Network We conducted the experiment on a 3D human dataset which contains 1706 examples Ourresults demonstrate the effectiveness of the proposed framework with the average error 772 and fine visualization is studyindicates that paying more attention to local features is worthwhile when dealing with 3D shapes

1 Introduction

A fundamental characteristic of computer-based models isthe capability of describing in detail the topology and ge-ometry structure of realistic objects 3D modeling tech-niques are increasingly becoming the discipline in thecomputer-aided design community In addition many ap-plications requiring 3D models such as human animationgarment industry and medical research have a great impacton various aspects of human life

Although considerable research has been devoted topracticality and visualization of 3D shapes less attention hasbeen paid to the problem of automatically generating a 3Dmodel In practice the measurement parameters like lengthperimeter and curvature have been widely used to describethe shape of realistic objects However reconstructing acomputer-based model from these measurements has still

many gaps in approach e major reason is that the set ofsparse measurements fail to capture the complex shapevariations necessary for reality On the other hand it isimpractical to resort to scanning equipment which is time-consuming and expensive

e aim of this study is to formulate a novel repre-sentation of a 3D model based on point cloud that wouldmake it easy to explore the relationship between the mea-surements and 3D shapes using the Neural Networks systemOverall our proposed framework creates the 3D point cloudwhen considering a set of measurements as input Key to ourapproach is to divide an object into independent compo-nents and slices is secession allows us to specificallydefine architecture of the Neural Network for each sliceshape instead of working on a whole 3D shape e pointcloud not only has simple and unified textures compared tothe diversities and complexities of mesh but also remains

HindawiComputational Intelligence and NeuroscienceVolume 2019 Article ID 1353601 15 pageshttpsdoiorg10115520191353601

meaningful structure of objectrsquos boundaries and skeletonTaking the 3D human model for an application we heredemonstrate an end-to-end procedure of synthesizing a newhuman model given anthropometric measurements and aset of parameters learned from training data

2 Related Works

One of the first attempts to solve for 3D model re-construction problem was template model based Moreprecisely this method produces a newmodel by deforming atemplate model Allen at el formulated an optimizationproblem to find an affine transformation at each vertex of thedesigned template model for fitting a 3D scanned humanbody ey defined three types of error and combined themto create the objective function eir approach also dealtwith incomplete surface data and filled inmissing and poorlycaptured areas caused by the scanner [1] Modifying themethod of Allen Hasler performed nonrigid registrationwith the aim of fitting pose and shape of 3D scans form atemplate model [2] Seo and Magenat deformed an existingmodel to obtain the new one based on two stages pre-processing e skeleton fitting found the skeleton structurethat approximates the corresponding 3D human body eskin fitting calculated the displacement vector of each vertexbetween the template model after skeletal fitting and the scanmesh fitting [3]

e other approach is 2D-based reconstruction ismethod reduces the cost because it only requires a set ofimages However the image data often contain noises andbackground which are hard to remove Blanzrsquos approachtook a human face color image as an input and generated thecorresponding 3D face model New faces and expressioncould be described by forming linear combinations ofprototypes [4] In their work the weight vector was assumedto distribute as multivariate Gaussian and could be found bymaximum posterior probability Chen attempted to auto-matically reconstruct more complex 3D shapes like humanbodies from 2D silhouettes with the shape prior which waslearned directly from existing 3Dmodels under a frameworkbased on GPLVM [5] However this approach is not realisticbecause relying on the silhouettes only will cause the loss ofdepth information of a human body

Most of the solutions come from the statistics-basedapproach Similar to our approach these methods use thetraining set to learn the correlation between input andoutput or construct an example space for extrapolationInspiring form DeCarlo et alrsquos work [6] the statistics-basedmodel has become a powerful tool for demonstrating thefeature space of the 3D model In their study human facemeasurements were used to generate 3D face shapes byvariational modeling while a prototype shape was consid-ered as a reference Allen reduced the dimension of 3Dhuman meshes from 180000 elements to 40 or fewer byusing principal component analysis (PCA) en linearregression was used as a technique to find the relationshipbetween six different anthropometrics and 3D humanmodel[7] Seo defined two synthesizers which were joint synthe-sizer and displacement synthesizer Joint synthesizer handles

each degree of freedom of the joints in other words thissynthesizer constructs the skeleton for the model whileanother synthesizer was used to find the appropriate dis-placement on the template skin ese synthesizers were alllearned from eight body measurements with the corre-sponding model by the use of Gaussian radial basis functions[8] With the same approach to Allenrsquos research Chu et alattached a procedure of feasibility check to determinewhether the semantic parameter values input by the user isrational e feasibility check was based on the mathematicconcept of the convex hull and if the input parameters failedthe check their system would return the most similar modelin the training data [9] Wang analyzed a human body fromlaser-scanned 3D unorganized points through many steps[10] He built the feature wireframe on the cloud points byfinding the key points and linking all of them with curveinterpolation After that feature patches were generated byusing the Gregory patch and updated by a voxel-based al-gorithm According to the introduced feature model an-thropometric measurements are easily extracted so that heused numerical optimization to generate a new 3D humanbody which is extracted measurements are likely to the userinput sizes Baek and Lee performed PCA on both the bodysize and body shape vectors then they found the weightvalues of the new model based on the parameter optimi-zation problem with the constraints were the 25 user inputmeasurements [11] ey also clustered hierarchically theirshape vector space by an agglomerative cluster tree to re-main small variation in each cluster Wuhrer and Shu in-troduced a technique that extrapolates the statisticallyinferred shape to fit the measurement data using nonlinearoptimization [12] First PCA is applied to produce a humanshape feature space then shape refinement is used to refinethe predicted model e objective function is formulatedbased on the sum of square error of three types of mea-surements e author announced that the method couldgenerate human-like 3D models with a smaller trainingdataset e above methods have been suffered from acommon drawback which is the limitation of generatedshapes to the space spanned by the training data In otherwords finding a large number of variables by optimizing onthe small dataset would lead to the underfitting problem

3 Methodology

In this section we demonstrate our method which con-sists of two main steps generating primary slices andrefining 3D point cloud 3D objects are formed by a set ofplanes which are perpendicular to the axial height of theobject In other words building 3D shapes is equivalent tobuilding all these planes Normally if the surfaces aresmoothly divided (the distance between two adjacentplanes is very small) adjacent surfaces will have nearlysimilar shapes Moreover not all measurements areavailable in practice thus we only considered someavailable ones as the measurements corresponding withprimary planes erefore selecting the main planes helpsus to reduce the number of calculations and also necessarymeasurements

2 Computational Intelligence and Neuroscience

Let us assume that the set of all surfaces that are per-pendicular to the axial height of a 3D object isS Si| i 1 m1113864 1113865 e primary set is a subset of S PS

Si isin S| i isin PI sub 1 2 m 1113864 1113865 such that for allSi Sj isin PS ine j Si and Sj do not have a common shape Weassessed the degree of differences of two shapes based onobserving the 3D object structure To learn the relationshipbetween measurements and each primary surface weconstruct a map from an initial set to a target set

fi Ci (x y) isin R2x2

+ y2 le

mi

2π1113874 1113875

211138681113868111386811138681113868111386811138681113896 1113897⟶ Siprime (1)

such that the difference of Si and Siprime is smallest If we consider

hollow 3D objects and the surfaces turn into the slicesdefined in the following section C will be a circle with itsradius is computed by the perimeter of the correspondingslice

From the principal surfaces we can interpolate the whole3D object since the surfaces between two principal sliceswhose shape gradually changing to match the shape of thesetwo principal slices However the interpolated surfaces arenot as practical as the actual ones We overcame thisproblem by using the adjusting model that will be clarified inthe next section

31 Building Primary Slices We restricted our study to aclass of surfaces which can be written under the trigono-metric formula Represent a surface of 3D point cloud by aset of points Szo

(x y z) isin R3 | z z01113864 1113865 so that for allθ isin [0 2π] and rgt 0 there is no more than one point(x y z) isin Sz which satisfied

x x0 + r cos θ

y y0 + r sin θ1113896 (2)

where (x0 y0) is former given in this study we called it asldquoanchor pointrdquo which is the center of a slice (Figure 1) Wenamed the data structure defined above as ldquoslice structurerdquo

e above surface description has an advantage that theredundancy of the third dimension is eliminated A point(x y) could be replaced by a pair (r θ) but the θ variablesare actually in common for all slices ereby a slice iswritten as a vector of the distances between the anchor pointand points on this Moreover this representation is invariantunder translation because of the equability of r when wetranslate 3Dmodels e rotation is also easy to handle sincewe merely shift the components of slice vectors

Let PI sub 1 2 m is an index set of main slices weapproximated the target slices Si

prime i isin PI by formula (3) LetSi i 1 m is the n-dimensional vector representing the i

slice the kth component of it is the distance between thecenter and the point at θ 2πk minus 1n k 1 n Wedefined the deformation function fi Z+ntimes1⟶ Z+ntimes1 as

Siprime fi Xi( 1113857 W

21113872 1113873

Tα W

11113872 1113873

TXi1113874 1113875 (3)

where W1 isin RntimesL1 W2 isin RL1timesn α is a nonlinear function Xi

is an initial slice and fi is also called as theMultilayer NeuralNetwork (MNN) model

Algorithm 1 summarizes the learning procedure ofgenerating principal slices

e key idea of the first model is to deform an initialshape into the desired shape controlled by the perimetersand the training data Object circumferences are only usefulwhen the object shape is revealed hence using circumfer-ences alone to construct an object in detail is insufficienterefore our approach also based on the shape of objectsthat can be extracted by NN model from the training set Inthis work the learning model seeks for positions on theinitial slice that needs to be shrunk or dilated (Figure 2)

32 Generating Point Cloud Based on the results of theabove step we performed interpolation on all the remainingslices In more detail considering θ 2π(k minus 1)n we cal-culated sik

prime i notin SP based on sikprime i isin SP and this simple task

was done by linear interpolation (Figure 3) We used theseinterpolated slices as the input for the second model Weconstructed the second synthesizer based on the Convolu-tional Neural Network (CNN) [13] because its kernels havean ability to capture local characteristics and that is espe-cially useful when we have to take the relationship of ad-jacent slices into account is model corrected wronginterpolated points by using information on the training setvia CNN architecture e local structure of 3D shapes wasretained by convolutional layers in CNN hence resulting infine refinement We defined our CNN model as a functiong R+mtimesn⟶ R+mtimesn

Y g(X) WL lowast αLminus 1 W

Lminus 1 lowast αLminus 2 middot middot middot α3 W3 lowastX1113872 11138731113872 11138731113872 1113873

(4)

where al l 3 L minus 1 is a nonlinear activation functionand X is formed by stacking both principal and interpolatedslices in rows

A rational choice of loss function for this problem isMean Square Error (MSE) In this study MSE calculated thedifference between the generated and the actual value of eachpoint distance on each slice We used this metric to evaluatethe error on both learning models (Algorithms 1 and 2) Wealso added the error term of perimeter into the first modelrsquosloss function

4 An Application for Building 3DHuman Model

41 Dataset e datasets used in this work were in-dependently developed by two universities in VietnamTable 1 summarizes our datasets (Table 1)

Each sample on both datasets was generated by the 3Dscanning device and saved under ldquoobjrdquo format Each persononly provided one 3D scan of the body hence the number ofparticipants and samples is equal Participants were sug-gested wearing a tight suit and complied with the standardpose when scanning their bodyWe split a 3D avatar into fiveparts are torso left leg right leg left arm and right arm

In detail these datasets were built from different devicesthus they have some distinct features (Figure 4) e mostnoticeable thing is that the point density of the male avatars

Computational Intelligence and Neuroscience 3

is not as dense as that of females 3D female avatars haveunified structure and each their vertex was distributed intoone of five above parts Each point on torso slices leg slicesarm slices is 3 5 10 degrees respectively apart In additionall slices are equally spaced by the same distance in heightMeanwhile the male dataset did notmeet the ideal conditionlike its counterpart Not only it has no predefined boundarybetween two parts but also the point cloud does not followour slice-structure For this reason the creator of the maledataset provided a set of landmarks for each avatar and weused them as reference points to perform partition on theman model (Figure 5) Moreover our slice-structure couldbe achieved by proper preprocessing steps

42 Preprocessing We split the whole 3D human model intofive parts (Figure 6) as the following manner and the po-sitions mentioned below are in the landmarks set

(i) Torso

(a) Upper torso From neck to armpit limited by leftelbow and right elbow

(b) Lower torso From armpit to hip limited by leftand right hip or limited by left and right stomach

(ii) Arm (LeftRight)

(a) Upper arm From armpit to elbow limited byarmpit and elbow

(b) Lower arm From elbow to wrist limited byelbow and wrist

(iii) Leg (LeftRight)

(a) Upper leg From hip to knee limited by crotchpoint and knee

(b) Upper leg From knee to ankle limited by kneeand ankle

After determining all parts of a human model we madedividing slices based on planes perpendicular to the highaxis Let us assume that the set of all points containing in ahuman part is S we assigned

x0 y0 z0( 1113857 ≔ x0 y0 minHz + idz

m minus 11113888 1113889 (5)

If

minHz + idz

m minus 1le zo ltminHz +(i + 1)

dz

m minus 1 (6)

where Hz z isin R (x y z) isin S1113864 1113865 dz maxHz minus minHz

i 0 m minus 1 and m is the number of slices (50 in ourexperiment) Si (x0 y0 z0)|z0 minHz + idzm minus 11113864 1113865

(Figure 7(a))e next step is to construct the slice vectors First we

calculated the position of an anchor point on each slice emean formula is suitable to find these points

x(i)

y(i)

z(i)

1113872 1113873 1Si

11138681113868111386811138681113868111386811138681113868

1113944(xyz)isinSi

(x y z) (7)

However there are some downsides on the approachdiscussed above Firstly there are some slices that the countof points on them is not sufficient enough to approximatethe actual center point e second thing is when con-structing a new human model we need a skeleton of it Inother words it requires an available set of anchor pointsanks to the landmark set we could approximate theskeleton of male avatars Take the torso for example weconstituted its skeleton by the line connecting the center offour neck landmarks and the crotch point (Figure 8) Oncethe anchor lines were found calculating the anchor points atany height is a trivial task e template skeleton was formedbased on analyzing the position of all anchor points on thewhole training dataset In our work we simply built theskeleton template by taking the average of the anchor pointsof each slice

Given (x0 y0 z0) isin Si the angle established by theanchor point (x(i) y(i) z(i)) and this point is computed by

a0 arctany0 minus y(i)

x0 minus x(i)1113888 1113889 (8)

e jth component of a slice vector represents the dis-tance between the anchor point and the point atθ 2πj minus 1n and n is the dimension of the slice vectorsOne point is distributed to the jth position if the followingcondition is satisfied

2πj minus 1

nle a0 lt 2π

j

n (9)

where j 1 n e distance is directly calculated byEuclid metric

d(i)j

x0 minus x(i)( 11138572

+ y0 minus y(i)( 11138572

1113969

(10)

Both male and female avatars suffer from missingdata problem In the female dataset the reasons are thecarelessness during the scanning process and the outdatedequipment On the other hand the missing value issue onpreprocessed male models is inevitable because theiroriginal point cloud is not ideal Furthermore the pointdensity is not sufficiently dense to divide the male bodyinto many slices We tackled this problem by performinglinear interpolation on grid data of slice vectors(Figure 7(b))

43 Measurements e male dataset supplied us a set ofanthropometric measurements with 178 categories com-prising slice perimeters width and height of body partsNevertheless the measurements are not in the same unitwith distances computed on the point cloud Meanwhile thefemale dataset provided no measurements Due to thesereasons we decided to recalculate the measurements to beconsistent in both datasets e simple way to compute aslice circumference is summing all distances of two adjacentpoints but it does not seem realistic when measuringnonconvex shapes We proposed using the circumference ofthe convex hull of a slice for its measurements ese sizeswere calculated on the primary slices (Figure 9)


In summary there are 28 slice measurements but we canreduce the number of measures to 17 because of the similarityof the right and left sides In addition it is necessary to recordthe height (length) of each body to entirely build up the 3Dhuman model is would lead to 20 measurements in totale primary positions were chosen based on the statistics onthe dataset and the standard ratio of the human body [14]

44 Learning Model To construct primary slides we builtNeural Network (NN) models with one hidden layer asdescribed in Section 31 ese models deformed input slicesinto target slices (Figure 10)

ese models take an initial circle as input and learn thedeformation from the input shape into the target shape eradius of the initial circle is r p2π where p is the pe-rimeter of the slice being considered e input and outputsize depends on the body part in our experiment n equals20 30 and 60 for the arm leg and torso respectively e

error between a predicted slice and the actual slice is cal-culated by

L y yprime( 1113857 1n

1113944

n

i1yi minus yiprime( 11138572

+ c 2π

maxyprime( 11138572

+ minyprime( 11138572

2

1113971

minus p⎛⎜⎝ ⎞⎟⎠

(11)

where the second error term comes from the differencebetween the approximation of the circumference of pre-dicted slice and the actual onee objective function reflectsthe error not only at each component (local information)bust also the perimeter of the slice (global information)

Once the entire main slices had been found linearinterpolation was used to infer all remaining slices eseinterpolated slices are the input for the second NN modelas described in Section 32 (Figure 11) We used ReLU[15] as the activation function in both architectures

e convolutional layers help the model to learn thelocal correlation of adjacent slices As a result theremaining slices would be corrected based on the primary

1300

1200

1100

1000

900

800

7002001000ndash100ndash200

500ndash50ndash100X

Y

Z

ndash150

Interpolated point

Figure 3 Interpolation of intermediate slices

Shrink

Dila

teD

ilate

Figure 2 Deforming an initial slice (red circle) into the target slice(blue curve)

250

200

150

100

50

0

ndash50

ndash100

ndash150

ndash200

ndash250ndash250 250ndash200 200ndash150 150ndash100 100ndash50 500

(a)

100

50

0

ndash50

ndash100

150ndash50 0 50 100

3deg

(b)

Figure 1 Example for our defined slice each point is 3∘ apart


slices e most cautious thing when building CNN for thisproblem is padding To retain the size of data whentransferring through multiple layers we performed reflex

padding in vertical and symmetric padding in horizontal(Figure 12) Padding this way retains circularly linkedcharacteristic of slices

We defined the loss function on this second model byusing MSE

Torso

Upper

LowerArm

Upper

Lower

LegUpper

Lower

Figure 6 3D human model partition

Figure 5 Some anatomical landmarks of a male model

Figure 4 Avatars in male and female dataset and its point cloud

Input Set of measurements P Set of 3D shapes in which S(i) isin D is a sample following the slice-structureOutput Set of learned parameters W

for h isin SP dolossh 0for each sample S(i) isin D do

w length of vector S(i)h

r (P(i)h )2π

init X as w-dimensions array with Xk r

Y f(X)

max maxY

min minY

lossh lossh + (1w)Y minus S(i)h + (2π

(((max)2 + (min)2)2) minus P(i)h

1113969

)

W(h) argmin(lossh)

ALGORITHM 1 Building primary slices form measurements


L yprime y( 1113857 1

mn1113944

m

i11113944

n

j1yij minus yijprime1113872 1113873

2 (12)

where y yprime are respectively a matrix of the actual andpredicted distances to the anchor point of a body part

5 Experiments and Results

We trained our NN models on the Linux server with 24GBRAM GPU with 12GB RAM and Xeon CPU with 22GHzWe used Python as the implementing language and the mainlibraries using in our experiment are pytorch and numpy Weused Adam algorithm [16] to minimize the objective function

Overarm

NeckShoulder

ChestWaist

HipAbdomen

BicepsElbow

ForearmWrist

ThighMiddle thigh

KneeUnder knee

CalfAnkle

Figure 9 Position of primary slicesFigure 8 Anchor lines of a human model

150100

500

ndash50ndash100

ndash100 ndash50 50 1000 ndash100 ndash50 50 1000 ndash100 ndash50 50 1000

ndash150

150100

500

ndash50ndash100ndash150

200

100

0

ndash100

ndash200

(a)


150100

500


150100

500


200

100

0

ndash100

ndash200

(b)


150100

500


150100

500


150

100

0

ndash100

ndash200

(c)

Figure 7 Preprocessing step (a) Original slices (b) After selecting slices components (c) After filling missing data


(50 times n) times 1(50 times n) times 4

(50 times n) times 16


Conv4 3 times 3Conv3 5 times 5Conv2 7 times 7Conv1 7 times 7

1300120011001000

900

ndash100ndash50050100800

ndash200 ndash100 0Y label

X la

bel

Z la

bel

100 200

1300120011001000900



X la

belZ

labe

l

100 200

Figure 11 Neural Network model for adjusting entire slices

1024 times 1

n times 1n times 1

Max

Min

0

ndash25

ndash50

ndash75

ndash100

ndash100 ndash75 ndash50 ndash20 0 25 50 75 100

25

50

75

100

0

ndash50

ndash100

ndash150

ndash100 ndash50 0 50 100

50

150

100

Figure 10 Neural Network model for generating the primary slices


the meta parameters were set according to recommendationof the authors (learning rateα 0001 β1 09 β2 0999)We evaluated the error by the average relative error

L y yprime( 1113857 1

mn1113944

n

i11113944

m

j1

yij minus yijprime

11138681113868111386811138681113868

11138681113868111386811138681113868

yij

times 100 (13)

where y yprime are respectively a matrix of the actual andpredicted distances to the anchor point of a body part eabove error formula is not affected by the heterogeneity insize on different body parts and also on different datasets Inthe male dataset we used 1066 samples as training data and100 samples as testing data while 500 and 100 as trainingand testing data in the female dataset the samples wereselected randomly Table 2 shows the average error on eachprimary slice after training 1000 epochs on the male andfemale datasets

Learning the relationship between the size and corre-sponding slice shape is a hard problem because of the curseof dimension Despite the fact that the input is just scalar wehave to predict the slice vector with at least 20 componentsTo solve this problem we used initial shapes e initialshape not only is a rough approximation for the target slicebut also helps the NN model increase the number of pa-rameters and avoid underfitting In our work we limited theclass of initial shapes to circles that their radius is calculatedby the slice perimeters Geometrically the first NN modelsact as a figure deformation controlled by the slice sizes eNN models are the nonlinear transformations from straight

lines to the particular ldquoslice vector curvesrdquo which are the sliceshapes after converting into the slice vector representationese curves have analogous shapes if they are placed at thesame position (Figure 13)

In the torso part the neck slices have the highest averageerror because these slices are not clearly separated from thehead and the anatomical landmarks at neck position areplaced at the wrong locations like collar or chin is reasonleads to that the shape of the neck slices varies considerablye same thing happens with overarm slicese boundariesbetween arms and shoulder are not accurately determinedbased on the landmarks Another problem is the lack of alarge number of components on overarm slice vectors be-cause of the obstructed locations such as armpits which areignored by the 3D scanner (Figure 14)

Table 3 shows the result after training the CNN models toentirely construct a full human body To conduct this sectionwe also used Adam algorithm with 1000 epochs We chose 50good samples and 50 damaged samples to form the test setus we could evaluate the influence of bad patters on theoverall test accuracy e results show that the errors in theundamaged test sets are approximate to the training errors Onthe other hand the errors in the damaged test sets are not aslow as the good ones Based on the results we can conclude thatour framework is nonsensitive to the small amount of damagedsamples Moreover the amount of samples in the training set issufficient to do inference on the shape of testing samples

While analyzing the database we realized that there aremany damaged samples in both datasets e issues in the

Input Set of generated primary slices Dprime in which Sprime(i) isin Dprime comes from Algorithm 1 Set of 3D shapes in which S(i) isin D is a samplefollowing the slice-structureOutput Set of learned parameters W

loss 0for each sample S(i) isin D do

n the number of rows of S(i)

m the number of column of S(i)

init X as n times m matrixfor k from 1 to m do

for h from 1 to n dostartmax x isin PI | xle h

endmin x isin PI | xge h

Xhk Sprime(i)

startk + (Sprime(i)

startk minus Sprime(i)

endk)lowast (h minus start)(end minus start)Y g(X)

loss loss + 1mnY minus S(i)

W argmin(loss)

ALGORITHM 2 Constructing 3D point cloud

Symmetric

Reflex

3 2 1 2 3 1 23 2 1 2 3 1 26 5 4 5 6 4 59 8 7 8 9 7 89 8 7 8 9 7 8

Figure 12 Padding strategy


140

120

100

80

Dist

ance

60

40

20

01 3 5 7 9 11 13 15 17 19 21 23 25 27

Angle (times6 degree)29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59

(a)

Dist

ance

80

70

40

50

60

30

20

10

01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Angle (times12 degree)

(b)

Figure 14 Continued

250

200

150

100Dist

ance

50

01 3 5 7 9 11 13 15 17 19 21 23 25 27


Hip

29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59

50

4045

3530252015

Dist

ance

1050

1 2 3 4 5 6 7 8 9 10 11 12 13 14Angle (times12 degree)

Middle thigh

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

50

4045

3530252015

Dist

ance

1050


Forearm

15 16 17 18 19 20

(a)

250

200

150

100Dist

ance

50

01 3 5 7 9 11 13 15 17 19 21 23 25 27


Hip

29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59

40

45

35

30

25

20

15

Dist

ance

10

5

01 2 3 4 5 6 7 8 9 10 11 12 13 14


Middle thigh

15 16 17 18 19 20 21 22 23 24 25 26 27 2829 30

50

4045

3530252015

Dist

ance

1050

1 2 3 4 5 6 7 8 9 10 11 12 13 14Degree (times18)

Forearm

15 16 17 18 19 20

(b)

Figure 13 Slice vector ldquocurvesrdquo of wrist hip and thigh of 20 examples in male dataset


Figure 15 Examples for the damaged 3D human model

Table 1 Summary of dataset

Owner Gender (age) e amount of avatars e amount of damaged avatarsIndustrial University of Ho Chi Minh City (IUH) Male (20ndash60) 1106 65Hanoi University of Science and Technology (HUST) Female (20ndash60) 600 63

Dist

ance

90

80

70

40

50

60

30

20

10

01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


(c)

Figure 14 Slice vector ldquocurvesrdquo of neck left and right overarm of 10 examples in the male dataset


Table 4 Average error on each part of 3D male and female models on the undamaged datasets before and after activating the CNNmodel

Trainmale (before) Trainfemale (before) Testmale(before)

Testfemale(before)

Trainmale(after)

Trainfemale(after)

Testmale(after)

Testfemale(after)

Torso 690 804 721 827 668 713 794 794Left arm 762 1277 831 1381 715 1260 767 1383Right arm 814 1081 827 1094 715 1070 735 1072Left leg 702 632 774 651 731 577 790 596Right leg 753 663 812 708 690 589 739 613Average error 742 891 793 932 703 841 765 891

Table 3 Average error on each part of 3Dmale and female models after activating the CNNmodel (the test set is comprised of damaged andundamaged samples)

Part Trainmale()

Trainfemale()

Testmale (undamaged)()

Testfemale(undamaged)

()

Testmale(damaged)

()

Testfemale(damaged)

()

Testmale(average)

()

Testfemale(average)

()Torso 742 1126 646 974 1073 1579 859 12765Left arm 824 1520 668 1583 1087 2611 877 2097Rightarm 1299 1223 1083 1233 1472 1382 1277 13075

Left leg 878 726 759 740 1122 992 940 866Rightleg 839 801 781 745 1181 1326 981 1035

Average 916 1059 787 1055 1187 1578 986 1316

Table 2 Average error on each principal slice on the training data of male and female datasets (full dataset)

Slice Trainmale () Trainfemale ()Hip 839 468Abdomen 441 346Waist 534 490Chest 580 1125Shoulder 618 937Neck 1355 2161Left wrist 777 1099Left forearm 553 748Left elbow 421 772Left biceps 622 880Left overarm 1054 1566Right wrist 1343 812Right forearm 1269 763Right elbow 836 701Right biceps 884 669Right overarm 1220 1264Left ankle 793 738Left calf 773 462Left under knee 1180 330Left knee 631 440Left middle thigh 363 472Left thigh 646 967Right ankle 954 664Right calf 752 466Right under knee 1067 309Right knee 580 445Right middle thigh 341 505Right thigh 603 1021


i

j j + 1

i + 1

Figure 16 Remeshing based on triangular mesh

Table 5 Average training and testing time on both datasets

Part Train (s) Test a sample (s)Torso (primarytimes 6) 474 0013Torso (all) 1484 0121Arm (primarytimes 10) 540 0032Arm (all) 133 0098Leg (primarytimes 12) 780 0035Leg (all) 764 0108Total 4175 0407

Figure 17 3D avatars of male and female First row generated shapes second row original shapes


female dataset almost come from the scanning device whilethe problems in the male dataset are due to the non-cooperation of participants (Figure 15) We eliminated allunqualified samples from both datasets Overall there are 65samples in the male dataset and 63 samples in the femaledataset After removing these patterns we conducted a newtraining procedure on the new training and testing sets andthe results are shown in Table 4 In themale dataset there are1001 training samples and 100 testing samples while thereare 437 and 100 samples as training and testing data in thefemale dataset e average errors after feeding the in-terpolated primary slices into the CNN models are lowerthan their own errors when compared to the ground truth

e average training and testing time per body part areshown in Table 5

Once all necessary slices are ready to build a 3D modelwe perform remeshing counted on the triangular meshmethod is simple rule constitutes a mesh by using threepoints e points at (i j) (i j + 1) (i + 1 j) on two ad-jacent slices would form a mesh Likewise the points at (i +

1 j) (i j + 1) (i + 1 j + 1) would also produces a mesh(Figure 16)

6 Discussion and Conclusion

Generating 3D models has been becoming an attractive fieldin recent years ere is no doubt about the versatility of the3Dmodel in computer graphics applications such as gamingfilms and garments However constructing a 3D shape isnot a trivial task since the complexity of the model usuallydemands careful design the power of computer hardwareand modern scanning devices To tackle this problem weintroduced a novel method to create a new 3D model simplyby taking the measurements as input Our main contribu-tions include (1) describing a formula to represent 3D dataunder slices of point cloud (2) introducing two-stepframework based on Neural Networks for generating theprimary slices and impaling entire slices and (3) conductingthe experiment and unveiling a benchmark on the IUH andHUST 3D human dataset

It is difficult to compare the present studyrsquos finding withother previous studies because of the different dataset andevaluating metrics However the results confirm the effec-tiveness of our approach because the generated 3D pointcloudmodels are fine enough for visualization with the smallerror during the rational running time (Figure 17) Ourproposed framework not only explores the correlation be-tween the shape and the size of a human body but alsocaptures the local information among adjacent slices In-stead of directly inferring a whole 3D model we divided theobjective model into specific parts and defined suitable NNarchitecture for each part In the spirit of learning in detailslice shapes rather than learning overall structure the hi-erarchical learning strategy was introduced in which theshapes of slices corresponding to user-defined measure-ments are the foundation of all other slicesrsquo shape

e slice structure that we used in this study is notrestricted in the static case It is also effective when applyingto 3D dynamic models via a morphable skeleton e key

idea to generate a new slice shape is to deform an initialshape depending on the training dataset Because everysingle step of our method does not need to change thecoordinate or reduce the dimension we ensure that agenerated point cloud still look like the samples in thetraining data e main drawback of our approach is datadeficiency We suffer from the underfitting problem hencethe NN systems cannot achieve the ideal generalization esecond weakness is that we concentrate on constructingpoint clouds not meshes erefore any application re-quiring 3Dmodels with full mesh reconstructionmight needmore processing steps Although slice structure is verysimple it is challenging to achieve its status especially whendisjointing 3D shapes with complex designs

In conclusion this study suggests that a 3D point cloudbe constructed completely when giving a set of essentialmeasurements On the other hand it is necessary to considerthe shape in more detail when dealing with complicated 3Dstructures such as human bodies Our proposed frameworkshed the light on this concern since it has the ability toanalyze local shape features

Data Availability

e data used to support the findings of this study have notbeen made available because they are private

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e 3D human datasets are sponsored by Industrial Uni-versity of Ho Chi Minh City (IUH) and Hanoi University ofScience and Technology (HUST) Vietnam e authorsgreatly appreciate these agents who provided us the in-formation of these datasets Especially the authors wouldlike to thank the Faculty of Garment Technology andFashion Design Industrial University of Ho Chi Minh Cityfor the powerful equipment which helped to complete thisstudy

References

[1] B Allen B Curless and Z Popovic ldquoe space of humanbody shapesrdquo ACM Transactions on Graphics vol 22 no 3pp 587ndash594 2003

[2] N Hasler C Stoll M Sunkel B Rosenhahn and H-P SeidelldquoA statistical model of human pose and body shaperdquo Com-puter Graphics Forum vol 28 no 2 pp 337ndash346 2009

[3] H Seo and N T Magenat ldquoAn automatic modeling of humanbodies from sizing parametersrdquo in Proceedings of the 2003Symposium on Interactive 3D Graphics pp 19ndash26 MontereyCA USA April 2003

[4] V Blanz and T Vetter ldquoA morphable model for the synthesisof 3D facesrdquo in Proceedings of the 26th Annual Conference onComputer Graphics and Interactive Techniques pp 187ndash194New York NY USA August 1999

[5] Y Chen and R Cipolla ldquoLearning shape priors for single viewreconstructionrdquo in Proceedings of the 2009 IEEE 12th


International Conference on Computer Vision WorkshopsICCV Workshops Kyoto Japan October 2009

[6] D DeCarlo D Metaxas and M Stone ldquoAn anthropometricface model using variational techniquesrdquo in Proceedings of the25th Annual Conference on Computer Graphics and InteractiveTechniques pp 67ndash74 Orlando FL USA July 1998

[7] B Allen B Curless and Z Popovic ldquoExploring the space ofhuman body shapes data-driven synthesis under anthropo-metric controlrdquo in Proceedings of the Digital HumanModelingfor Design and Engineering Symposium pp 1ndash4 RochesterMI USA June 2004

[8] H Seo and N Magnenat-almann ldquoAn example-basedapproach to human body manipulationrdquo Graphical Modelsvol 66 no 1 pp 1ndash23 2004

[9] C-H Chu Y-T Tsai C C L Wang and T-H KwokldquoExemplar-based statistical model for semantic parametricdesign of human bodyrdquo Computers in Industry vol 61 no 6pp 541ndash549 2010

[10] C C L Wang ldquoParameterization and parametric design ofmannequinsrdquo Computer-Aided Design vol 37 no 1pp 83ndash98 2005

[11] S-Y Baek and K Lee ldquoParametric human body shapemodeling framework for human-centered product designrdquoComputer-Aided Design vol 44 no 1 pp 56ndash67 2012

[12] S Wuhrer and C Shu ldquoEstimating 3D human shapes frommeasurementsrdquo Machine Vision and Applications vol 24no 6 pp 1133ndash1147 2013

[13] Y Lecun L Bottou Y Bengio and P Haffner ldquoGradient-based learning applied to document recognitionrdquo Proceedingsof the IEEE vol 86 no 11 pp 2278ndash2324 1998

[14] T A Davis and R Altervogt ldquoGolden mean of the humanbodyrdquo Fibonacci Quarterly vol 17 pp 340ndash344 1979

[15] V Nair and G Hinton Rectified Linear Units Improve Re-stricted Boltzmann Machines ACM Press New York NYUSA 2010

[16] D Kingma and B Jimmy ldquoAdam a method for stochasticoptimizationrdquo in Proceedings of the 3rd International Con-ference for Learning Representations San Diego CA USAMay 2015


Computer Games Technology

International Journal of

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Advances in

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Volume 2018


ReconfigurableComputing



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Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018


Human-ComputerInteraction

Advances in


Scientic Programming

Submit your manuscripts atwwwhindawicom

meaningful structure of objectrsquos boundaries and skeletonTaking the 3D human model for an application we heredemonstrate an end-to-end procedure of synthesizing a newhuman model given anthropometric measurements and aset of parameters learned from training data

2 Related Works

One of the first attempts to solve for 3D model re-construction problem was template model based Moreprecisely this method produces a newmodel by deforming atemplate model Allen at el formulated an optimizationproblem to find an affine transformation at each vertex of thedesigned template model for fitting a 3D scanned humanbody ey defined three types of error and combined themto create the objective function eir approach also dealtwith incomplete surface data and filled inmissing and poorlycaptured areas caused by the scanner [1] Modifying themethod of Allen Hasler performed nonrigid registrationwith the aim of fitting pose and shape of 3D scans form atemplate model [2] Seo and Magenat deformed an existingmodel to obtain the new one based on two stages pre-processing e skeleton fitting found the skeleton structurethat approximates the corresponding 3D human body eskin fitting calculated the displacement vector of each vertexbetween the template model after skeletal fitting and the scanmesh fitting [3]

e other approach is 2D-based reconstruction ismethod reduces the cost because it only requires a set ofimages However the image data often contain noises andbackground which are hard to remove Blanzrsquos approachtook a human face color image as an input and generated thecorresponding 3D face model New faces and expressioncould be described by forming linear combinations ofprototypes [4] In their work the weight vector was assumedto distribute as multivariate Gaussian and could be found bymaximum posterior probability Chen attempted to auto-matically reconstruct more complex 3D shapes like humanbodies from 2D silhouettes with the shape prior which waslearned directly from existing 3Dmodels under a frameworkbased on GPLVM [5] However this approach is not realisticbecause relying on the silhouettes only will cause the loss ofdepth information of a human body

Most of the solutions come from the statistics-basedapproach Similar to our approach these methods use thetraining set to learn the correlation between input andoutput or construct an example space for extrapolationInspiring form DeCarlo et alrsquos work [6] the statistics-basedmodel has become a powerful tool for demonstrating thefeature space of the 3D model In their study human facemeasurements were used to generate 3D face shapes byvariational modeling while a prototype shape was consid-ered as a reference Allen reduced the dimension of 3Dhuman meshes from 180000 elements to 40 or fewer byusing principal component analysis (PCA) en linearregression was used as a technique to find the relationshipbetween six different anthropometrics and 3D humanmodel[7] Seo defined two synthesizers which were joint synthe-sizer and displacement synthesizer Joint synthesizer handles

each degree of freedom of the joints in other words thissynthesizer constructs the skeleton for the model whileanother synthesizer was used to find the appropriate dis-placement on the template skin ese synthesizers were alllearned from eight body measurements with the corre-sponding model by the use of Gaussian radial basis functions[8] With the same approach to Allenrsquos research Chu et alattached a procedure of feasibility check to determinewhether the semantic parameter values input by the user isrational e feasibility check was based on the mathematicconcept of the convex hull and if the input parameters failedthe check their system would return the most similar modelin the training data [9] Wang analyzed a human body fromlaser-scanned 3D unorganized points through many steps[10] He built the feature wireframe on the cloud points byfinding the key points and linking all of them with curveinterpolation After that feature patches were generated byusing the Gregory patch and updated by a voxel-based al-gorithm According to the introduced feature model an-thropometric measurements are easily extracted so that heused numerical optimization to generate a new 3D humanbody which is extracted measurements are likely to the userinput sizes Baek and Lee performed PCA on both the bodysize and body shape vectors then they found the weightvalues of the new model based on the parameter optimi-zation problem with the constraints were the 25 user inputmeasurements [11] ey also clustered hierarchically theirshape vector space by an agglomerative cluster tree to re-main small variation in each cluster Wuhrer and Shu in-troduced a technique that extrapolates the statisticallyinferred shape to fit the measurement data using nonlinearoptimization [12] First PCA is applied to produce a humanshape feature space then shape refinement is used to refinethe predicted model e objective function is formulatedbased on the sum of square error of three types of mea-surements e author announced that the method couldgenerate human-like 3D models with a smaller trainingdataset e above methods have been suffered from acommon drawback which is the limitation of generatedshapes to the space spanned by the training data In otherwords finding a large number of variables by optimizing onthe small dataset would lead to the underfitting problem

3 Methodology

In this section we demonstrate our method which con-sists of two main steps generating primary slices andrefining 3D point cloud 3D objects are formed by a set ofplanes which are perpendicular to the axial height of theobject In other words building 3D shapes is equivalent tobuilding all these planes Normally if the surfaces aresmoothly divided (the distance between two adjacentplanes is very small) adjacent surfaces will have nearlysimilar shapes Moreover not all measurements areavailable in practice thus we only considered someavailable ones as the measurements corresponding withprimary planes erefore selecting the main planes helpsus to reduce the number of calculations and also necessarymeasurements





+ y2 le

mi

2π1113874 1113875

211138681113868111386811138681113868111386811138681113896 1113897⟶ Siprime (1)






x x0 + r cos θ

y y0 + r sin θ1113896 (2)







21113872 1113873

Tα W

11113872 1113873

TXi1113874 1113875 (3)










(4)










(i) Torso










x0 y0 z0( 1113857 ≔ x0 y0 minHz + idz

m minus 11113888 1113889 (5)

If

minHz + idz


dz

m minus 1 (6)





x(i)

y(i)

z(i)

1113872 1113873 1Si

11138681113868111386811138681113868111386811138681113868

1113944(xyz)isinSi

(x y z) (7)




x0 minus x(i)1113888 1113889 (8)


2πj minus 1

nle a0 lt 2π

j

n (9)


d(i)j

x0 minus x(i)( 11138572

+ y0 minus y(i)( 11138572

1113969

(10)









1113944

n


+ c 2π

maxyprime( 11138572


2

1113971


(11)




1300

1200

1100

1000

900

800

7002001000ndash100ndash200

500ndash50ndash100X

Y

Z

ndash150

Interpolated point


Shrink

Dila

teD

ilate


250

200

150

100

50

0

ndash50

ndash100

ndash150

ndash200


(a)

100

50

0

ndash50

ndash100

150ndash50 0 50 100

3deg

(b)






Torso

Upper

LowerArm

Upper

Lower

LegUpper

Lower







r (P(i)h )2π


Y f(X)

max maxY

min minY



1113969

)

W(h) argmin(lossh)



L yprime y( 1113857 1

mn1113944

m

i11113944

n


2 (12)




Overarm

NeckShoulder

ChestWaist

HipAbdomen

BicepsElbow

ForearmWrist

ThighMiddle thigh

KneeUnder knee

CalfAnkle


150100

500

ndash50ndash100


ndash150

150100

500


200

100

0

ndash100

ndash200

(a)


150100

500


150100

500


200

100

0

ndash100

ndash200

(b)


150100

500


150100

500


150

100

0

ndash100

ndash200

(c)







1300120011001000

900



X la

bel

Z la

bel

100 200

1300120011001000900



X la

belZ

labe

l

100 200


1024 times 1

n times 1n times 1

Max

Min

0

ndash25

ndash50

ndash75

ndash100


25

50

75

100

0

ndash50

ndash100

ndash150


50

150

100




L y yprime( 1113857 1

mn1113944

n

i11113944

m

j1

yij minus yijprime

11138681113868111386811138681113868

11138681113868111386811138681113868

yij

times 100 (13)














Xhk Sprime(i)

startk + (Sprime(i)




W argmin(loss)


Symmetric

Reflex

3 2 1 2 3 1 23 2 1 2 3 1 26 5 4 5 6 4 59 8 7 8 9 7 89 8 7 8 9 7 8



140

120

100

80

Dist

ance

60

40

20

01 3 5 7 9 11 13 15 17 19 21 23 25 27


(a)

Dist

ance

80

70

40

50

60

30

20

10

01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


(b)

Figure 14 Continued

250

200

150

100Dist

ance

50

01 3 5 7 9 11 13 15 17 19 21 23 25 27


Hip

29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59

50

4045

3530252015

Dist

ance

1050


Middle thigh

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

50

4045

3530252015

Dist

ance

1050


Forearm

15 16 17 18 19 20

(a)

250

200

150

100Dist

ance

50

01 3 5 7 9 11 13 15 17 19 21 23 25 27


Hip

29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59

40

45

35

30

25

20

15

Dist

ance

10

5

01 2 3 4 5 6 7 8 9 10 11 12 13 14


Middle thigh

15 16 17 18 19 20 21 22 23 24 25 26 27 2829 30

50

4045

3530252015

Dist

ance

1050

1 2 3 4 5 6 7 8 9 10 11 12 13 14Degree (times18)

Forearm

15 16 17 18 19 20

(b)






Dist

ance

90

80

70

40

50

60

30

20

10

01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


(c)





Testfemale(before)

Trainmale(after)

Trainfemale(after)

Testmale(after)

Testfemale(after)



Part Trainmale()

Trainfemale()



()

Testmale(damaged)

()

Testfemale(damaged)

()

Testmale(average)

()

Testfemale(average)



Average 916 1059 787 1055 1187 1578 986 1316




i

j j + 1

i + 1
















Data Availability




Acknowledgments


References

























Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in







+ y2 le

mi

2π1113874 1113875

211138681113868111386811138681113868111386811138681113896 1113897⟶ Siprime (1)






x x0 + r cos θ

y y0 + r sin θ1113896 (2)







21113872 1113873

Tα W

11113872 1113873

TXi1113874 1113875 (3)










(4)










(i) Torso










x0 y0 z0( 1113857 ≔ x0 y0 minHz + idz

m minus 11113888 1113889 (5)

If

minHz + idz


dz

m minus 1 (6)





x(i)

y(i)

z(i)

1113872 1113873 1Si

11138681113868111386811138681113868111386811138681113868

1113944(xyz)isinSi

(x y z) (7)




x0 minus x(i)1113888 1113889 (8)


2πj minus 1

nle a0 lt 2π

j

n (9)


d(i)j

x0 minus x(i)( 11138572

+ y0 minus y(i)( 11138572

1113969

(10)









1113944

n


+ c 2π

maxyprime( 11138572


2

1113971


(11)




1300

1200

1100

1000

900

800

7002001000ndash100ndash200

500ndash50ndash100X

Y

Z

ndash150

Interpolated point


Shrink

Dila

teD

ilate


250

200

150

100

50

0

ndash50

ndash100

ndash150

ndash200


(a)

100

50

0

ndash50

ndash100

150ndash50 0 50 100

3deg

(b)






Torso

Upper

LowerArm

Upper

Lower

LegUpper

Lower







r (P(i)h )2π


Y f(X)

max maxY

min minY



1113969

)

W(h) argmin(lossh)



L yprime y( 1113857 1

mn1113944

m

i11113944

n


2 (12)




Overarm

NeckShoulder

ChestWaist

HipAbdomen

BicepsElbow

ForearmWrist

ThighMiddle thigh

KneeUnder knee

CalfAnkle


150100

500

ndash50ndash100


ndash150

150100

500


200

100

0

ndash100

ndash200

(a)


150100

500


150100

500


200

100

0

ndash100

ndash200

(b)


150100

500


150100

500


150

100

0

ndash100

ndash200

(c)







1300120011001000

900



X la

bel

Z la

bel

100 200

1300120011001000900



X la

belZ

labe

l

100 200


1024 times 1

n times 1n times 1

Max

Min

0

ndash25

ndash50

ndash75

ndash100


25

50

75

100

0

ndash50

ndash100

ndash150


50

150

100




L y yprime( 1113857 1

mn1113944

n

i11113944

m

j1

yij minus yijprime

11138681113868111386811138681113868

11138681113868111386811138681113868

yij

times 100 (13)














Xhk Sprime(i)

startk + (Sprime(i)




W argmin(loss)


Symmetric

Reflex

3 2 1 2 3 1 23 2 1 2 3 1 26 5 4 5 6 4 59 8 7 8 9 7 89 8 7 8 9 7 8



140

120

100

80

Dist

ance

60

40

20

01 3 5 7 9 11 13 15 17 19 21 23 25 27


(a)

Dist

ance

80

70

40

50

60

30

20

10

01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


(b)

Figure 14 Continued

250

200

150

100Dist

ance

50

01 3 5 7 9 11 13 15 17 19 21 23 25 27


Hip

29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59

50

4045

3530252015

Dist

ance

1050


Middle thigh

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

50

4045

3530252015

Dist

ance

1050


Forearm

15 16 17 18 19 20

(a)

250

200

150

100Dist

ance

50

01 3 5 7 9 11 13 15 17 19 21 23 25 27


Hip

29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59

40

45

35

30

25

20

15

Dist

ance

10

5

01 2 3 4 5 6 7 8 9 10 11 12 13 14


Middle thigh

15 16 17 18 19 20 21 22 23 24 25 26 27 2829 30

50

4045

3530252015

Dist

ance

1050

1 2 3 4 5 6 7 8 9 10 11 12 13 14Degree (times18)

Forearm

15 16 17 18 19 20

(b)






Dist

ance

90

80

70

40

50

60

30

20

10

01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


(c)





Testfemale(before)

Trainmale(after)

Trainfemale(after)

Testmale(after)

Testfemale(after)



Part Trainmale()

Trainfemale()



()

Testmale(damaged)

()

Testfemale(damaged)

()

Testmale(average)

()

Testfemale(average)



Average 916 1059 787 1055 1187 1578 986 1316




i

j j + 1

i + 1
















Data Availability




Acknowledgments


References

























Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in






(i) Torso










x0 y0 z0( 1113857 ≔ x0 y0 minHz + idz

m minus 11113888 1113889 (5)

If

minHz + idz


dz

m minus 1 (6)





x(i)

y(i)

z(i)

1113872 1113873 1Si

11138681113868111386811138681113868111386811138681113868

1113944(xyz)isinSi

(x y z) (7)




x0 minus x(i)1113888 1113889 (8)


2πj minus 1

nle a0 lt 2π

j

n (9)


d(i)j

x0 minus x(i)( 11138572

+ y0 minus y(i)( 11138572

1113969

(10)









1113944

n


+ c 2π

maxyprime( 11138572


2

1113971


(11)




1300

1200

1100

1000

900

800

7002001000ndash100ndash200

500ndash50ndash100X

Y

Z

ndash150

Interpolated point


Shrink

Dila

teD

ilate


250

200

150

100

50

0

ndash50

ndash100

ndash150

ndash200


(a)

100

50

0

ndash50

ndash100

150ndash50 0 50 100

3deg

(b)






Torso

Upper

LowerArm

Upper

Lower

LegUpper

Lower







r (P(i)h )2π


Y f(X)

max maxY

min minY



1113969

)

W(h) argmin(lossh)



L yprime y( 1113857 1

mn1113944

m

i11113944

n


2 (12)




Overarm

NeckShoulder

ChestWaist

HipAbdomen

BicepsElbow

ForearmWrist

ThighMiddle thigh

KneeUnder knee

CalfAnkle


150100

500

ndash50ndash100


ndash150

150100

500


200

100

0

ndash100

ndash200

(a)


150100

500


150100

500


200

100

0

ndash100

ndash200

(b)


150100

500


150100

500


150

100

0

ndash100

ndash200

(c)







1300120011001000

900



X la

bel

Z la

bel

100 200

1300120011001000900



X la

belZ

labe

l

100 200


1024 times 1

n times 1n times 1

Max

Min

0

ndash25

ndash50

ndash75

ndash100


25

50

75

100

0

ndash50

ndash100

ndash150


50

150

100




L y yprime( 1113857 1

mn1113944

n

i11113944

m

j1

yij minus yijprime

11138681113868111386811138681113868

11138681113868111386811138681113868

yij

times 100 (13)














Xhk Sprime(i)

startk + (Sprime(i)




W argmin(loss)


Symmetric

Reflex

3 2 1 2 3 1 23 2 1 2 3 1 26 5 4 5 6 4 59 8 7 8 9 7 89 8 7 8 9 7 8



140

120

100

80

Dist

ance

60

40

20

01 3 5 7 9 11 13 15 17 19 21 23 25 27


(a)

Dist

ance

80

70

40

50

60

30

20

10

01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


(b)

Figure 14 Continued

250

200

150

100Dist

ance

50

01 3 5 7 9 11 13 15 17 19 21 23 25 27


Hip

29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59

50

4045

3530252015

Dist

ance

1050


Middle thigh

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

50

4045

3530252015

Dist

ance

1050


Forearm

15 16 17 18 19 20

(a)

250

200

150

100Dist

ance

50

01 3 5 7 9 11 13 15 17 19 21 23 25 27


Hip

29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59

40

45

35

30

25

20

15

Dist

ance

10

5

01 2 3 4 5 6 7 8 9 10 11 12 13 14


Middle thigh

15 16 17 18 19 20 21 22 23 24 25 26 27 2829 30

50

4045

3530252015

Dist

ance

1050

1 2 3 4 5 6 7 8 9 10 11 12 13 14Degree (times18)

Forearm

15 16 17 18 19 20

(b)






Dist

ance

90

80

70

40

50

60

30

20

10

01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


(c)





Testfemale(before)

Trainmale(after)

Trainfemale(after)

Testmale(after)

Testfemale(after)



Part Trainmale()

Trainfemale()



()

Testmale(damaged)

()

Testfemale(damaged)

()

Testmale(average)

()

Testfemale(average)



Average 916 1059 787 1055 1187 1578 986 1316




i

j j + 1

i + 1
















Data Availability




Acknowledgments


References

























Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in









1113944

n


+ c 2π

maxyprime( 11138572


2

1113971


(11)




1300

1200

1100

1000

900

800

7002001000ndash100ndash200

500ndash50ndash100X

Y

Z

ndash150

Interpolated point


Shrink

Dila

teD

ilate


250

200

150

100

50

0

ndash50

ndash100

ndash150

ndash200


(a)

100

50

0

ndash50

ndash100

150ndash50 0 50 100

3deg

(b)






Torso

Upper

LowerArm

Upper

Lower

LegUpper

Lower







r (P(i)h )2π


Y f(X)

max maxY

min minY



1113969

)

W(h) argmin(lossh)



L yprime y( 1113857 1

mn1113944

m

i11113944

n


2 (12)




Overarm

NeckShoulder

ChestWaist

HipAbdomen

BicepsElbow

ForearmWrist

ThighMiddle thigh

KneeUnder knee

CalfAnkle


150100

500

ndash50ndash100


ndash150

150100

500


200

100

0

ndash100

ndash200

(a)


150100

500


150100

500


200

100

0

ndash100

ndash200

(b)


150100

500


150100

500


150

100

0

ndash100

ndash200

(c)







1300120011001000

900



X la

bel

Z la

bel

100 200

1300120011001000900



X la

belZ

labe

l

100 200


1024 times 1

n times 1n times 1

Max

Min

0

ndash25

ndash50

ndash75

ndash100


25

50

75

100

0

ndash50

ndash100

ndash150


50

150

100




L y yprime( 1113857 1

mn1113944

n

i11113944

m

j1

yij minus yijprime

11138681113868111386811138681113868

11138681113868111386811138681113868

yij

times 100 (13)














Xhk Sprime(i)

startk + (Sprime(i)




W argmin(loss)


Symmetric

Reflex

3 2 1 2 3 1 23 2 1 2 3 1 26 5 4 5 6 4 59 8 7 8 9 7 89 8 7 8 9 7 8



140

120

100

80

Dist

ance

60

40

20

01 3 5 7 9 11 13 15 17 19 21 23 25 27


(a)

Dist

ance

80

70

40

50

60

30

20

10

01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


(b)

Figure 14 Continued

250

200

150

100Dist

ance

50

01 3 5 7 9 11 13 15 17 19 21 23 25 27


Hip

29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59

50

4045

3530252015

Dist

ance

1050


Middle thigh

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

50

4045

3530252015

Dist

ance

1050


Forearm

15 16 17 18 19 20

(a)

250

200

150

100Dist

ance

50

01 3 5 7 9 11 13 15 17 19 21 23 25 27


Hip

29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59

40

45

35

30

25

20

15

Dist

ance

10

5

01 2 3 4 5 6 7 8 9 10 11 12 13 14


Middle thigh

15 16 17 18 19 20 21 22 23 24 25 26 27 2829 30

50

4045

3530252015

Dist

ance

1050

1 2 3 4 5 6 7 8 9 10 11 12 13 14Degree (times18)

Forearm

15 16 17 18 19 20

(b)






Dist

ance

90

80

70

40

50

60

30

20

10

01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


(c)





Testfemale(before)

Trainmale(after)

Trainfemale(after)

Testmale(after)

Testfemale(after)



Part Trainmale()

Trainfemale()



()

Testmale(damaged)

()

Testfemale(damaged)

()

Testmale(average)

()

Testfemale(average)



Average 916 1059 787 1055 1187 1578 986 1316




i

j j + 1

i + 1
















Data Availability




Acknowledgments


References

























Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in







Torso

Upper

LowerArm

Upper

Lower

LegUpper

Lower







r (P(i)h )2π


Y f(X)

max maxY

min minY



1113969

)

W(h) argmin(lossh)



L yprime y( 1113857 1

mn1113944

m

i11113944

n


2 (12)




Overarm

NeckShoulder

ChestWaist

HipAbdomen

BicepsElbow

ForearmWrist

ThighMiddle thigh

KneeUnder knee

CalfAnkle


150100

500

ndash50ndash100


ndash150

150100

500


200

100

0

ndash100

ndash200

(a)


150100

500


150100

500


200

100

0

ndash100

ndash200

(b)


150100

500


150100

500


150

100

0

ndash100

ndash200

(c)







1300120011001000

900



X la

bel

Z la

bel

100 200

1300120011001000900



X la

belZ

labe

l

100 200


1024 times 1

n times 1n times 1

Max

Min

0

ndash25

ndash50

ndash75

ndash100


25

50

75

100

0

ndash50

ndash100

ndash150


50

150

100




L y yprime( 1113857 1

mn1113944

n

i11113944

m

j1

yij minus yijprime

11138681113868111386811138681113868

11138681113868111386811138681113868

yij

times 100 (13)














Xhk Sprime(i)

startk + (Sprime(i)




W argmin(loss)


Symmetric

Reflex

3 2 1 2 3 1 23 2 1 2 3 1 26 5 4 5 6 4 59 8 7 8 9 7 89 8 7 8 9 7 8



140

120

100

80

Dist

ance

60

40

20

01 3 5 7 9 11 13 15 17 19 21 23 25 27


(a)

Dist

ance

80

70

40

50

60

30

20

10

01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


(b)

Figure 14 Continued

250

200

150

100Dist

ance

50

01 3 5 7 9 11 13 15 17 19 21 23 25 27


Hip

29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59

50

4045

3530252015

Dist

ance

1050


Middle thigh

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

50

4045

3530252015

Dist

ance

1050


Forearm

15 16 17 18 19 20

(a)

250

200

150

100Dist

ance

50

01 3 5 7 9 11 13 15 17 19 21 23 25 27


Hip

29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59

40

45

35

30

25

20

15

Dist

ance

10

5

01 2 3 4 5 6 7 8 9 10 11 12 13 14


Middle thigh

15 16 17 18 19 20 21 22 23 24 25 26 27 2829 30

50

4045

3530252015

Dist

ance

1050

1 2 3 4 5 6 7 8 9 10 11 12 13 14Degree (times18)

Forearm

15 16 17 18 19 20

(b)






Dist

ance

90

80

70

40

50

60

30

20

10

01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


(c)





Testfemale(before)

Trainmale(after)

Trainfemale(after)

Testmale(after)

Testfemale(after)



Part Trainmale()

Trainfemale()



()

Testmale(damaged)

()

Testfemale(damaged)

()

Testmale(average)

()

Testfemale(average)



Average 916 1059 787 1055 1187 1578 986 1316




i

j j + 1

i + 1
















Data Availability




Acknowledgments


References

























Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in




L yprime y( 1113857 1

mn1113944

m

i11113944

n


2 (12)




Overarm

NeckShoulder

ChestWaist

HipAbdomen

BicepsElbow

ForearmWrist

ThighMiddle thigh

KneeUnder knee

CalfAnkle


150100

500

ndash50ndash100


ndash150

150100

500


200

100

0

ndash100

ndash200

(a)


150100

500


150100

500


200

100

0

ndash100

ndash200

(b)


150100

500


150100

500


150

100

0

ndash100

ndash200

(c)







1300120011001000

900



X la

bel

Z la

bel

100 200

1300120011001000900



X la

belZ

labe

l

100 200


1024 times 1

n times 1n times 1

Max

Min

0

ndash25

ndash50

ndash75

ndash100


25

50

75

100

0

ndash50

ndash100

ndash150


50

150

100




L y yprime( 1113857 1

mn1113944

n

i11113944

m

j1

yij minus yijprime

11138681113868111386811138681113868

11138681113868111386811138681113868

yij

times 100 (13)














Xhk Sprime(i)

startk + (Sprime(i)




W argmin(loss)


Symmetric

Reflex

3 2 1 2 3 1 23 2 1 2 3 1 26 5 4 5 6 4 59 8 7 8 9 7 89 8 7 8 9 7 8



140

120

100

80

Dist

ance

60

40

20

01 3 5 7 9 11 13 15 17 19 21 23 25 27


(a)

Dist

ance

80

70

40

50

60

30

20

10

01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


(b)

Figure 14 Continued

250

200

150

100Dist

ance

50

01 3 5 7 9 11 13 15 17 19 21 23 25 27


Hip

29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59

50

4045

3530252015

Dist

ance

1050


Middle thigh

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

50

4045

3530252015

Dist

ance

1050


Forearm

15 16 17 18 19 20

(a)

250

200

150

100Dist

ance

50

01 3 5 7 9 11 13 15 17 19 21 23 25 27


Hip

29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59

40

45

35

30

25

20

15

Dist

ance

10

5

01 2 3 4 5 6 7 8 9 10 11 12 13 14


Middle thigh

15 16 17 18 19 20 21 22 23 24 25 26 27 2829 30

50

4045

3530252015

Dist

ance

1050

1 2 3 4 5 6 7 8 9 10 11 12 13 14Degree (times18)

Forearm

15 16 17 18 19 20

(b)






Dist

ance

90

80

70

40

50

60

30

20

10

01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


(c)





Testfemale(before)

Trainmale(after)

Trainfemale(after)

Testmale(after)

Testfemale(after)



Part Trainmale()

Trainfemale()



()

Testmale(damaged)

()

Testfemale(damaged)

()

Testmale(average)

()

Testfemale(average)



Average 916 1059 787 1055 1187 1578 986 1316




i

j j + 1

i + 1
















Data Availability




Acknowledgments


References

























Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in








1300120011001000

900



X la

bel

Z la

bel

100 200

1300120011001000900



X la

belZ

labe

l

100 200


1024 times 1

n times 1n times 1

Max

Min

0

ndash25

ndash50

ndash75

ndash100


25

50

75

100

0

ndash50

ndash100

ndash150


50

150

100




L y yprime( 1113857 1

mn1113944

n

i11113944

m

j1

yij minus yijprime

11138681113868111386811138681113868

11138681113868111386811138681113868

yij

times 100 (13)














Xhk Sprime(i)

startk + (Sprime(i)




W argmin(loss)


Symmetric

Reflex

3 2 1 2 3 1 23 2 1 2 3 1 26 5 4 5 6 4 59 8 7 8 9 7 89 8 7 8 9 7 8



140

120

100

80

Dist

ance

60

40

20

01 3 5 7 9 11 13 15 17 19 21 23 25 27


(a)

Dist

ance

80

70

40

50

60

30

20

10

01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


(b)

Figure 14 Continued

250

200

150

100Dist

ance

50

01 3 5 7 9 11 13 15 17 19 21 23 25 27


Hip

29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59

50

4045

3530252015

Dist

ance

1050


Middle thigh

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

50

4045

3530252015

Dist

ance

1050


Forearm

15 16 17 18 19 20

(a)

250

200

150

100Dist

ance

50

01 3 5 7 9 11 13 15 17 19 21 23 25 27


Hip

29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59

40

45

35

30

25

20

15

Dist

ance

10

5

01 2 3 4 5 6 7 8 9 10 11 12 13 14


Middle thigh

15 16 17 18 19 20 21 22 23 24 25 26 27 2829 30

50

4045

3530252015

Dist

ance

1050

1 2 3 4 5 6 7 8 9 10 11 12 13 14Degree (times18)

Forearm

15 16 17 18 19 20

(b)






Dist

ance

90

80

70

40

50

60

30

20

10

01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


(c)





Testfemale(before)

Trainmale(after)

Trainfemale(after)

Testmale(after)

Testfemale(after)



Part Trainmale()

Trainfemale()



()

Testmale(damaged)

()

Testfemale(damaged)

()

Testmale(average)

()

Testfemale(average)



Average 916 1059 787 1055 1187 1578 986 1316




i

j j + 1

i + 1
















Data Availability




Acknowledgments


References

























Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in





L y yprime( 1113857 1

mn1113944

n

i11113944

m

j1

yij minus yijprime

11138681113868111386811138681113868

11138681113868111386811138681113868

yij

times 100 (13)














Xhk Sprime(i)

startk + (Sprime(i)




W argmin(loss)


Symmetric

Reflex

3 2 1 2 3 1 23 2 1 2 3 1 26 5 4 5 6 4 59 8 7 8 9 7 89 8 7 8 9 7 8



140

120

100

80

Dist

ance

60

40

20

01 3 5 7 9 11 13 15 17 19 21 23 25 27


(a)

Dist

ance

80

70

40

50

60

30

20

10

01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


(b)

Figure 14 Continued

250

200

150

100Dist

ance

50

01 3 5 7 9 11 13 15 17 19 21 23 25 27


Hip

29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59

50

4045

3530252015

Dist

ance

1050


Middle thigh

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

50

4045

3530252015

Dist

ance

1050


Forearm

15 16 17 18 19 20

(a)

250

200

150

100Dist

ance

50

01 3 5 7 9 11 13 15 17 19 21 23 25 27


Hip

29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59

40

45

35

30

25

20

15

Dist

ance

10

5

01 2 3 4 5 6 7 8 9 10 11 12 13 14


Middle thigh

15 16 17 18 19 20 21 22 23 24 25 26 27 2829 30

50

4045

3530252015

Dist

ance

1050

1 2 3 4 5 6 7 8 9 10 11 12 13 14Degree (times18)

Forearm

15 16 17 18 19 20

(b)






Dist

ance

90

80

70

40

50

60

30

20

10

01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


(c)





Testfemale(before)

Trainmale(after)

Trainfemale(after)

Testmale(after)

Testfemale(after)



Part Trainmale()

Trainfemale()



()

Testmale(damaged)

()

Testfemale(damaged)

()

Testmale(average)

()

Testfemale(average)



Average 916 1059 787 1055 1187 1578 986 1316




i

j j + 1

i + 1
















Data Availability




Acknowledgments


References

























Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in




140

120

100

80

Dist

ance

60

40

20

01 3 5 7 9 11 13 15 17 19 21 23 25 27


(a)

Dist

ance

80

70

40

50

60

30

20

10

01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


(b)

Figure 14 Continued

250

200

150

100Dist

ance

50

01 3 5 7 9 11 13 15 17 19 21 23 25 27


Hip

29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59

50

4045

3530252015

Dist

ance

1050


Middle thigh

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

50

4045

3530252015

Dist

ance

1050


Forearm

15 16 17 18 19 20

(a)

250

200

150

100Dist

ance

50

01 3 5 7 9 11 13 15 17 19 21 23 25 27


Hip

29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59

40

45

35

30

25

20

15

Dist

ance

10

5

01 2 3 4 5 6 7 8 9 10 11 12 13 14


Middle thigh

15 16 17 18 19 20 21 22 23 24 25 26 27 2829 30

50

4045

3530252015

Dist

ance

1050

1 2 3 4 5 6 7 8 9 10 11 12 13 14Degree (times18)

Forearm

15 16 17 18 19 20

(b)






Dist

ance

90

80

70

40

50

60

30

20

10

01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


(c)





Testfemale(before)

Trainmale(after)

Trainfemale(after)

Testmale(after)

Testfemale(after)



Part Trainmale()

Trainfemale()



()

Testmale(damaged)

()

Testfemale(damaged)

()

Testmale(average)

()

Testfemale(average)



Average 916 1059 787 1055 1187 1578 986 1316




i

j j + 1

i + 1
















Data Availability




Acknowledgments


References

























Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in







Dist

ance

90

80

70

40

50

60

30

20

10

01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


(c)





Testfemale(before)

Trainmale(after)

Trainfemale(after)

Testmale(after)

Testfemale(after)



Part Trainmale()

Trainfemale()



()

Testmale(damaged)

()

Testfemale(damaged)

()

Testmale(average)

()

Testfemale(average)



Average 916 1059 787 1055 1187 1578 986 1316




i

j j + 1

i + 1
















Data Availability




Acknowledgments


References

























Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in






Testfemale(before)

Trainmale(after)

Trainfemale(after)

Testmale(after)

Testfemale(after)



Part Trainmale()

Trainfemale()



()

Testmale(damaged)

()

Testfemale(damaged)

()

Testmale(average)

()

Testfemale(average)



Average 916 1059 787 1055 1187 1578 986 1316




i

j j + 1

i + 1
















Data Availability




Acknowledgments


References

























Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in




i

j j + 1

i + 1
















Data Availability




Acknowledgments


References

























Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in














Data Availability




Acknowledgments


References

























Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in






















Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in









Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in




Documents

GeneratingPointCloudfromMeasurementsandShapesBasedon ...downloads.hindawi.com/journals/cin/2019/1353601.pdf · θ 2πj−1/n, and nis the dimension of the slice vectors. Onepointisdistributedtothejth