Gesture Recognition: Hand Pose EstimationUbiquitous computing seminar FS2014

Student report

Adrian SpurrETH Zurich

spurra@student.ethz.ch

ABSTRACTIn this report, different vision-based approaches to solve theproblem of hand pose estimation are reviewed. The firstthree methods presented utilize random forest, whereas thelast tackles the problem of pose estimation of two stronglyinteracting hands. Lastly, an outlook at the future of the fieldis given.

ACM Classification: H5.2 [Information interfaces and pre-sentation]: User Interfaces. - Graphical user interfaces.

General terms: Algorithms, Human Factors.

Keywords: Ubiquitous computing, gesture recognition, handpose estimation, human computer interaction.

1. INTRODUCTIONIn today’s environment, computers have become ubiquitous.They are so seamlessly integrated in the lives of people, thatwe barely notice their presence and influence. Efficient inter-action with these devices is vital for a productive society. Toavoid having to spend too much time on learning on how toproperly interact with them, it is vital that the interfaces are asnatural to human action as possible. This is where hand poseestimation comes into play. Due to being a natural part ofhuman interaction, as well as being the most dexterous bodypart human beings possess, there has been a great empha-sis on enabling the computers to recognize and understandhand gestures. This ability can be used for a wide area ofapplication, such as virtual/augmented reality, gaming, robotcontrol/learning, and even medical applications. One of thefirst attempts to solve this problem was the data glove. Eventhough being highly accurate and having the possibility toprovide haptic feedback, its disadvantages are too many forwide and practical use. These include, amongst others, thelong calibration time, invasiveness and hindrance of natu-ral movements being cabled, therefore unsuitable for mobileuse. Vision-based systems are believed to be a promisingalternative, not possessing any of these disadvantages. How-ever, these systems bring with them an array of challengingproblems, which need to be solved to achieve widespread

utilization. These include self-occlusion, viewpoint change,noisy data, accuracy and performance. The field of hand poseestimation has made a rapid progress in recent years, mainlydue to the availability of cheap enabling hardware, such asRGB-D cameras, or high powered GPUs. In this report, ap-proaches on how these problems can be solved with the helpof state-of-the-art algorithms are provided. Each approachwill be summarized in detail and its extent of accuracy pre-sented.

2. OVERVIEWThe general approach is similar for each algorithm assistedby a RGB-D camera, which provide the computer with eithercolour or depth images, or both. Normally the depth imageis preferable, as it is easier to segment. However, inclusionof the colour image into the estimation process helps to per-form more accurate prediction. The images are then prepro-cessed to assist in the estimation step. The main predictionis performed and the result is an output, in the form of thehand skeleton. This computer-usable form is a succinct andconvenient way to represent the current configuration of thehand.

DifficultiesPose estimation, specifically hand pose estimation comeswith challenging difficulties, which need to be considered tohave an accurate and robust classifier.

Noisy Data and segmentation. Noisy data, which includelow resolution images from low resolution cameras or if theperson is far away. Noise also includes anything else in theimage that is not of interest for pose estimation, in otherwords, the background. This can be seen as well as a segmen-tation problem. One would like to have the hand segmentedwithout any additional noise. There are several approachesto solving this, such as a simple threshold on the depth, dis-playing only close up body parts, which ideally would be thehand. Or alternatively, one can segment based on the skincolour, with help of the colour image.

Self-Occlusion and Viewpoint change. Frequently, fingerswill be covering other fingers and not all hand parts will bevisible from the depth image. One has to therefore infer theposition of occluded hand parts from what is visible. Thechange of viewpoint introduces additional occlusion, whichhave to be accounted for. Accurate approaches are able todeal with these situations.

High Degree of Freedom per Hand Each hand has 27 de-grees of freedom, which account for about 280 trillion handposes. These either have to be learned, or should be able togeneralize to do so.

Performance. Low computational cost is critical. Any prac-tical application of hand pose estimation requires real timeperformance. This is an issue for many approaches, whichgenerally have high computational cost due to sophisticatedalgorithms. However, with today’s widespread availabilityof high powered GPU’s and CPU’s, these are becoming in-creasingly more applicable for real time application.

ApproachesIn general, there are two main approaches used in today’s al-gorithms and both have their advantages and disadvantages.

Discriminative Approach This approach maps the input di-rectly to a hand skeleton configuration, with the help of theknowledge it gained through a training phase. This is bothan advantage and a disadvantage, as often the quality of theprediction depends on the quality and quantity of the train-ing data and not only on the actual approach. Access to goodtraining data is laborious. For supervised methods, one hasto either utilize synthetic data as proposed by [1] or manuallylabel all the realistic data. It is hard to compare discrimina-tive approaches with each other, as they are trained and testedon different data. Nevertheless, the advantage of the discrim-inative approach is that it is reasonably robust, both to noisydata and rapid change of hand movement.

Model-Based Approach In this approach, the algorithm keepstrack of the hand pose internally, called hypothesis, and es-timates the current hand pose with the help of the hypoth-esis and the observation delivered by the RGB-D camera.It therefore naturally exploits temporal information and re-quires no training. This is a huge advantage over the dis-criminative approach, as the accuracy of it is only dependenton the implementation of the algorithm and not on trainingdata. However, due to using temporal information it is alsovery sensitive towards rapid changes in pose. In other words,the approach tends to be especially prone to errors duringrapid hand movements.

Random ForestsRandom Forests were first proposed by [5]. They consistof decision trees that performs regression or classification.The final result of the Forest is the average of all the treescontained within. It belongs to a class of machine learningalgorithm called ensemble method. These methods are par-ticularly robust to noise due to the averaging step done toperform the final decision. They can be implemented effi-ciently on GPUs and are therefore fast. To classify an inputx, one starts at the root of the tree and assigns it to the eitherleft child or the right child, based on the feature θ(x) anda threshold τ . Once a leaf node is reached, the containinglearned distribution is used as the output of that tree. To per-form the final classification, the distributions of each tree arethen averaged over all the trees, and a final classification isperformed, according to equation 1:

P (c, x) =1

T

T∑t=1

Pt(c, x) (1)

To build such a tree, a training phase is required. One canuse either synthetic or realistic training data, provided thatthey are labelled. Each tree is trained on a separate randomsubset of the training data. On each split node the trainingset is separated according to formula 2 and 3.

Q1(θ, τ) = {x|θ(x) < τ} (2)

Q2(θ, τ) = {x|θ(x) ≥ τ} (3)

The feature θ and the threshold τ chosen for the split is thepair which maximizes the information gain, computed by aquality function. They are selected out of a random subsetsampled from the full set of features and thresholds. Thisnode splitting is recursively applied to each child node, untila maximum tree depth is reached or until the child nodesare pure enough, with respect to the quality function. Thedistribution of the leaf node is computed according to thelabelled training data reaching the node. Random Forestsare utilized in many discriminative approaches. They can beused to classify elements according to body parts, creating abody label distribution out of which a 3D joint proposal canbe done. This is applied in [1, 2]. Alternatively they can beused to perform regression, such as in [3], to directly inferthe position of the joints.

Particle Swarm OptimizationParticle Swarm Optimization (PSO) is a method to optimizean objective function defined over a parameter space. Tomake use of the algorithm, one needs to define a parameterspace and an objective function f to optimize. To initial-ize, n particles are randomly sampled across the parameterspace, each assigned a velocity, uniformly distributed overa defined region. These particles iterate over the parameterspace according to their velocity. Once a maximum num-ber of iterations is reached, the algorithm is terminated andthe best position found is output. At each iteration k, eachparticle i updates their position xk,i according to 4:

xk+1,i = xk,i + vk,i (4)

At the same time, the velocity vk,i gets updated according to5:

vk+1,i = vk,i + r1(Pk,i − xk,i) + r2(Gk − xk,i) (5)

Where Pk,i is the best position found by particle i and Gk isthe best position found over all particles, both until genera-tion k. In terms of equations:

Figure 1: First the depth image is obtained. After pass-ing through the random forest, a body label distributionis returned, with which the 3D joint proposals can beformed with help of mean shift algorithm.

Pk+1,i =

{Pk,i if f(Pk,i) ≥ f(xk+1,i)xk+1,i else

Gk+1 = Pk+1,i, where i = argmaxi f(Pk+1,i)

The advantage of PSO over other optimization methods isthat it makes very little assumption over the objective func-tion used. However, neither convergence nor finding the op-timal position is guaranteed. One can assume that havingenough particles and allowing the algorithm to iterate enoughtimes, a sufficiently close position can be found. PSO is usedin the last method presented in this report, a model-based ap-proach using a objective function to penalize the discrepancybetween the hypothesis and the observation.

3. METHODSThe first three methods described here all utilize randomforests for the first part of the estimation step. The excep-tion is the last method, which attempts to estimate the handpose of two strongly interacting hand with the help of PSO.

Real-Time Human Pose Recognition from Depth Image[1] provides a solid basis for many, at that time, future pa-pers to come. They were the first to propose the use of syn-thetic training data, that makes methods which have a train-ing phase a lot easier. The idea is to use Random Forests toclassify the depth image into body parts, resulting in a bodypart label distribution. These are then used to form the finaljoint proposals.

Synthetic Training Data. The idea is as simple as it is pow-erful. To have an accurate classifier, one needs enough vari-ation in the training data to generalize well to all possibleposes and to do so, one can vary real data. These are typi-cally variations in body height, weight or clothing and hair.The advantage of this approach is, that one does not have tomanually label the entire training set, as it suffices to haveone labelled element upon which the variation bases on. Ageneral overview can be seen in Figure 1.

Figure 2: An example of a failed prediction of [1] dueto occlusion.

Training and Prediction. To perform classification with ran-dom forest, the following feature is used.

f(I, x)(u,v) = I(x+u

I(x))− I(x+

v

I(x)) (6)

Where I(x) is the depth value at location of pixel x. The off-sets u and v are normalized to provide 3D translation invari-ance. This function compares two depth values with respectto x. This aims to convey spatial context of x. These featuresare very efficient to compute, but are weak individually, yetwhen used in conjunction with random forest, they providesufficient spatial information. When training the random for-est, the trees randomly sample a set of u, v and τ , boundedwithin an interval, and select the best according to the equa-tion 7

G(u, v, τ) = H(Q)−∑

s∈{l,r}

|Qs(u, v, τ)||Q| H(Qs(u, v, τ)) (7)

where H(Q) denotes the Shannon entropy function and Qare the sets or subsets respectfully. Once the random forest istrained one can acquire the body part distribution. The meanof each distribution is computed with help of the mean shiftalgorithm [10]. Depending on the body part, the 3D jointproposals are set at the mean of each distribution or averaged,that average being then the proposal. However, because themean lies on the surface of the body, it is pushed within it bya learned offset λ.

Accuracy. Accuracy of the random forest for body part la-belling depends on a variety of different parameters. First,increasing the number of training images results in a loga-rithmic increase of label accuracy. This is intuitively clear,as the random forest has more information on how to clas-sify. Allowing the trees of the random forest to have a greatermaximum depth leads to a positive increase in correct la-belling. By having deeper trees, we allow more splits to beperformed, thus the end nodes can be more pure with respectto their labels. However, when using a smaller test set, over-fitting is observed after a certain depth. This effect is coun-teracted by training on a bigger test set. Lastly, by havinga larger interval to choose the offsets u and v of function6 from, we allow the classifier to use more spatial context

Figure 3: Keskins approach. Similarity can be seen to[1]

to perform its splitting decisions. The joint prediction ac-curacy using the predicted body parts suffers slightly whencompared to the accuracy using the ground truth labels. Nev-ertheless, this occurs mainly for smaller body parts, such asthe elbows and the arms. Overall, the body position is pre-dicted fairly accurately. Miss-predictions occur mainly forheavily occluded body parts or for unseen poses, which dif-fer by a lot from the training set, as shown in Figure .

Multi-layered Random ForestsBuilding up on [1] and proposed first by [2], this approachtackles the problem of having a big training set and appliedfor hand pose estimation. It divides the hand part label clas-sification into two layers by first clustering the training databased on similarity, then training a random forest on and foreach of these clusters. To perform prediction, the input istaken and fed into the first layer, which assigns it to the cor-rect cluster. The assigned cluster performs the final hand partlabel classification. The first layer can be seen as a roughclassification, the second a more fine tuned one. Once thehand part distribution is obtained, mean shift can be used toacquire the mean of each distribution, where the hand jointproposal get set, resulting in the hand skeleton. An overviewis shown in Figure 3

Clustering Clustering is performed with the help of thespectral clustering algorithm. This separates the training databased on weighted difference, which can be fine tuned to re-duce the workload on the second cluster, increasing the over-all accuracy of the method. The procedure is based on dis-tance of two skeletal configuration vi,vj and the distance

Dij = |W (vi − vj)| (8)

Where Dij is the diagonal weight matrix. To perform the fi-nal clustering, k-means gets applied on D. These clustersare assigned their own label, after which a random forestis trained using these labels. The same features and qualityfunction gets used as in [2]. This forms the first layer.

Second Layer. The second layer formed by training a ran-dom forest for each cluster, this time using the hand part la-bels, but using the same features and quality function. Eachrandom forest is called expert.

Prediction. Predicting can be performed using one of twomethods. Global Expert Network (GEN) assigns the inputinto the first layer, which outputs the votes for each cluster.This is averaged and the entire input is assigned to the topthree clusters. The outputs get averaged and the final handpart label classification is performed. Local Expert Network(LEN) goes through the first layer, but assigns each pixel tothe cluster it voted for. This results in LEN being able togeneralize better than GEN, however GEN is more robust to

noise due to the averaging step. Then, one can get the meanof each distribution utilizing mean shift algorithm, resultingin the 3D joint proposals, with which we can form the finalhand skeleton.

Accuracy. The accuracy of the first layer is high. More-over, it is very fast due to utilizing random forest, and canbe trained using real images as well, as the clustering stepis a form of unsupervised learning. An accuracy of 84 %on a testing set is reported. The second layer accuracy de-pends on similar parameters as in [1]. Additionally, two newfactors are introduced: The number of clusters K and theweight matrix W . By increasing K, it is ensured that onlysimilar configurations fall into the same cluster. Therefore,it has a positive effect on the accuracy of both layers, reduc-ing the complexity of them. On the other hand, W can bedetermined in such a way that variations which are harderto detect are already clustered in the first layer, reducing theworkload the second layer has. The accuracy difference ofLEN and GEN are negligible, both having high accuracy ofroughly 90%, with GEN being slightly better.

Semi-Supervised Transductive Regression ForestThe approach described in [3] aims to reduce the accuracyerrors which occur when using synthetic training data duringthe training phase, such as in [1, 2], due to realistic-syntheticdiscrepancies. This is performed with help of transductivelearning, which means one can learn from a target domain,in our case a labelled set of images, and apply knowledgetransform onto a unlabelled image set. With this, the algo-rithm learns how to train with both labelled and unlabelledtraining data. The random forest used performs regression.The multi-layered aspect of [2] is combined into one layer, byutilizing different quality functions while growing the tree,and subsequently controlling what kind of classification isperformed. The final output of the regression forest is the3D joint location. One can utilize kinematic refinement onthe output, to enforce bio-mechanical constraints of the hand,thus further increasing the accuracy of the prediction.

Training. Training is performed with both labelled realisticand synthetic training data, as well as with unlabelled real-istic training data. The labelled elements consist of imagepatches, each label being a tuple (a, p, v), with a being theviewpoint, p being the label of the closest joint and v beinga 16x3 vote vector, containing the 3D location of all jointsof that image. Additionally, realistic-synthetic associationsψ are established by comparing their 3D joint location, con-tained in v:

ψ(r, s) =

{1 if r matches s0 else

Where r ∈ Rl, the labelled realistic training data and s ∈ S,the synthetic training data.When trees of the random forests are being grown, they ran-domly choose between two quality functions

Qapv = αQa + (1− α)βQp + (1− α)(1− β)Qv (9)

Qtss = Qωt Qu (10)

Figure 4: A tree in the regression forest of [3]. First,classification is performed based on the viewpoint la-bel, then the joint label, and finally regression is donewith the help of the vote vectors v

Where equation 9 is the classification-regression term, whichcontrols the classification and regression performed in thetree, and equation 10 is the transductive term, performingtransductive learning. Equation 9 consists of three terms:Qa is the viewpoint classification term, measuring the infor-mation gain with respect to the viewpoint label a.Qp is the joint classification term. Similar to Qa it measuresthe information gain with respect to the joint label p.Qv is the regression term. It measures the compactness ofthe vote vector v. This is defined as

Qv =

[1 +|Llc||L|

λ(J(Llc)) +|Llr||L|

λ(J(Llr))

]−1(11)

Where λ(x) = trace(var(x)).Qt represents the transductive term, preserving the cross-domain association ψ:

Qt =|{r, s} ⊂ Ll,c|+ |{r, s} ⊂ Lr,c|

|{r, s} ⊂ L|(12)

∀{r, s} ⊂ L where ψ(r, s) = 1Qu is the unsupervised term, evaluating the appearance sim-ilarities of all realistic patches R within a node:

Qu =

[1 +|Rlc||R|

λ(Rlc) +|Rrc||R|

λ(Rrc)

]−1(13)

The parameters α and β are dynamically set according thepurity of the child nodes of the tree. With help of these andω, which can be set to weigh Qt against Qu, one can choosebased on what the tree classifies on each layer. The chosenmode for the approach is shown in Figure 4

Prediction and Kinematic Joint Refinement. When formingthe prediction, the input is directly fed into the RegressionForest, returning the 3D joint location of the image directly.However, the results lack structural information to recoverpoorly detected joints due to occlusion. To avoid having anexplicit hand model, a kinematic model is created with help

of large hand pose data base K, which is specifically madefor this cause. To create the models, K gets split with re-spect to the viewpoint label A, i.e K = {K1, ...K|A|}. Then,for each viewpoint i in A, a N-Part Gaussian Mixture ModelGi of the dataset Ki gets fit, so that Gi = {µ1

i ,...,µni ,...,µN

i ;σ1i ,...,σn

i ,...,σNi }, where µn

i and σni denote the mean and

diagonal variance of the n-th Gaussian component in Gi ofview i. After obtaining the models, the Kinematic Joint Re-finement step can be applied to compute the final joint loca-tion. To perform this step, the set of votes received by the j-th joint is fitted a 2-part GMM Gj = {µ1

j , σ1j , ρ

1j , µ

2j , σ

2j , ρ

2j},

where µ is the mean, σ the variance and ρ the weight of theGaussian components. If a joint prediction has high confi-dence, it forms a compact cluster of votes, which is shownby a high weighting and low variance of the GMM. On thecontrary, a joint prediction containing distributed votes is asign of low confidence. In mathematical terms, a strong de-tection is a joint having the Euclidean distance between µ1

j

and µ2j below a threshold tq . These high confidence predic-

tions remain as the final position and the joint refinement pro-cess is applied to the low-confidence votes. To perform this,a nearest-neighbour search (NN-search) is done, using onlythe high confidence joint location. The final joint positiongets computed with respect to the weak joint location andthe high confidence joint position found in the NN-search.

Accuracy. This approach has a high reported accuracy. Incombination with kinematic joint refinement, it representsstate-of-the-art accuracy. Testing was performed in manyscenarios, including rapid changing and heavily occludedhand poses, each resulting in accurate prediction.

Estimating the Pose of Two Strongly Interacting HandsThis approach, proposed by [4] aims to solve the interestingproblem of detecting the position and configuration of twostrongly entangled hands. It does this with a model-based ap-proach in mind, utilizing PSO described earlier. It is not suf-ficient to utilize a single hand pose estimator twice for eachhand, as the additional occlusion resulting from the hand in-teraction must be accounted for. Its important to note thatthis approach does not run in real time.

Tracking. Tracking utilizes both depth and RGB image. Fromthe RGB image, a skin map is obtained, with which the depthimage is segmented, obtaining the hand part of the depth im-age. To use particle swarm optimization, a parameter spaceneeds to be defined. Because the hand contains 27 degreesof freedom, a 54-dimensional parameter space, representingall the possible configuration of both hands, is used. Therange of each dimension is linearly bounded, according tobio-mechanical constraints of the hand. Each point in theparameter space represents a configuration of both hands.These are appropriately artificially skinned, so that a skinmap can be obtained for later use in the objective function.This function is essentially a penalty function to be mini-mized, defined as:

E(O, h,C) = P (h) + λkD(O, h,C) (14)

Where λk is a regularisation parameter, O is the observationdelivered by the RGB-D Camera, h is the current hypothesis

held and C is calibration information of the camera, to syn-thesize more accurately the skin map from h.P (h) penalizes invalid articulation hypothesis. Because thelinear constraints on the parameter space are not sufficientenough to avoid such configurations, P (h) is needed.D(O, h,C) penalizes the discrepancies between the O andh. This is performed with help of the skin maps, as well asthe depth images. Essentially, it measures the differences be-tween both, summing and clamping them. Clamping is nec-essary to make the function robust to noise which could dom-inate and produce false high penalties. Additionally, throughclamping, the function results in being smother. When utiliz-ing PSO, function 5 gets adjusted to:

vk+1,i = w(vk,i+c1r1(Pk,i−xk,i)+c2r2(Gk−xk,i)) (15)

It introduces three new weight parameters c1, c2 and w. Asproposed in [8], w is set as

w =2

|2− ψ −√ψ2 − 4ψ|

(16)

where ψ = c1 + c2.

A new instance of PSO is performed by each observation de-livered by the RGB-D camera. Each instance delivers hmin,so that:

hmin = argminhE(O, h,C) (17)

To exploit temporal information, the hypothesis hmin getsstored. When a new instance of PSO starts, the particlesare sampled randomly in and around hmin, boosting perfor-mance and accuracy of method. However, this approach re-sults in bad accuracy when the hands rapidly changes pose.Additionally, it needs to be initialized at the beginning. Thenature of PSO allows for easy parallelization, increasing per-formance. Some example prediction can be seen in Figure5.

Accuracy. Utilizing PSO, this approach has two main pa-rameters to choose from: Number of particles and maximumnumber of iterations. Naturally, increasing either has a pos-itive effect in accuracy. In the first case, we have more par-ticles searching for the optimal position, therefore a higherprobability of finding a sufficient close point in the parame-ter space. In the latter case, we allow the algorithm to searchlonger, again increasing the chances of finding the best or asufficient close enough position. However, increasing bothparameters has a detrimental effect on performance and aflat-off of accuracy can be observed after a certain thresh-old of the parameters is reached. It is important to note herethat unlike the previous methods, this approach does not runin real-time.

Figure 5: Some example results of [4].

4. FUTURE OUTLOOKResearch in the area of hand pose estimation has shiftedits focus to recovering more information than just the handpose. For example, there is a growing interest in recover-ing the hand and skin model, for use in areas like Telepres-ence or Virtual Reality. Conducting is required further re-search in areas of new features, as these heavily influenceaccuracy and robustness of estimation algorithms. Addition-ally semi-supervised approaches or unsupervised methods,not presented here, show a lot of potential in reducing theamount of synthetic training data needed, hence reducing therealistic-synthetic discrepancies, further increasing accuracy.

5. CONCLUSIONWith all the different approaches presented here, tackling theproblem of hand pose estimation. [1] was an essential build-ing block for future methods, and was the first to utilize syn-thetic training data. This solves the problem of body poseestimation and is used in today’s Kinect system. It uses ran-dom forest to assign a body label distribution over the depthimage, and then places the 3D joint proposals based on thedistribution. The next method, [2], tackles hand pose esti-mation. It introduced multi-layered random forests, a tool todivide the problem into sub-problems by clustering the train-ing data and having a random forest trained on the clustersand for each cluster. This approach takes inspiration from[1], by assigning the depth images a hand label distributionand then, using the same approach, form the 3D joint propos-als of the hand. [3] implements random regression forests,and combines the multi-layer aspect of [2] into one layerthrough varied use of different information gain function.The output of the regression forest directly form the 3D jointproposal. To further enhance the accuracy and robustnessto occlusion, kinematic refinement is employed. This en-

forces somewhat bio-mechanical constraints which normallydiscriminative approaches lack. Lastly, [4], a model-basedapproach tries to solve the problem of pose estimation of twohands, which could be strongly interacting. It uses PSO toseek for a minimum of the objective function defined overthe 54-dimensional parameter space. This objective functionpenalizes the discrepancies between the observation and thecurrently held model of the hand, the hypothesis, and invalidhand configurations, such as two fingers occupying the samephysical space. However, this approach does not run in realtime.

REFERENCES1. J. Shotton, A. Fitzgibbon, M. Cook, T. Sharp, M. Finoc-

chio, R. Moore, A. Kipman and A. Blake. Real-TimeHuman Pose Recognition in Parts from Single Depth Im-ages. In: CVPR, 2011.

2. C. Keskin, F. Kirac, Y. E. Kara, and L. Akarun. Handpose estimation and hand shape classification usingmulti-layered randomized decision forests. In ECCV,2012.

3. D. Tang, T. Yu, T. Kim. Real-time Articulated Hand PoseEstimation using Semi-supervised Transductive Regres-sion Forests. In ICCV, 2013.

4. I. Oikonomidis, N. Kyriazis, A.A. Argyros. Tracking theArticulated Motion of Two Strongly Interacting Hands.In CVPR, 2012.

5. L. Breiman. Random Forests. 1999.

6. A. Erol, G. Bebis, M. Nicolescu, R. D. Boyle, X.Twombly. Vision-based hand pose estimation: A review.2005

7. S. S. Rautaray, A. Agrawal. Vision based hand gesturerecognition for human computer interaction: a survey.2012. 11

8. M. Clerc and J. Kennedy. The Particle Swarm - Explo-sion, Stability, and Convergence in a MultidimensionalComplex Space. Transactions on Evolutionary Compu-tation, 6(1):58? 73, 2002

9. J. Gall, A. Yao, N. Razavi, L. Van Gool, and V. Lem-pitsky. Hough forests for object detection, tracking, andaction recognition. PAMI, 2011.

10. D. Comaniciu and P. Meer. Mean shift: A robustapproach toward feature space analysis. IEEE Trans.PAMI, 24(5), 2002.