《机器学习 Machine Learning》课程教学资源（书籍文献）Real-Time Human Pose Recognition in Parts from Single Depth Images

Real-Time Human Pose Recognition in Parts from Single Depth Images Jamie Shotton Andrew Fitzgibbon Mat Cook Toby Sharp Mark Finocchio Richard Moore Alex Kipman Andrew Blake Microsoft Research Cambridge Xbox Incubation Abstract We propose a new method to quickly and accurately pre- dict 3D positions of body joints from a single depth image, using no temporal information.We take an object recog- nition approach,designing an intermediate body parts rep- ont resentation that maps the difficult pose estimation problem into a simpler per-pixel classification problem.Our large and highly varied training dataset allows the classifier to estimate body parts invariant to pose,body shape,clothing, etc.Finally we generate confidence-scored 3D proposals of several body joints by reprojecting the classification result front and finding local modes. The system runs at 200 frames per second on consumer depth image body parts ◆ 3D joint proposals hardware.Our evaluation shows high accuracy on both Figure 1.Overview.From an single input depth image,a per-pixel synthetic and real test sets,and investigates the effect of sev- body part distribution is inferred.(Colors indicate the most likely eral training parameters.We achieve state of the art accu- part labels at each pixel,and correspond in the joint proposals). racy in our comparison with related work and demonstrate Local modes of this signal are estimated to give high-quality pro- improved generalization over exact whole-skeleton nearest posals for the 3D locations of body joints,even for multiple users. neighbor matching. joints of interest.Reprojecting the inferred parts into world 1.Introduction space,we localize spatial modes of each part distribution Robust interactive human body tracking has applica- and thus generate (possibly several)confidence-weighted tions including gaming,human-computer interaction,secu- proposals for the 3D locations of each skeletal joint. rity,telepresence,and even health-care.The task has re- We treat the segmentation into body parts as a per-pixel cently been greatly simplified by the introduction of real- classification task(no pairwise terms or CRF have proved time depth cameras [16,19,44,37,28,13].However,even necessary).Evaluating each pixel separately avoids a com- the best existing systems still exhibit limitations.In partic- binatorial search over the different body joints,although ular,until the launch of Kinect [21],none ran at interactive within a single part there are of course still dramatic dif- rates on consumer hardware while handling a full range of ferences in the contextual appearance.For training data, human body shapes and sizes undergoing general body mo- we generate realistic synthetic depth images of humans of tions.Some systems achieve high speeds by tracking from many shapes and sizes in highly varied poses sampled from frame to frame but struggle to re-initialize quickly and so a large motion capture database.We train a deep ran- are not robust.In this paper,we focus on pose recognition domized decision forest classifier which avoids overfitting in parts:detecting from a single depth image a small set of by using hundreds of thousands of training images.Sim- 3D position candidates for each skeletal joint.Our focus on ple,discriminative depth comparison image features yield per-frame initialization and recovery is designed to comple- 3D translation invariance while maintaining high computa- ment any appropriate tracking algorithm [7,39,16,42,13] tional efficiency.For further speed,the classifier can be run that might further incorporate temporal and kinematic co- in parallel on each pixel on a GPU [34].Finally,spatial herence.The algorithm presented here forms a core com- modes of the inferred per-pixel distributions are computed ponent of the Kinect gaming platform [21]. using mean shift [10]resulting in the 3D joint proposals. Illustrated in Fig.1 and inspired by recent object recog- An optimized implementation of our algorithm runs in nition work that divides objects into parts (e.g.[12,43]), under 5ms per frame (200 frames per second)on the Xbox our approach is driven by two key design goals:computa- 360 GPU,at least one order of magnitude faster than exist- tional efficiency and robustness.A single input depth image ing approaches.It works frame-by-frame across dramati- is segmented into a dense probabilistic body part labeling, cally differing body shapes and sizes,and the learned dis- with the parts defined to be spatially localized near skeletal criminative approach naturally handles self-occlusions and

Real-Time Human Pose Recognition in Parts from Single Depth Images Jamie Shotton Andrew Fitzgibbon Mat Cook Toby Sharp Mark Finocchio Richard Moore Alex Kipman Andrew Blake Microsoft Research Cambridge & Xbox Incubation Abstract We propose a new method to quickly and accurately pre￾dict 3D positions of body joints from a single depth image, using no temporal information. We take an object recog￾nition approach, designing an intermediate body parts rep￾resentation that maps the difficult pose estimation problem into a simpler per-pixel classification problem. Our large and highly varied training dataset allows the classifier to estimate body parts invariant to pose, body shape, clothing, etc. Finally we generate confidence-scored 3D proposals of several body joints by reprojecting the classification result and finding local modes. The system runs at 200 frames per second on consumer hardware. Our evaluation shows high accuracy on both synthetic and real test sets, and investigates the effect of sev￾eral training parameters. We achieve state of the art accu￾racy in our comparison with related work and demonstrate improved generalization over exact whole-skeleton nearest neighbor matching. 1. Introduction Robust interactive human body tracking has applica￾tions including gaming, human-computer interaction, secu￾rity, telepresence, and even health-care. The task has re￾cently been greatly simplified by the introduction of real￾time depth cameras [16, 19, 44, 37, 28, 13]. However, even the best existing systems still exhibit limitations. In partic￾ular, until the launch of Kinect [21], none ran at interactive rates on consumer hardware while handling a full range of human body shapes and sizes undergoing general body mo￾tions. Some systems achieve high speeds by tracking from frame to frame but struggle to re-initialize quickly and so are not robust. In this paper, we focus on pose recognition in parts: detecting from a single depth image a small set of 3D position candidates for each skeletal joint. Our focus on per-frame initialization and recovery is designed to comple￾ment any appropriate tracking algorithm [7, 39, 16, 42, 13] that might further incorporate temporal and kinematic co￾herence. The algorithm presented here forms a core com￾ponent of the Kinect gaming platform [21]. Illustrated in Fig. 1 and inspired by recent object recog￾nition work that divides objects into parts (e.g. [12, 43]), our approach is driven by two key design goals: computa￾tional efficiency and robustness. A single input depth image is segmented into a dense probabilistic body part labeling, with the parts defined to be spatially localized near skeletal CVPR Teaser seq 1: frame 15 seq 2: frame 236 seq 5: take 1, 72 depth image body parts 3D joint proposals Figure 1. Overview. From an single input depth image, a per-pixel body part distribution is inferred. (Colors indicate the most likely part labels at each pixel, and correspond in the joint proposals). Local modes of this signal are estimated to give high-quality pro￾posals for the 3D locations of body joints, even for multiple users. joints of interest. Reprojecting the inferred parts into world space, we localize spatial modes of each part distribution and thus generate (possibly several) confidence-weighted proposals for the 3D locations of each skeletal joint. We treat the segmentation into body parts as a per-pixel classification task (no pairwise terms or CRF have proved necessary). Evaluating each pixel separately avoids a com￾binatorial search over the different body joints, although within a single part there are of course still dramatic dif￾ferences in the contextual appearance. For training data, we generate realistic synthetic depth images of humans of many shapes and sizes in highly varied poses sampled from a large motion capture database. We train a deep ran￾domized decision forest classifier which avoids overfitting by using hundreds of thousands of training images. Sim￾ple, discriminative depth comparison image features yield 3D translation invariance while maintaining high computa￾tional efficiency. For further speed, the classifier can be run in parallel on each pixel on a GPU [34]. Finally, spatial modes of the inferred per-pixel distributions are computed using mean shift [10] resulting in the 3D joint proposals. An optimized implementation of our algorithm runs in under 5ms per frame (200 frames per second) on the Xbox 360 GPU, at least one order of magnitude faster than exist￾ing approaches. It works frame-by-frame across dramati￾cally differing body shapes and sizes, and the learned dis￾criminative approach naturally handles self-occlusions and 1

poses cropped by the image frame.We evaluate on both real matched by parameter sensitive hashing.Agarwal Triggs and synthetic depth images,containing challenging poses of [1]learn a regression from kernelized image silhouettes fea- a varied set of subjects.Even without exploiting temporal tures to pose.Sigal et al.[39]use eigen-appearance tem- or kinematic constraints,the 3D joint proposals are both ac- plate detectors for head,upper arms and lower legs pro- curate and stable.We investigate the effect of several train- posals.Felzenszwalb Huttenlocher [11]apply pictorial ing parameters and show how very deep trees can still avoid structures to estimate pose efficiently.Navaratnam et al. overfitting due to the large training set.We demonstrate [25]use the marginal statistics of unlabeled data to im- that our part proposals generalize at least as well as exact prove pose estimation.Urtasun Darrel [41]proposed a nearest-neighbor in both an idealized and realistic setting, local mixture of Gaussian Processes to regress human pose. and show a substantial improvement over the state of the Auto-context was used in [40]to obtain a coarse body part art.Further,results on silhouette images suggest more gen- labeling but this was not defined to localize joints and clas- eral applicability of our approach. sifying each frame took about 40 seconds.Rogez et al.[32] Our main contribution is to treat pose estimation as ob- train randomized decision forests on a hierarchy of classes ject recognition using a novel intermediate body parts rep- defined on a torus of cyclic human motion patterns and cam- resentation designed to spatially localize joints of interest era angles.Wang Popovic [42]track a hand clothed in a at low computational cost and high accuracy.Our experi- colored glove.Our system could be seen as automatically ments also carry several insights:(i)synthetic depth train- inferring the colors of an virtual colored suit from a depth ing data is an excellent proxy for real data;(ii)scaling up image.Bourdev Malik [6]present 'poselets'that form the learning problem with varied synthetic data is important tight clusters in both 3D pose and 2D image appearance. for high accuracy;and(iii)our parts-based approach gener- detectable using SVMs. alizes better than even an oracular exact nearest neighbor. 2.Data Related Work.Human pose estimation has generated a vast literature(surveyed in [22.29)).The recent availability Pose estimation research has often focused on techniques of depth cameras has spurred further progress [16,19.28]. to overcome lack of training data [25],because of two prob- Grest et al.[16]use Iterated Closest Point to track a skele- lems.First,generating realistic intensity images using com- ton of a known size and starting position.Anguelov et al. puter graphics techniques [33,27,26]is hampered by the [3]segment puppets in 3D range scan data into head,limbs, huge color and texture variability induced by clothing,hair, torso,and background using spin images and a MRF.In and skin,often meaning that the data are reduced to 2D sil- [44.Zhu Fujimura build heuristic detectors for coarse houettes [1].Although depth cameras significantly reduce upper body parts(head,torso,arms)using a linear program- this difficulty,considerable variation in body and clothing ming relaxation,but require a T-pose initialization to size shape remains.The second limitation is that synthetic body the model.Siddiqui Medioni [37]hand craft head,hand, pose images are of necessity fed by motion-capture(mocap) and forearm detectors,and show data-driven MCMC model data.Although techniques exist to simulate human motion fitting outperforms ICP.Kalogerakis et al.[18]classify and (e.g.[38])they do not yet produce the range of volitional segment vertices in a full closed 3D mesh into different motions of a human subject. parts,but do not deal with occlusions and are sensitive to In this section we review depth imaging and show how mesh topology.Most similar to our approach,Plagemann we use real mocap data,retargetted to a variety of base char- et al.[28]build a 3D mesh to find geodesic extrema inter- acter models,to synthesize a large,varied dataset.We be- est points which are classified into 3 parts:head,hand,and lieve this dataset to considerably advance the state of the art foot.Their method provides both a location and orientation in both scale and variety,and demonstrate the importance estimate of these parts,but does not distinguish left from of such a large dataset in our evaluation. right and the use of interest points limits the choice of parts. 2.1.Depth imaging Advances have also been made using conventional in- Depth imaging technology has advanced dramatically tensity cameras,though typically at much higher computa- over the last few years,finally reaching a consumer price tional cost.Bregler Malik [7]track humans using twists point with the launch of Kinect[21].Pixels in a depth image and exponential maps from a known initial pose.Ioffe indicate calibrated depth in the scene,rather than a measure Forsyth [17]group parallel edges as candidate body seg- of intensity or color.We employ the Kinect camera which ments and prune combinations of segments using a pro- gives a 640x480 image at 30 frames per second with depth jected classifier.Mori Malik [24]use the shape con- resolution of a few centimeters. text descriptor to match exemplars.Ramanan Forsyth Depth cameras offer several advantages over traditional [31]find candidate body segments as pairs of parallel lines, intensity sensors,working in low light levels,giving a cali- clustering appearances across frames.Shakhnarovich et al. brated scale estimate,being color and texture invariant,and [33]estimate upper body pose,interpolating k-NN poses resolving silhouette ambiguities in pose.They also greatly

poses cropped by the image frame. We evaluate on both real and synthetic depth images, containing challenging poses of a varied set of subjects. Even without exploiting temporal or kinematic constraints, the 3D joint proposals are both ac￾curate and stable. We investigate the effect of several train￾ing parameters and show how very deep trees can still avoid overfitting due to the large training set. We demonstrate that our part proposals generalize at least as well as exact nearest-neighbor in both an idealized and realistic setting, and show a substantial improvement over the state of the art. Further, results on silhouette images suggest more gen￾eral applicability of our approach. Our main contribution is to treat pose estimation as ob￾ject recognition using a novel intermediate body parts rep￾resentation designed to spatially localize joints of interest at low computational cost and high accuracy. Our experi￾ments also carry several insights: (i) synthetic depth train￾ing data is an excellent proxy for real data; (ii) scaling up the learning problem with varied synthetic data is important for high accuracy; and (iii) our parts-based approach gener￾alizes better than even an oracular exact nearest neighbor. Related Work. Human pose estimation has generated a vast literature (surveyed in [22, 29]). The recent availability of depth cameras has spurred further progress [16, 19, 28]. Grest et al. [16] use Iterated Closest Point to track a skele￾ton of a known size and starting position. Anguelov et al. [3] segment puppets in 3D range scan data into head, limbs, torso, and background using spin images and a MRF. In [44], Zhu & Fujimura build heuristic detectors for coarse upper body parts (head, torso, arms) using a linear program￾ming relaxation, but require a T-pose initialization to size the model. Siddiqui & Medioni [37] hand craft head, hand, and forearm detectors, and show data-driven MCMC model fitting outperforms ICP. Kalogerakis et al. [18] classify and segment vertices in a full closed 3D mesh into different parts, but do not deal with occlusions and are sensitive to mesh topology. Most similar to our approach, Plagemann et al. [28] build a 3D mesh to find geodesic extrema inter￾est points which are classified into 3 parts: head, hand, and foot. Their method provides both a location and orientation estimate of these parts, but does not distinguish left from right and the use of interest points limits the choice of parts. Advances have also been made using conventional in￾tensity cameras, though typically at much higher computa￾tional cost. Bregler & Malik [7] track humans using twists and exponential maps from a known initial pose. Ioffe & Forsyth [17] group parallel edges as candidate body seg￾ments and prune combinations of segments using a pro￾jected classifier. Mori & Malik [24] use the shape con￾text descriptor to match exemplars. Ramanan & Forsyth [31] find candidate body segments as pairs of parallel lines, clustering appearances across frames. Shakhnarovich et al. [33] estimate upper body pose, interpolating k-NN poses matched by parameter sensitive hashing. Agarwal & Triggs [1] learn a regression from kernelized image silhouettes fea￾tures to pose. Sigal et al. [39] use eigen-appearance tem￾plate detectors for head, upper arms and lower legs pro￾posals. Felzenszwalb & Huttenlocher [11] apply pictorial structures to estimate pose efficiently. Navaratnam et al. [25] use the marginal statistics of unlabeled data to im￾prove pose estimation. Urtasun & Darrel [41] proposed a local mixture of Gaussian Processes to regress human pose. Auto-context was used in [40] to obtain a coarse body part labeling but this was not defined to localize joints and clas￾sifying each frame took about 40 seconds. Rogez et al. [32] train randomized decision forests on a hierarchy of classes defined on a torus of cyclic human motion patterns and cam￾era angles. Wang & Popovic [ ´ 42] track a hand clothed in a colored glove. Our system could be seen as automatically inferring the colors of an virtual colored suit from a depth image. Bourdev & Malik [6] present ‘poselets’ that form tight clusters in both 3D pose and 2D image appearance, detectable using SVMs. 2. Data Pose estimation research has often focused on techniques to overcome lack of training data [25], because of two prob￾lems. First, generating realistic intensity images using com￾puter graphics techniques [33, 27, 26] is hampered by the huge color and texture variability induced by clothing, hair, and skin, often meaning that the data are reduced to 2D sil￾houettes [1]. Although depth cameras significantly reduce this difficulty, considerable variation in body and clothing shape remains. The second limitation is that synthetic body pose images are of necessity fed by motion-capture (mocap) data. Although techniques exist to simulate human motion (e.g. [38]) they do not yet produce the range of volitional motions of a human subject. In this section we review depth imaging and show how we use real mocap data, retargetted to a variety of base char￾acter models, to synthesize a large, varied dataset. We be￾lieve this dataset to considerably advance the state of the art in both scale and variety, and demonstrate the importance of such a large dataset in our evaluation. 2.1. Depth imaging Depth imaging technology has advanced dramatically over the last few years, finally reaching a consumer price point with the launch of Kinect [21]. Pixels in a depth image indicate calibrated depth in the scene, rather than a measure of intensity or color. We employ the Kinect camera which gives a 640x480 image at 30 frames per second with depth resolution of a few centimeters. Depth cameras offer several advantages over traditional intensity sensors, working in low light levels, giving a cali￾brated scale estimate, being color and texture invariant, and resolving silhouette ambiguities in pose. They also greatly

鲁游大冷棉 Figure 2.Synthetic and real data.Pairs of depth image and ground truth body parts.Note wide variety in pose,shape,clothing.and crop. simplify the task of background subtraction which we as- the appearance variations we hope to recognize at test time. sume in this work.But most importantly for our approach, While depth/scale and translation variations are handled ex- it is straightforward to synthesize realistic depth images of plicitly in our features(see below).other invariances cannot people and thus build a large training dataset cheaply. be encoded efficiently.Instead we learn invariance from the 2.2.Motion capture data data to camera pose,body pose,and body size and shape. The synthesis pipeline first randomly samples a set of The human body is capable of an enormous range of parameters,and then uses standard computer graphics tech- poses which are difficult to simulate.Instead,we capture a niques to render depth and(see below)body part images large database of motion capture(mocap)of human actions. from texture mapped 3D meshes.The mocap is retarget- Our aim was to span the wide variety of poses people would ting to each of 15 base meshes spanning the range of body make in an entertainment scenario.The database consists of shapes and sizes,using [4].Further slight random vari- approximately 500k frames in a few hundred sequences of ation in height and weight give extra coverage of body driving,dancing,kicking,running,navigating menus,etc. shapes.Other randomized parameters include the mocap We expect our semi-local body part classifier to gener- frame,camera pose,camera noise,clothing and hairstyle. alize somewhat to unseen poses.In particular,we need not We provide more details of these variations in the supple- record all possible combinations of the different limbs;in mentary material.Fig.2 compares the varied output of the practice,a wide range of poses proves sufficient.Further, pipeline to hand-labeled real camera images. we need not record mocap with variation in rotation about the vertical axis,mirroring left-right,scene position,body 3.Body Part Inference and Joint Proposals shape and size,or camera pose,all of which can be added In this section we describe our intermediate body parts in (semi-)automatically. representation,detail the discriminative depth image fea- Since the classifier uses no temporal information,we tures,review decision forests and their application to body are interested only in static poses and not motion.Often, part recognition,and finally discuss how a mode finding al- changes in pose from one mocap frame to the next are so gorithm is used to generate joint position proposals. small as to be insignificant.We thus discard many similar, redundant poses from the initial mocap data using 'furthest 3.1.Body part labeling neighbor'clustering [15]where the distance between poses A key contribution of this work is our intermediate body pi and p2 is defined as maxjpp2,the maximum Eu- part representation.We define several localized body part clidean distance over body joints j.We use a subset of 100k labels that densely cover the body,as color-coded in Fig.2. poses such that no two poses are closer than 5cm. Some of these parts are defined to directly localize partic- We have found it necessary to iterate the process of mo- ular skeletal joints of interest,while others fill the gaps or tion capture,sampling from our model,training the classi- could be used in combination to predict other joints.Our in- fier,and testing joint prediction accuracy in order to refine termediate representation transforms the problem into one the mocap database with regions of pose space that had been that can readily be solved by efficient classification algo- previously missed out.Our early experiments employed rithms;we show in Sec.4.3 that the penalty paid for this the CMU mocap database [9]which gave acceptable results transformation is small. though covered far less of pose space. The parts are specified in a texture map that is retargetted to skin the various characters during rendering.The pairs of 2.3.Generating synthetic data depth and body part images are used as fully labeled data for We build a randomized rendering pipeline from which learning the classifier(see below).For the experiments in we can sample fully labeled training images.Our goals in this paper,we use 31 body parts:LU/RU/LW/RW head,neck, building this pipeline were twofold:realism and variety.For L/R shoulder,LU/RU/LW/RW arm,L/R elbow,L/R wrist,L/R the learned model to work well,the samples must closely hand,LU/RU/LW/RW torso,LU/RU/LW/RW leg,L/R knee, resemble real camera images,and contain good coverage of L/R ankle,L/R foot (Left,Right,Upper,lower).Distinct

Training & Test Data synthetic (train & test) real (test) synthetic (train & test) real (test) Figure 2. Synthetic and real data. Pairs of depth image and ground truth body parts. Note wide variety in pose, shape, clothing, and crop. simplify the task of background subtraction which we as￾sume in this work. But most importantly for our approach, it is straightforward to synthesize realistic depth images of people and thus build a large training dataset cheaply. 2.2. Motion capture data The human body is capable of an enormous range of poses which are difficult to simulate. Instead, we capture a large database of motion capture (mocap) of human actions. Our aim was to span the wide variety of poses people would make in an entertainment scenario. The database consists of approximately 500k frames in a few hundred sequences of driving, dancing, kicking, running, navigating menus, etc. We expect our semi-local body part classifier to gener￾alize somewhat to unseen poses. In particular, we need not record all possible combinations of the different limbs; in practice, a wide range of poses proves sufficient. Further, we need not record mocap with variation in rotation about the vertical axis, mirroring left-right, scene position, body shape and size, or camera pose, all of which can be added in (semi-)automatically. Since the classifier uses no temporal information, we are interested only in static poses and not motion. Often, changes in pose from one mocap frame to the next are so small as to be insignificant. We thus discard many similar, redundant poses from the initial mocap data using ‘furthest neighbor’ clustering [15] where the distance between poses p1 and p2 is defined as maxj kp j 1 −p j 2 k2, the maximum Eu￾clidean distance over body joints j. We use a subset of 100k poses such that no two poses are closer than 5cm. We have found it necessary to iterate the process of mo￾tion capture, sampling from our model, training the classi- fier, and testing joint prediction accuracy in order to refine the mocap database with regions of pose space that had been previously missed out. Our early experiments employed the CMU mocap database [9] which gave acceptable results though covered far less of pose space. 2.3. Generating synthetic data We build a randomized rendering pipeline from which we can sample fully labeled training images. Our goals in building this pipeline were twofold: realism and variety. For the learned model to work well, the samples must closely resemble real camera images, and contain good coverage of the appearance variations we hope to recognize at test time. While depth/scale and translation variations are handled ex￾plicitly in our features (see below), other invariances cannot be encoded efficiently. Instead we learn invariance from the data to camera pose, body pose, and body size and shape. The synthesis pipeline first randomly samples a set of parameters, and then uses standard computer graphics tech￾niques to render depth and (see below) body part images from texture mapped 3D meshes. The mocap is retarget￾ting to each of 15 base meshes spanning the range of body shapes and sizes, using [4]. Further slight random vari￾ation in height and weight give extra coverage of body shapes. Other randomized parameters include the mocap frame, camera pose, camera noise, clothing and hairstyle. We provide more details of these variations in the supple￾mentary material. Fig. 2 compares the varied output of the pipeline to hand-labeled real camera images. 3. Body Part Inference and Joint Proposals In this section we describe our intermediate body parts representation, detail the discriminative depth image fea￾tures, review decision forests and their application to body part recognition, and finally discuss how a mode finding al￾gorithm is used to generate joint position proposals. 3.1. Body part labeling A key contribution of this work is our intermediate body part representation. We define several localized body part labels that densely cover the body, as color-coded in Fig. 2. Some of these parts are defined to directly localize partic￾ular skeletal joints of interest, while others fill the gaps or could be used in combination to predict other joints. Our in￾termediate representation transforms the problem into one that can readily be solved by efficient classification algo￾rithms; we show in Sec. 4.3 that the penalty paid for this transformation is small. The parts are specified in a texture map that is retargetted to skin the various characters during rendering. The pairs of depth and body part images are used as fully labeled data for learning the classifier (see below). For the experiments in this paper, we use 31 body parts: LU/RU/LW/RW head, neck, L/R shoulder, LU/RU/LW/RW arm, L/R elbow, L/R wrist, L/R hand, LU/RU/LW/RW torso, LU/RU/LW/RW leg, L/R knee, L/R ankle, L/R foot (Left, Right, Upper, loWer). Distinct

(1,3 (1,x) tree 1 tree 2 P(C Figure 3.Depth image features.The yellow crosses indicates the Figure 4.Randomized Decision Forests.A forest is an ensemble pixel x being classified.The red circles indicate the offset pixels of trees.Each tree consists of split nodes (blue)and leaf nodes as defined in Eq.1.In (a),the two example features give a large (green).The red arrows indicate the different paths that might be depth difference response.In (b),the same two features at new taken by different trees for a particular input. image locations give a much smaller response. 3.3.Randomized decision forests parts for left and right allow the classifier to disambiguate Randomized decision trees and forests [35,30.2.8]have the left and right sides of the body. proven fast and effective multi-class classifiers for many Of course,the precise definition of these parts could be tasks [20,23,36],and can be implemented efficiently on the changed to suit a particular application.For example,in an GPU [34].As illustrated in Fig.4,a forest is an ensemble upper body tracking scenario,all the lower body parts could of T decision trees,each consisting of split and leaf nodes. be merged.Parts should be sufficiently small to accurately Each split node consists of a feature fe and a threshold T. localize body joints,but not too numerous as to waste ca- To classify pixel x in image I.one starts at the root and re- pacity of the classifier. peatedly evaluates Eq.1,branching left or right according 3.2.Depth image features to the comparison to threshold T.At the leaf node reached We employ simple depth comparison features,inspired in tree t,a learned distribution P(cI,x)over body part la- by those in [20].At a given pixel x,the features compute bels c is stored.The distributions are averaged together for all trees in the forest to give the final classification u=(+)-d(+) (1 T P(cl,x)= 1>P(dI,x)· (2) where d(x)is the depth at pixel x in image 1,and parame- t=1 ters =(u.v)describe offsets u and v.The normalization Training.Each tree is trained on a different set of randomly of the offsets by ensures the features are depth invari- synthesized images.A random subset of 2000 example pix- ant:at a given point on the body,a fixed world space offset els from each image is chosen to ensure a roughly even dis- will result whether the pixel is close or far from the camera. tribution across body parts.Each tree is trained using the The features are thus 3D translation invariant(modulo per- following algorithm [20]: spective effects).If an offset pixel lies on the background 1.Randomly propose a set of splitting candidates= or outside the bounds of the image,the depth probe d(x') (0,T)(feature parameters 0 and thresholds T). is given a large positive constant value. Fig.3 illustrates two features at different pixel locations 2.Partition the set of examples Q={(I,x)}into left x.Feature fe,looks upwards:Eq.1 will give a large pos- and right subsets by each o: itive response for pixels x near the top of the body,but a Q(o)={(I,x)1f(I,x)<T} (3) value close to zero for pixels x lower down the body.Fea- Q.(o)=Q\Q(⊙) (4) ture fo may instead help find thin vertical structures such as the arm. 3.Compute the o giving the largest gain in information: Individually these features provide only a weak signal about which part of the body the pixel belongs to,but in =argmax G(o) (5) combination in a decision forest they are sufficient to accu- rately disambiguate all trained parts.The design of these G(o) =H(Q)- 1Q.(o刨H(Q.()(6 features was strongly motivated by their computational effi- sEfL,r 121 ciency:no preprocessing is needed;each feature need only read at most 3 image pixels and perform at most 5 arithmetic where Shannon entropy H(Q)is computed on the nor- operations;and the features can be straightforwardly imple- malized histogram of body part labels l(x)for all mented on the GPU.Given a larger computational budget, (I,x)∈Q one could employ potentially more powerful features based 4.If the largest gain G(*)is sufficient,and the depth in on,for example,depth integrals over regions,curvature,or the tree is below a maximum,then recurse for left and local descriptors e.g.[5]. right subsets (*and ()

(a) body parts Image Features (b) 𝜃2 𝜃1 𝜃2 𝜃2 𝜃1 𝜃2 Figure 3. Depth image features. The yellow crosses indicates the pixel x being classified. The red circles indicate the offset pixels as defined in Eq. 1. In (a), the two example features give a large depth difference response. In (b), the same two features at new image locations give a much smaller response. parts for left and right allow the classifier to disambiguate the left and right sides of the body. Of course, the precise definition of these parts could be changed to suit a particular application. For example, in an upper body tracking scenario, all the lower body parts could be merged. Parts should be sufficiently small to accurately localize body joints, but not too numerous as to waste ca￾pacity of the classifier. 3.2. Depth image features We employ simple depth comparison features, inspired by those in [20]. At a given pixel x, the features compute fθ(I, x) = dI  x + u dI (x)  − dI  x + v dI (x)  , (1) where dI (x) is the depth at pixel x in image I, and parame￾ters θ = (u, v) describe offsets u and v. The normalization of the offsets by 1 dI (x) ensures the features are depth invari￾ant: at a given point on the body, a fixed world space offset will result whether the pixel is close or far from the camera. The features are thus 3D translation invariant (modulo per￾spective effects). If an offset pixel lies on the background or outside the bounds of the image, the depth probe dI (x 0 ) is given a large positive constant value. Fig. 3 illustrates two features at different pixel locations x. Feature fθ1 looks upwards: Eq. 1 will give a large pos￾itive response for pixels x near the top of the body, but a value close to zero for pixels x lower down the body. Fea￾ture fθ2 may instead help find thin vertical structures such as the arm. Individually these features provide only a weak signal about which part of the body the pixel belongs to, but in combination in a decision forest they are sufficient to accu￾rately disambiguate all trained parts. The design of these features was strongly motivated by their computational effi- ciency: no preprocessing is needed; each feature need only read at most 3 image pixels and perform at most 5 arithmetic operations; and the features can be straightforwardly imple￾mented on the GPU. Given a larger computational budget, one could employ potentially more powerful features based on, for example, depth integrals over regions, curvature, or local descriptors e.g. [5]. Random Forests … tree 1 tree 𝑇 (𝐼, x) (𝐼, x) 𝑃𝑇(𝑐) 𝑃1(𝑐) Figure 4. Randomized Decision Forests. A forest is an ensemble of trees. Each tree consists of split nodes (blue) and leaf nodes (green). The red arrows indicate the different paths that might be taken by different trees for a particular input. 3.3. Randomized decision forests Randomized decision trees and forests [35, 30, 2, 8] have proven fast and effective multi-class classifiers for many tasks [20, 23, 36], and can be implemented efficiently on the GPU [34]. As illustrated in Fig. 4, a forest is an ensemble of T decision trees, each consisting of split and leaf nodes. Each split node consists of a feature fθ and a threshold τ . To classify pixel x in image I, one starts at the root and re￾peatedly evaluates Eq. 1, branching left or right according to the comparison to threshold τ . At the leaf node reached in tree t, a learned distribution Pt(c|I, x) over body part la￾bels c is stored. The distributions are averaged together for all trees in the forest to give the final classification P(c|I, x) = 1 T X T t=1 Pt(c|I, x) . (2) Training. Each tree is trained on a different set of randomly synthesized images. A random subset of 2000 example pix￾els from each image is chosen to ensure a roughly even dis￾tribution across body parts. Each tree is trained using the following algorithm [20]: 1. Randomly propose a set of splitting candidates φ = (θ, τ ) (feature parameters θ and thresholds τ ). 2. Partition the set of examples Q = {(I, x)} into left and right subsets by each φ: Ql(φ) = { (I, x) | fθ(I, x) < τ } (3) Qr(φ) = Q \ Ql(φ) (4) 3. Compute the φ giving the largest gain in information: φ ? = argmax φ G(φ) (5) G(φ) = H(Q) − X s∈{l,r} |Qs(φ)| |Q| H(Qs(φ)) (6) where Shannon entropy H(Q) is computed on the nor￾malized histogram of body part labels lI (x) for all (I, x) ∈ Q. 4. If the largest gain G(φ ? ) is sufficient, and the depth in the tree is below a maximum, then recurse for left and right subsets Ql(φ ? ) and Qr(φ ? )

Figure 5.Example inferences.Synthetic(top row);real (middle):failure modes(bottom).Left column:ground truth for a neutral pose as a reference.In each example we see the depth image,the inferred most likely body part labels,and the joint proposals show as front,right, and top views (overlaid on a depth point cloud).Only the most confident proposal for each joint above a fixed,shared threshold is shown. To keep the training times down we employ a distributed The detected modes lie on the surface of the body.Each implementation.Training 3 trees to depth 20 from 1 million mode is therefore pushed back into the scene by a learned images takes about a day on a 1000 core cluster. z offset Ce to produce a final joint position proposal.This 3.4.Joint position proposals simple,efficient approach works well in practice.The band- Body part recognition as described above infers per-pixel widths be,probability threshold Ac,and surface-to-interior z offset C are optimized per-part on a hold-out validation information.This information must now be pooled across pixels to generate reliable proposals for the positions of 3D set of 5000 images by grid search.(As an indication,this resulted in mean bandwidth 0.065m,probability threshold skeletal joints.These proposals are the final output of our 0.14.and z offset 0.039m). algorithm,and could be used by a tracking algorithm to self- initialize and recover from failure. 4.Experiments A simple option is to accumulate the global 3D centers In this section we describe the experiments performed to of probability mass for each part,using the known cali- evaluate our method.We show both qualitative and quan- brated depth.However,outlying pixels severely degrade titative results on several challenging datasets,and com- the quality of such a global estimate.Instead we employ a pare with both nearest-neighbor approaches and the state local mode-finding approach based on mean shift [10]with of the art [13].We provide further results in the supple- a weighted Gaussian kernel. mentary material.Unless otherwise specified,parameters We define a density estimator per body part as below were set as:3 trees,20 deep,300k training images per tree,2000 training example pixels per image,2000 can- fe()>Wic exp didate features 0,and 50 candidate thresholdsr per feature Test data.We use challenging synthetic and real depth im- where x is a coordinate in 3D world space.N is the number ages to evaluate our approach.For our synthetic test set, of image pixels,wic is a pixel weighting,x;is the reprojec- we synthesize 5000 depth images,together with the ground tion of image pixel x;into world space given depth dr(xi), truth body part labels and joint positions.The original mo- and be is a learned per-part bandwidth.The pixel weighting cap poses used to generate these images are held out from wie considers both the inferred body part probability at the the training data.Our real test set consists of 8808 frames of pixel and the world surface area of the pixel: real depth images over 15 different subjects,hand-labeled wie=P(cI,xi).dI(xi)2. (8) with dense body parts and 7 upper body joint positions.We also evaluate on the real depth data from [131.The results This ensures density estimates are depth invariant and gave suggest that effects seen on synthetic data are mirrored in a small but significant improvement in joint prediction ac- the real data,and further that our synthetic test set is by far curacy.Depending on the definition of body parts,the pos- the 'hardest'due to the extreme variability in pose and body terior P(cI,x)can be pre-accumulated over a small set of shape.For most experiments we limit the rotation of the parts.For example,in our experiments the four body parts user to +120 in both training and synthetic test data since covering the head are merged to localize the head joint. the user is facing the camera(0)in our main entertainment Mean shift is used to find modes in this density effi- scenario,though we also evaluate the full 360 scenario. ciently.All pixels above a learned probability threshold Ac Error metrics.We quantify both classification and joint are used as starting points for part c.A final confidence es- prediction accuracy.For classification,we report the av- timate is given as a sum of the pixel weights reaching each erage per-class accuracy,i.e.the average of the diagonal of mode.This proved more reliable than taking the modal den- the confusion matrix between the ground truth part label and sity estimate. the most likely inferred part label.This metric weights each

• depth, map, front/right/top • pose, distances, cropping, camera angles, body size and shape (e.g. small child, thin/fat), • failure modes: underlying probability correct, can detect failures with confidence • synthetic / real / failures Example inferences Figure 5. Example inferences. Synthetic (top row); real (middle); failure modes (bottom). Left column: ground truth for a neutral pose as a reference. In each example we see the depth image, the inferred most likely body part labels, and the joint proposals show as front, right, and top views (overlaid on a depth point cloud). Only the most confident proposal for each joint above a fixed, shared threshold is shown. To keep the training times down we employ a distributed implementation. Training 3 trees to depth 20 from 1 million images takes about a day on a 1000 core cluster. 3.4. Joint position proposals Body part recognition as described above infers per-pixel information. This information must now be pooled across pixels to generate reliable proposals for the positions of 3D skeletal joints. These proposals are the final output of our algorithm, and could be used by a tracking algorithm to self￾initialize and recover from failure. A simple option is to accumulate the global 3D centers of probability mass for each part, using the known cali￾brated depth. However, outlying pixels severely degrade the quality of such a global estimate. Instead we employ a local mode-finding approach based on mean shift [10] with a weighted Gaussian kernel. We define a density estimator per body part as fc(xˆ) ∝ X N i=1 wic exp − xˆ − xˆi bc 2 ! , (7) where xˆ is a coordinate in 3D world space, N is the number of image pixels, wic is a pixel weighting, xˆi is the reprojec￾tion of image pixel xi into world space given depth dI (xi), and bc is a learned per-part bandwidth. The pixel weighting wic considers both the inferred body part probability at the pixel and the world surface area of the pixel: wic = P(c|I, xi) · dI (xi) 2 . (8) This ensures density estimates are depth invariant and gave a small but significant improvement in joint prediction ac￾curacy. Depending on the definition of body parts, the pos￾terior P(c|I, x) can be pre-accumulated over a small set of parts. For example, in our experiments the four body parts covering the head are merged to localize the head joint. Mean shift is used to find modes in this density effi- ciently. All pixels above a learned probability threshold λc are used as starting points for part c. A final confidence es￾timate is given as a sum of the pixel weights reaching each mode. This proved more reliable than taking the modal den￾sity estimate. The detected modes lie on the surface of the body. Each mode is therefore pushed back into the scene by a learned z offset ζc to produce a final joint position proposal. This simple, efficient approach works well in practice. The band￾widths bc, probability threshold λc, and surface-to-interior z offset ζc are optimized per-part on a hold-out validation set of 5000 images by grid search. (As an indication, this resulted in mean bandwidth 0.065m, probability threshold 0.14, and z offset 0.039m). 4. Experiments In this section we describe the experiments performed to evaluate our method. We show both qualitative and quan￾titative results on several challenging datasets, and com￾pare with both nearest-neighbor approaches and the state of the art [13]. We provide further results in the supple￾mentary material. Unless otherwise specified, parameters below were set as: 3 trees, 20 deep, 300k training images per tree, 2000 training example pixels per image, 2000 can￾didate features θ, and 50 candidate thresholds τ per feature. Test data. We use challenging synthetic and real depth im￾ages to evaluate our approach. For our synthetic test set, we synthesize 5000 depth images, together with the ground truth body part labels and joint positions. The original mo￾cap poses used to generate these images are held out from the training data. Our real test set consists of 8808 frames of real depth images over 15 different subjects, hand-labeled with dense body parts and 7 upper body joint positions. We also evaluate on the real depth data from [13]. The results suggest that effects seen on synthetic data are mirrored in the real data, and further that our synthetic test set is by far the ‘hardest’ due to the extreme variability in pose and body shape. For most experiments we limit the rotation of the user to ±120◦ in both training and synthetic test data since the user is facing the camera (0 ◦ ) in our main entertainment scenario, though we also evaluate the full 360◦ scenario. Error metrics. We quantify both classification and joint prediction accuracy. For classification, we report the av￾erage per-class accuracy, i.e. the average of the diagonal of the confusion matrix between the ground truth part label and the most likely inferred part label. This metric weights each