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## Human action recognition by representing 3d skeletons as points in a lie group. In (2014)

Venue: | CVPR, |

Citations: | 16 - 0 self |

### Citations

1060 | Mathematical Introduction to Robotic Manipulation
- Murray, Li, et al.
- 1994
(Show Context)
Citation Context ...tly connected by a joint) provides a more meaningful description than their absolute locations (clapping is more intuitively described using the relative geometry between the two hands), we explicitly model the relative 3D geometry between different body parts in our skeletal representation. Given two rigid body parts, their relative geometry can be described using the rotation and translation required to take one body part to the position and orientation of the other (figure 3). Mathematically, rigid body rotations and translations in 3D space are members of the special Euclidean group SE(3) [11], which is a matrix Lie group. Hence, we represent the relative geometry between a pair of body parts as a point in SE(3), and the entire human skeleton as a point in the Lie group SE(3) × . . . × SE(3), where × denotes the direct product between Lie groups. With the proposed skeletal representation, human actions can be modeled as curves (figure 1) in the Lie group SE(3) × . . . × SE(3), and action recognition can be performed by classifying these curves. Note that the Lie group SE(3) × . . . × SE(3) is a curved manifold and classification of curves in this space is not a trivial task. Moreov... |

834 |
Visual perception of biological motion and a model for its analysis”. In: Perception and Psychophysics
- Johansson
- 1973
(Show Context)
Citation Context ...of the scene, which is robust to illumination changes and offers more useful information to recover 3D human skeletons. Recently, Shotton et al. [16] proposed a method to quickly and accurately estimate the 3D positions of skeletal joints using a single depth image. These recent advances have resulted in a renewed interest in skeleton-based human action recognition. 1 Existing skeleton-based action recognition approaches can be broadly grouped into two main categories: jointbased approaches and body part-based approaches. Inspired by the classical moving lights display experiment by Johansson [6], joint-based approaches consider the human skeleton simply as a set of points. These approaches try to model the motion of either individual joints or combinations of joints using various features like joint positions [5, 8], joint orientations with respect to a fixed coordinate axis [20], pairwise relative joint positions [19, 22], etc. On the other hand, body part-based approaches consider the human skeleton as a connected set of rigid segments (body parts). These approaches either model the temporal evolution of individual body parts [21] or focus on (directly) connected pairs of body part... |

568 | Real-time human pose recognition in parts from single depth images
- Shotton, Sharp, et al.
- 2013
(Show Context)
Citation Context ...monocular RGB videos is a very difficult task [9]. Sophisticated motion capture systems can be used to obtain the 3D locations of landmarks placed on the human body. But, such systems are very expensive, and require the user to wear a motion capture suit with markers which can hinder natural movements. With the recent advent of costeffective depth sensors, extracting the human skeleton has become relatively easier. These sensors provide 3D depth data of the scene, which is robust to illumination changes and offers more useful information to recover 3D human skeletons. Recently, Shotton et al. [16] proposed a method to quickly and accurately estimate the 3D positions of skeletal joints using a single depth image. These recent advances have resulted in a renewed interest in skeleton-based human action recognition. 1 Existing skeleton-based action recognition approaches can be broadly grouped into two main categories: jointbased approaches and body part-based approaches. Inspired by the classical moving lights display experiment by Johansson [6], joint-based approaches consider the human skeleton simply as a set of points. These approaches try to model the motion of either individual join... |

203 | Parameterized Modeling and Recognition of Activities.
- Yacoob, Black
- 1998
(Show Context)
Citation Context ...ssical moving lights display experiment by Johansson [6], joint-based approaches consider the human skeleton simply as a set of points. These approaches try to model the motion of either individual joints or combinations of joints using various features like joint positions [5, 8], joint orientations with respect to a fixed coordinate axis [20], pairwise relative joint positions [19, 22], etc. On the other hand, body part-based approaches consider the human skeleton as a connected set of rigid segments (body parts). These approaches either model the temporal evolution of individual body parts [21] or focus on (directly) connected pairs of body parts and model the temporal evolution of joint angles [12, 13]. In this paper, we propose a new body part-based skeletal representation for action recognition. Inspired by the observation that for human actions, the relative geometry between various body parts (though not directly connected by a joint) provides a more meaningful description than their absolute locations (clapping is more intuitively described using the relative geometry between the two hands), we explicitly model the relative 3D geometry between different body parts in our skele... |

140 |
Information retrieval for music and motion,
- Muller
- 2007
(Show Context)
Citation Context ...aches like Fourier analysis are not directly applicable to this curved space. To overcome these difficulties, we map the action curves from SE(3)× . . .× SE(3) to its Lie algebra se(3) × . . . × se(3), which is the tangent space at the identity element of the group. Irrespective of the skeletal representation being used, classification of temporal sequences into different action categories is a difficult problem due to issues like rate variations, temporal misalignment, noise, etc. To handle rate variations, for each action category, we compute a nominal curve using dynamic time warping (DTW) [10], and warp all the curves to this nominal curve. To handle the temporal misalignment and noise issues, we represent the warped curves using the Fourier temporal pyramid (FTP) representation proposed in [19]. Final classification is performed using FTP and a linear SVM classifier. Figure 4 presents an overview of the proposed approach. Contributions: 1) We represent human skeletons as points in the Lie group SE(3)× . . .×SE(3). The proposed representation explicitly models the 3D geometric relationships between various body parts using rotations and translations. 2) Since SE(3) × . . . × SE(3) ... |

136 |
Lie Groups, Lie Algebras, and Representations: an Elementary Introduction (Springer-Verlag
- Hall
- 2003
(Show Context)
Citation Context ...ive skeletal joints were automatically selected at each time instance based on highly interpretable measures such as mean or variance of the joint angles, maximum angular velocity of the joints, etc. Human actions were then represented as sequences of these informative joints, which were compared using the Levenshtein distance. Skeletal sequences were represented in [13] using pairwise affinities between joint angle trajectories, and then classified using linear SVM. 3. Special Euclidean Group SE(3) In this section, we briefly discuss the special Euclidean group SE(3). We refer the readers to [4] for a general introduction to Lie groups and [11] for further details on SE(3) and rigid body kinematics. The special Euclidean group, denoted by SE(3), is the set of all 4 by 4 matrices of the form P (R, ~d) = [ R ~d 0 1 ] , (1) where ~d ∈ R3, and R ∈ R3×3 is a rotation matrix. Members of SE(3) act on points z ∈ R3 by rotating and translating them: [ R ~d 0 1 ] [ z 1 ] = [ Rz + ~d 1 ] . (2) Elements of this set interact by the usual matrix multiplication, and from a geometrical point of view, can be smoothly organized to form a curved 6 dimensional manifold, giving them the structure of a Li... |

110 | Action recognition based on a bag of 3d points.
- Li, Zhang, et al.
- 2010
(Show Context)
Citation Context ...Contributions: 1) We represent human skeletons as points in the Lie group SE(3)× . . .×SE(3). The proposed representation explicitly models the 3D geometric relationships between various body parts using rotations and translations. 2) Since SE(3) × . . . × SE(3) is a curved manifold, we map all the action curves from the Lie group to its Lie algebra, and perform temporal modeling and classification in the Lie algebra. 3) We experimentally show that the proposed representation performs better than many existing skeletal representations by evaluating it on three different datasets: MSR-Action3D [7], UTKinect-Action dataset [20] and Florence3D-Action dataset [14]. We also show that the proposed approach outperforms various state-of-the-art skeleton-based human action recognition approaches. Organization: We provide a brief review of the existing literature in section 2 and discuss the special Euclidean group SE(3) in section 3. Section 4 presents the proposed skeletal representation and section 5 describes the temporal modeling and classification approach. We present our experimental results in section 6 and conclude the paper in section 7. 2. Relevant Work In this section, we briefly re... |

104 | Towards 3-D model-based tracking and recognition of human movement: a multi-view approach.
- Gavrila, Davis
- 1995
(Show Context)
Citation Context ...using the motion parameters of individual body parts like horizontal and vertical translations, in-plane rotations, etc. Principal component analysis was used to represent an action as a linear combination of a set of action basis, and classification was performed by comparing the PCA coefficients. In [2], a human skeleton was hierarchically divided into smaller parts and each part was represented using certain bio-inspired shape features. The temporal evolutions of these bio-inspired features were modeled using linear dynamical systems. Human skeleton was represented using 3D joint angles in [3], and the temporal evolutions of these angles were compared using DTW. In [12], few informative skeletal joints were automatically selected at each time instance based on highly interpretable measures such as mean or variance of the joint angles, maximum angular velocity of the joints, etc. Human actions were then represented as sequences of these informative joints, which were compared using the Levenshtein distance. Skeletal sequences were represented in [13] using pairwise affinities between joint angle trajectories, and then classified using linear SVM. 3. Special Euclidean Group SE(3) In ... |

102 | Mining actionlet ensemble for action recognition with depth cameras.
- Wang, Liu, et al.
- 2012
(Show Context)
Citation Context ...keleton-based human action recognition. 1 Existing skeleton-based action recognition approaches can be broadly grouped into two main categories: jointbased approaches and body part-based approaches. Inspired by the classical moving lights display experiment by Johansson [6], joint-based approaches consider the human skeleton simply as a set of points. These approaches try to model the motion of either individual joints or combinations of joints using various features like joint positions [5, 8], joint orientations with respect to a fixed coordinate axis [20], pairwise relative joint positions [19, 22], etc. On the other hand, body part-based approaches consider the human skeleton as a connected set of rigid segments (body parts). These approaches either model the temporal evolution of individual body parts [21] or focus on (directly) connected pairs of body parts and model the temporal evolution of joint angles [12, 13]. In this paper, we propose a new body part-based skeletal representation for action recognition. Inspired by the observation that for human actions, the relative geometry between various body parts (though not directly connected by a joint) provides a more meaningful descri... |

58 | View invariant human action recognition using histograms of 3d joints.
- Xia, Chen, et al.
- 2012
(Show Context)
Citation Context ...have resulted in a renewed interest in skeleton-based human action recognition. 1 Existing skeleton-based action recognition approaches can be broadly grouped into two main categories: jointbased approaches and body part-based approaches. Inspired by the classical moving lights display experiment by Johansson [6], joint-based approaches consider the human skeleton simply as a set of points. These approaches try to model the motion of either individual joints or combinations of joints using various features like joint positions [5, 8], joint orientations with respect to a fixed coordinate axis [20], pairwise relative joint positions [19, 22], etc. On the other hand, body part-based approaches consider the human skeleton as a connected set of rigid segments (body parts). These approaches either model the temporal evolution of individual body parts [21] or focus on (directly) connected pairs of body parts and model the temporal evolution of joint angles [12, 13]. In this paper, we propose a new body part-based skeletal representation for action recognition. Inspired by the observation that for human actions, the relative geometry between various body parts (though not directly connected b... |

50 | Recognition and Segmentation of 3D Human Action Using HMM and Multi-class Adaboost. In ECCV,
- Lv, Nevatia
- 2006
(Show Context)
Citation Context ... skeletal joints using a single depth image. These recent advances have resulted in a renewed interest in skeleton-based human action recognition. 1 Existing skeleton-based action recognition approaches can be broadly grouped into two main categories: jointbased approaches and body part-based approaches. Inspired by the classical moving lights display experiment by Johansson [6], joint-based approaches consider the human skeleton simply as a set of points. These approaches try to model the motion of either individual joints or combinations of joints using various features like joint positions [5, 8], joint orientations with respect to a fixed coordinate axis [20], pairwise relative joint positions [19, 22], etc. On the other hand, body part-based approaches consider the human skeleton as a connected set of rigid segments (body parts). These approaches either model the temporal evolution of individual body parts [21] or focus on (directly) connected pairs of body parts and model the temporal evolution of joint angles [12, 13]. In this paper, we propose a new body part-based skeletal representation for action recognition. Inspired by the observation that for human actions, the relative geo... |

36 |
Eigenjoints-based action recognition using naive-bayesnearest-neighbor.
- Yang, Tian
- 2012
(Show Context)
Citation Context ...keleton-based human action recognition. 1 Existing skeleton-based action recognition approaches can be broadly grouped into two main categories: jointbased approaches and body part-based approaches. Inspired by the classical moving lights display experiment by Johansson [6], joint-based approaches consider the human skeleton simply as a set of points. These approaches try to model the motion of either individual joints or combinations of joints using various features like joint positions [5, 8], joint orientations with respect to a fixed coordinate axis [20], pairwise relative joint positions [19, 22], etc. On the other hand, body part-based approaches consider the human skeleton as a connected set of rigid segments (body parts). These approaches either model the temporal evolution of individual body parts [21] or focus on (directly) connected pairs of body parts and model the temporal evolution of joint angles [12, 13]. In this paper, we propose a new body part-based skeletal representation for action recognition. Inspired by the observation that for human actions, the relative geometry between various body parts (though not directly connected by a joint) provides a more meaningful descri... |

24 | Sequence of the most informative joints (SMIJ): a new representation for human skeletal action recognition,”
- Ofli, Chaudhry, et al.
- 2014
(Show Context)
Citation Context ...n simply as a set of points. These approaches try to model the motion of either individual joints or combinations of joints using various features like joint positions [5, 8], joint orientations with respect to a fixed coordinate axis [20], pairwise relative joint positions [19, 22], etc. On the other hand, body part-based approaches consider the human skeleton as a connected set of rigid segments (body parts). These approaches either model the temporal evolution of individual body parts [21] or focus on (directly) connected pairs of body parts and model the temporal evolution of joint angles [12, 13]. In this paper, we propose a new body part-based skeletal representation for action recognition. Inspired by the observation that for human actions, the relative geometry between various body parts (though not directly connected by a joint) provides a more meaningful description than their absolute locations (clapping is more intuitively described using the relative geometry between the two hands), we explicitly model the relative 3D geometry between different body parts in our skeletal representation. Given two rigid body parts, their relative geometry can be described using the rotation and... |

23 | Rate-invariant Recognition of Humans and Their Activities.
- Veeraraghavan, Srivastava, et al.
- 2009
(Show Context)
Citation Context ...m with respect to global x-axis and the translation ~dm of its starting point em1 from the origin (refer to figure 2(b)). But, using the absolute locations of body parts did not give any improvement, suggesting that the information about absolute locations is redundant for the actions used in our experiments. Hence, we just use the relative measurements in this paper. 5. Temporal Modeling and Classification Classification of curves in the Lie algebra into different action categories is not straightforward due to various issues like rate variations, temporal misalignment, noise, etc. Following [17], we use DTW [10] to handle rate variations. During training, for each action category, we compute a nominal curve using the algorithm described in Table 1, and warp all the training curves to this nominal curve using DTW. We use the squared Euclidean distance in the Lie algebra for DTW. Note that to compute a nominal curve all the curves should have equal number of samples. For this, we use the interpolation algorithm presented in section 3 and re-sample the curves in SE(3) × . . . × SE(3) before mapping them to Lie algebra. To handle the temporal misalignment and noise issues, we represent t... |

18 | Choice of Riemannian Metrics for Rigid Body Kinematics,”
- Zefran, Kumar, et al.
- 1996
(Show Context)
Citation Context ...the logarithm map logSE(3) : SE(3) → se(3) between the Lie algebra se(3) and the Lie group SE(3) are given by expSE(3)(B) = e B , logSE(3)(P ) = log(P ), (5) where e and log denote the usual matrix exponential and logarithm respectively. Since log(P ) is not unique, we use the value with smallest norm. Please refer to [11] for efficient implementations of the exponential and logarithm maps of SE(3). Interpolation on SE(3): Various approaches have been proposed in the past for interpolation on SE(3) [25]. In this paper, we use a very simple piecewise interpolation scheme based on screw motions [26]. Given Q1, Q2, . . . , Qn ∈ SE(3) at time instances t1, t2, . . . , tn respectively, we use the following curve for interpolation: γ(t) = QiexpSE(3) ( t− ti ti+1 − ti Bi ) for t ∈ [ti, ti+1], (6) where Bi = logSE(3) ( Q−1i Qi+1 ) for i = 1, 2, . . . , n− 1. SE(3) × . . . × SE(3) : We can combine multiple SE(3) using the direct product × to form a new Lie group M = SE(3) × . . . × SE(3) with identity element (I4, . . . , I4) and Lie algebra m = se(3)× . . .× se(3). The exponential and logarithm maps for (B1, . . . , BK) ∈ m and (P1, . . . , PK) ∈M are given by expM((B1, . . . , BK)) = (e B1 , ... |

14 | Human action recognition using a temporal hierarchy of covariance descriptors on 3d joint locations,”
- Hussein, Torki, et al.
- 2013
(Show Context)
Citation Context ... skeletal joints using a single depth image. These recent advances have resulted in a renewed interest in skeleton-based human action recognition. 1 Existing skeleton-based action recognition approaches can be broadly grouped into two main categories: jointbased approaches and body part-based approaches. Inspired by the classical moving lights display experiment by Johansson [6], joint-based approaches consider the human skeleton simply as a set of points. These approaches try to model the motion of either individual joints or combinations of joints using various features like joint positions [5, 8], joint orientations with respect to a fixed coordinate axis [20], pairwise relative joint positions [19, 22], etc. On the other hand, body part-based approaches consider the human skeleton as a connected set of rigid segments (body parts). These approaches either model the temporal evolution of individual body parts [21] or focus on (directly) connected pairs of body parts and model the temporal evolution of joint angles [12, 13]. In this paper, we propose a new body part-based skeletal representation for action recognition. Inspired by the observation that for human actions, the relative geo... |

12 | Fusing Spatiotemporal Features and Joints for 3D Action Recognition.
- Zhu, Chen, et al.
- 2013
(Show Context)
Citation Context ...ere modeled using a hierarchy of Fourier coefficients. Furthermore, an actionletbased approach was used, in which discriminative joint combinations were selected using a multiple kernel learning approach. In [22], a human skeleton was represented using relative joint positions, temporal displacement of joints and offset of the joints with respect to the initial frame. Action classification was performed using the Naive-Bayes nearest neighbor rule in a lower dimensional space constructed using principal component analysis (PCA). A similar skeletal representation was used with random forests in [27]. A view invariant representation of human skeleton was obtained in [20] by quantizing the 3D joint locations into histograms based on their orientations with respect to a coordinate system fixed at the hip center. The temporal evolutions of this view-invariant representation were modeled using HMMs. Part-based approaches: Human body was divided into five different parts in [21], and human actions were represented using the motion parameters of individual body parts like horizontal and vertical translations, in-plane rotations, etc. Principal component analysis was used to represent an action ... |

10 | Recognizing actions from depth cameras as weakly aligned multi-part bag-of-poses,”
- Seidenari, Varano, et al.
- 2013
(Show Context)
Citation Context ...Lie group SE(3)× . . .×SE(3). The proposed representation explicitly models the 3D geometric relationships between various body parts using rotations and translations. 2) Since SE(3) × . . . × SE(3) is a curved manifold, we map all the action curves from the Lie group to its Lie algebra, and perform temporal modeling and classification in the Lie algebra. 3) We experimentally show that the proposed representation performs better than many existing skeletal representations by evaluating it on three different datasets: MSR-Action3D [7], UTKinect-Action dataset [20] and Florence3D-Action dataset [14]. We also show that the proposed approach outperforms various state-of-the-art skeleton-based human action recognition approaches. Organization: We provide a brief review of the existing literature in section 2 and discuss the special Euclidean group SE(3) in section 3. Section 4 presents the proposed skeletal representation and section 5 describes the temporal modeling and classification approach. We present our experimental results in section 6 and conclude the paper in section 7. 2. Relevant Work In this section, we briefly review various skeleton-based human action recognition approaches. ... |

9 | A Survey on Human Motion Analysis from Depth Data.
- Ye, Zhang, et al.
- 2013
(Show Context)
Citation Context ...leton-based human action recognition approaches. Organization: We provide a brief review of the existing literature in section 2 and discuss the special Euclidean group SE(3) in section 3. Section 4 presents the proposed skeletal representation and section 5 describes the temporal modeling and classification approach. We present our experimental results in section 6 and conclude the paper in section 7. 2. Relevant Work In this section, we briefly review various skeleton-based human action recognition approaches. We refer the readers to [1] for a recent review of RGB video-based approaches and [23] for a recent review of depth map-based approaches. Existing skeleton-based human action recognition approaches can be broadly grouped into two main categories: joint-based approaches and body part-based approaches. Joint-based approaches consider human skeleton as a set of points, whereas body part-based approaches consider human skeleton as a connected set of rigid segments. Approaches that use joint angles can be classified as part-based approaches since joint angles measure the geometry between (directly) connected pairs of body parts. Joint-based approaches: Human skeletons were represent... |

7 | Bio-inspired Dynamic 3D Discriminative Skeletal Features for Human Action Recognition. In CVPRW,
- Chaudhry, Ofli, et al.
- 2013
(Show Context)
Citation Context ...rams based on their orientations with respect to a coordinate system fixed at the hip center. The temporal evolutions of this view-invariant representation were modeled using HMMs. Part-based approaches: Human body was divided into five different parts in [21], and human actions were represented using the motion parameters of individual body parts like horizontal and vertical translations, in-plane rotations, etc. Principal component analysis was used to represent an action as a linear combination of a set of action basis, and classification was performed by comparing the PCA coefficients. In [2], a human skeleton was hierarchically divided into smaller parts and each part was represented using certain bio-inspired shape features. The temporal evolutions of these bio-inspired features were modeled using linear dynamical systems. Human skeleton was represented using 3D joint angles in [3], and the temporal evolutions of these angles were compared using DTW. In [12], few informative skeletal joints were automatically selected at each time instance based on highly interpretable measures such as mean or variance of the joint angles, maximum angular velocity of the joints, etc. Human actio... |

6 | Joint Angles Similarities and HOG2 for Action Recognition. In
- Ohn-bar, Trivedi
- 2013
(Show Context)
Citation Context ...n simply as a set of points. These approaches try to model the motion of either individual joints or combinations of joints using various features like joint positions [5, 8], joint orientations with respect to a fixed coordinate axis [20], pairwise relative joint positions [19, 22], etc. On the other hand, body part-based approaches consider the human skeleton as a connected set of rigid segments (body parts). These approaches either model the temporal evolution of individual body parts [21] or focus on (directly) connected pairs of body parts and model the temporal evolution of joint angles [12, 13]. In this paper, we propose a new body part-based skeletal representation for action recognition. Inspired by the observation that for human actions, the relative geometry between various body parts (though not directly connected by a joint) provides a more meaningful description than their absolute locations (clapping is more intuitively described using the relative geometry between the two hands), we explicitly model the relative 3D geometry between different body parts in our skeletal representation. Given two rigid body parts, their relative geometry can be described using the rotation and... |

3 |
Exploring the Space of a Human Action. In ICCV,
- Sheikh, Sheikh, et al.
- 2005
(Show Context)
Citation Context ...of points, whereas body part-based approaches consider human skeleton as a connected set of rigid segments. Approaches that use joint angles can be classified as part-based approaches since joint angles measure the geometry between (directly) connected pairs of body parts. Joint-based approaches: Human skeletons were represented in [5] using the 3D joint locations, and the joint trajectories were modeled using a temporal hierarchy of covariance descriptors. A similar representation was used with Hidden Markov models (HMMs) in [8]. A set of 13 joint trajectories in a 4-D XYZT space was used in [15] to represent a human action, and their affine projections were compared using a subspace angles-based view-invariant similarity measure. In [19], a human skeleton was represented using pairwise relative positions of the joints, and the temporal evolutions of this representation were modeled using a hierarchy of Fourier coefficients. Furthermore, an actionletbased approach was used, in which discriminative joint combinations were selected using a multiple kernel learning approach. In [22], a human skeleton was represented using relative joint positions, temporal displacement of joints and offs... |

3 |
Kinematics of Human Motion. Human Kinetics Publishers,
- Zatsiorsky
- 1997
(Show Context)
Citation Context ...changes, variations in view-point, occlusions and background clutter. Moreover, monocular video sensors can not fully capture the human motion in 3D space. Hence, despite significant Figure 1: Representation of an action (skeletal sequence) as a curve in the Lie group SE(3)× . . .× SE(3). research efforts over the past few decades, action recognition still remains a challenging problem. A human body can be represented as an articulated system of rigid segments connected by joints, and human motion can be considered as a continuous evolution of the spatial configuration of these rigid segments [24]. Hence, if we can reliably extract and track the human skeleton, action recognition can be performed by classifying the temporal evolution of human skeleton. But, extracting the human skeleton reliably from monocular RGB videos is a very difficult task [9]. Sophisticated motion capture systems can be used to obtain the 3D locations of landmarks placed on the human body. But, such systems are very expensive, and require the user to wear a motion capture suit with markers which can hinder natural movements. With the recent advent of costeffective depth sensors, extracting the human skeleton has... |

3 | Two Methods for Interpolating Rigid Body Motions.
- Zefran, Kumar
- 1998
(Show Context)
Citation Context ...iven by vec(B) = [u1, u2, u3, w1, w2, w3]. (4) The exponential map expSE(3) : se(3) → SE(3) and the logarithm map logSE(3) : SE(3) → se(3) between the Lie algebra se(3) and the Lie group SE(3) are given by expSE(3)(B) = e B , logSE(3)(P ) = log(P ), (5) where e and log denote the usual matrix exponential and logarithm respectively. Since log(P ) is not unique, we use the value with smallest norm. Please refer to [11] for efficient implementations of the exponential and logarithm maps of SE(3). Interpolation on SE(3): Various approaches have been proposed in the past for interpolation on SE(3) [25]. In this paper, we use a very simple piecewise interpolation scheme based on screw motions [26]. Given Q1, Q2, . . . , Qn ∈ SE(3) at time instances t1, t2, . . . , tn respectively, we use the following curve for interpolation: γ(t) = QiexpSE(3) ( t− ti ti+1 − ti Bi ) for t ∈ [ti, ti+1], (6) where Bi = logSE(3) ( Q−1i Qi+1 ) for i = 1, 2, . . . , n− 1. SE(3) × . . . × SE(3) : We can combine multiple SE(3) using the direct product × to form a new Lie group M = SE(3) × . . . × SE(3) with identity element (I4, . . . , I4) and Lie algebra m = se(3)× . . .× se(3). The exponential and logarithm maps... |

2 |
An Approach to Posebased Action Recognition. In CVPR,
- Wang, Wang, et al.
- 2013
(Show Context)
Citation Context ...the actionletbased approach was applied to the entire dataset consisting of 20 actions. This experimental setting is more difficult compared to that of [7]. Some recent approaches like [13, 27] have reported recognition rates around 94.5% for MSR-Action3D dataset by combining skeletal features with additional depth-based features. Since this paper’s focus is not on combining multiTable 4: Comparison with the state-of-the-art results MSR-Action3D dataset (protocol of [7]) Histograms of 3D joints [20] 78.97 EigenJoints [22] 82.30 Joint angle similarities [13] 83.53 Spatial and temporal part-sets[18] 90.22 Covariance descriptors [5] 90.53 Random forests [27] 90.90 Proposed approach 92.46 MSR-Action3D dataset (protocol of [19]) Actionlets [19] 88.20 Proposed approach 89.48 UTKinect-Action dataset Histograms of 3D joints [20] 90.92 Random forests [27] 87.90 Proposed approach 97.08 Florence3D-Action dataset Multi-Part Bag-of-Poses [14] 82.00 Proposed approach 90.88 ple features, we only use the skeleton-based results reported in [13, 27] for comparison. It is interesting to note that even joint positions and relative joint positions (when used with the temporal modeling and classification ap... |