## 2 Handcrafted Representation-Based Approach
### Space-Time-Based Approaches
#### 2.1.2 Space-Time Trajectory  
Trajectory-based approaches interpret an activity as a set of space-time trajectories. In these approaches, a person is represented by 2-dimensional (\(XY\)) or 3-dimensional (\(XYZ\)) points corresponding to his/her joints position of the body. As person performs an action, there are certain changes in his/her joint positions according to the nature of the action. These changes are recoded as space-time trajectories, which construct a 3D \(XYZ\) or 4D \(XYZ\) representation of an action. The space-time trajectories work by tracking the joint position of the body for distinguishing different \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Feature Type** & **Performance (\%)** \\ \hline  & KTH [35] & \\ \hline Sadanand and Corso 2012 [36] & Space-time volumes & 98.2 \\ [PERSON] et al. 2011 [37] & Space-time volumes & 94.5 \\ [PERSON] and [PERSON] 2009 [38] & Space-time volumes & 89.4 \\ [PERSON] et al. 2013 [39] & Features & 95.6\% \\ [PERSON] et al. 2011 [40] & Features (Attributes) & 91.59 \\ [PERSON] et al. 2015 [41] & Features (mid-level) & 97.41 \\ [PERSON] et al. 2011 [42] & Dense trajectory & 95\% \\ \hline  & UCF (University of Central Florida) Sports [43, 44] & \\ \hline Sadanand and Corso 2012 [36] & Space-time volumes & 95.0 \\ [PERSON] et al. 2011 [37] & Space-time volumes & 91.30 \\ [PERSON] et al. 2015 [45] & Space-time volumes & 89.4 \\ [PERSON] et al. 2015 [41] & Features (mid-level) & 92.67 \\ [PERSON] et al. 2013 [46] & Features (Pose-based) & 90 \\ Sadanand and Corso 2012 [36] & STVs (space-time volumes) & 95.0 \\ \hline  & HDMB (Human Motion database)-51 [47] & \\ \hline [PERSON] and [PERSON] 2013 [48] & Dense trajectory & 57.2 \\ [PERSON] et al. 2012 [49] & Trajectory & 40.7 \\ [PERSON] et al. 2011 [42] & Dense trajectory & 46.6 \\ [PERSON] et al. 2012 [50] & Space-time volumes, bag-of-visual-words & 29.2 \\ [PERSON] and [PERSON] 2012 [36] & Space-time volumes & 26.9 \\ [PERSON] et al. 2011 [47] & Features & 23.0 \\ [PERSON] et al. 2013 [51] & Features (mid-level) & 33.7 \\ [PERSON] et al. 2014 [52] & Fisher vector and Stacked Fisher Vector & 66.79 \\ [PERSON] et al. 2013 [53] & Features & 52.1 \\ [PERSON] et al. 2015 [54] & Features (Video Darwin) & 63.7 \\ [PERSON] and [PERSON] 2014 [55] & Features & 65.9 \\ \hline  & Hollywood2 [56] & \\ \hline [PERSON] and [PERSON] 2013 [48] & Dense trajectory & 64.3 \\ [PERSON] et al. 2013 [53] & Trajectory & 62.5 \\ [PERSON] et al. 2012 [49] & Trajectory & 59.5 \\ [PERSON] et al. 2012 [57] & Trajectory & 59.4 \\ [PERSON] and [PERSON] 2012 [58] & Space-time volumes & 61.0 \\ [PERSON] et al. 2016 [59] & Features & 58.6 \\ [PERSON] et al. 2015 [60] & Features (mid-level) & 66.3 \\ [PERSON] et al. 2015 [54] & Features (Video Darwin) & 73.7 \\ [PERSON] and [PERSON] [55] & Features & 73.6 \\ \hline  & Microsoft Research Action3D [61] & \\ \hline  & Features (pose-based) & 90.22 \\  & [PERSON] et al. 2016 [62] & Trajectory & 89 \\ [PERSON] et al. 2013 [63] & 3D Pose & 91.7 \\ \hline  & YouTube action dataset [64] & \\ \hline [PERSON] et al. 2011 [42] & Dense trajectory & 84.1 \\ [PERSON] et al. 2014 [52] & Features (FV + SFV) & 93.38 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of Space-Time-based approaches for activity recognition on different datasets. types of actions. Following this idea many approaches have been proposed for action recognition based on the trajectories [46; 65; 66]. Inspired by the dense sampling in image classification, the concept of dense trajectories for action recognition from videos was introduced in [42]. The authors sampled the dense points from each image frame and tracked them using displacement information from a dense optical flow field. These types of trajectories cover the motion information and are robust to irregular motion changes. This method achieved state-of-the-art-results on challenging datasets. In [48], an extension to [42] was proposed for the improvement of performance regarding camera motion.