# A Literature Review: Geometric Methods and Their Applications in Human-Related Analysis

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## Abstract

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## 1. Introduction

- Geometric methods and their applications in human-related analysis are extensively studied.
- Geometric methods are studied based on the scope in which they are applied, and we classify them into: feature-oriented geometric methods, object-oriented geometric methods, and routine-based geometric methods.
- Geometric methods and their performances on standard datasets are collected so that researchers who are interested in this topic can identify the state of the art.

## 2. Basic Geometric Concepts

#### 2.1. Set Theory Concepts

#### 2.1.1. Metric

- $d(x,y)\le 0$ with equality iff $x=y$.
- $d(x,y)=d(y,x)$.
- $d(x,y)+d(y,z)\le d(x,z)$.

#### 2.1.2. Quotient Vector Space

#### 2.2. Topological Concepts

#### 2.2.1. Topology

- x lies in each of its neighborhoods.
- The intersection of two neighborhoods of x is a neighborhood of x.
- If N is a neighborhood of x and if U is a subset of X that contains N, then U is a neighborhood of x.
- If N is a neighborhood of x and if $\stackrel{\circ}{N}$ denotes the set $\{z\in N|N\phantom{\rule{4.pt}{0ex}}\mathrm{is}\phantom{\rule{4.pt}{0ex}}\mathrm{a}\phantom{\rule{4.pt}{0ex}}\mathrm{neighborhood}\phantom{\rule{4.pt}{0ex}}\mathrm{of}\phantom{\rule{4.pt}{0ex}}z\}$, then $\stackrel{\circ}{N}$ is a neighborhood of x (the set $\stackrel{\circ}{N}$ is called the interior of N).

- The empty set ∅ is in $\mathsf{\Omega}$.
- X is in $\mathsf{\Omega}$.
- The intersection of a finite number of sets in $\mathsf{\Omega}$ is also in $\mathsf{\Omega}$.
- The union of an arbitrary number of sets in $\mathsf{\Omega}$ is also in $\mathsf{\Omega}$.

#### 2.2.2. Homeomorphism

#### 2.2.3. Quotient Space

#### 2.3. Algebraic Topology Concepts

#### 2.4. Manifold Concepts

#### 2.4.1. Topological Manifold

- $\mathcal{M}$ is a Hausdorff space.
- $\mathcal{M}$ is second countable: there exists a countable basis for the topology of $\mathcal{M}$.
- $\mathcal{M}$ is locally Euclidean of dimension n: for each $p\in \mathcal{M}$, we can find an open set $U\in \mathcal{M}$ containing p, an open set ${U}^{\prime}\in {\mathbb{R}}^{n}$, and a homeomorphism $\phi :U\to {U}^{\prime}$ (i.e., a continuous bijective map with the continuous inverse).

#### 2.4.2. Chart

#### 2.4.3. Tangent Space/Tangent Bundle

- $v(\lambda f+\mu g)=\lambda v\left(f\right)+\mu v\left(g\right)$.
- $v\left(fg\right)=v\left(f\right)g\left(p\right)+f\left(p\right)v\left(g\right)$.

#### 2.4.4. Parallel Transport

#### 2.5. Lie Group and Lie Algebra

- Bilinearity: $[ax+by,z]=a[x,z]+b[y,z]$, $[z,ax+by]=a[z,x]+b[z,y]$ for all scalars a, b in F, and all elements x, y, z in $\mathfrak{g}$.
- Skew-symmetry or alternativity: $[x,x]=0$, which implies $[x,y]=-[y,x]$ for all $x,y\in \mathfrak{g}$.
- Jacobi Identity: $[x,[y,z\left]\right]+[y,[z,x\left]\right]+[z,[x,y\left]\right]=0$.

## 3. Geometric Methods for Generic Objects

#### 3.1. Feature-Oriented Geometric Methods

#### 3.1.1. Distance-Based Methods

#### 3.1.2. Positive Definite Manifold-Based Methods

#### 3.1.3. Kernels over a Manifold

#### 3.1.4. Moduli Space

#### 3.2. Object-Oriented Geometric Methods

#### 3.2.1. Tangent Space-Based Methods

#### 3.2.2. Conformal Geometry-Based Methods

#### 3.2.3. Principal Geodesic Analysis

#### 3.3. Routine-Based Geometric Methods

#### 3.3.1. Dimension Reduction-Based Methods

#### 3.3.2. Graph-Based Methods

#### 3.3.3. Topological Data Analysis

## 4. Geometric Method-Based Human-Related Analysis

#### 4.1. Human Shape Analysis

#### 4.1.1. Heat Kernel-Based Methods

#### 4.1.2. Wave Kernel Signature-Based Methods

#### 4.1.3. Learned Spectral Descriptor-Based Methods

#### 4.2. Human Pose-Related Analysis

#### 4.3. Human Action-Related Analysis

#### 4.3.1. Relative 3D Geometry-Based Methods for Human Action Recognition

#### 4.3.2. Matrix Embedding for 3D Human Action Recognition

#### 4.3.3. Graph-Based Human Action Recognition

#### 4.3.4. Lie Group-Based Human Action Recognition

#### 4.3.5. Dynamic Manifold Warping for Human Action Recognition

## 5. Geometric Deep Learning for Human-Related Analysis

#### 5.1. Geometric Feature Pooling

#### 5.2. Extrinsic Deep Learning

#### 5.2.1. Volumetric CNN for Shape Analysis

#### 5.2.2. Geometric Constrained Extrinsic CNN for Human Shape Analysis

#### 5.3. Intrinsic Deep Learning

#### 5.3.1. Spatial-Domain Geometric CNN for Human Shape Analysis

#### 5.3.2. Spectral Analysis-Based Intrinsic CNN

#### Localized Spectral CNN for Human Shape Analysis

#### 5.3.3. Heat Diffusion CNN for Human Shape Analysis

#### 5.4. A Unified Spatial-Domain Geometric Deep Learning Architecture for Human Shape Analysis

#### 5.5. Geometric Structures over Deep Learning for Human Action Recognition

## 6. Generalized Geometrics for Human-Related Analysis

#### 6.1. Spatial Geometrics for Human Pose-Related Analysis and Human Action-Related Analysis

#### 6.2. Temporal Geometrics for Human Action Recognition

#### 6.3. Spatial-Temporal Geometrics for Action Segmentation and Action Recognition

## 7. Validation Datasets

#### 7.1. 3D Human Datasets

#### 7.1.1. KIDS Dataset

#### 7.1.2. ShapeNet

- (1)
- ShapeNetCore [144], including 55 common object categories (approximately 51,300 unique 3D models), 12 object categories of PASCAL 3D+, and a popular computer vision 3D benchmark dataset.
- (2)
- ShapeNetSem [145], including 12,000 models of 270 categories and annotated with manually-verified category labels, consistent alignments, real-world dimensions, estimates of their material composition at the category level, and estimates of their total volume and weight.

#### 7.1.3. TOSCA High-Resolution Dataset

#### 7.1.4. Human 3.6M

#### 7.1.5. H3D Database

#### 7.1.6. 3D Shape Dataset with Noise

#### 7.1.7. Partial Shape Dataset

#### 7.1.8. SHREC

#### 7.2. 3D Human Action Datasets

#### 7.2.1. CMU Graphics Lab Motion Capture Database

#### 7.2.2. HumanEva Dataset

#### 7.3. RGB-D People Datasets

#### 7.3.1. RGB-D People Datasets

#### 7.3.2. RGB-D Human Tracking Dataset

#### 7.4. RGB-D Human Pose and Posture Datasets

#### Kinect Gesture Dataset

#### 7.5. RGB-D Human Action and Activity Datasets

#### 7.5.1. Human Daily Activity Dataset

#### 7.5.2. Cornell Activity Datasets

#### 7.5.3. 50 Salads Dataset

#### 7.5.4. UR Fall Detection Dataset

#### 7.5.5. Tum Kitchen Dataset

## 8. Performances of Related Works

## 9. Conclusions and Discussions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Set Theory Symbols | |

∼ | A relation |

$\left[x\right]$ | The equivalence class x |

V/${\sim}_{W}$ | The quotient space of V by W, also denoted as V/W |

Topological Symbols | |

$\mathsf{\Omega}$ | A topological space |

G | A topological group |

$GL$ | The general linear group |

Manifold Symbols | |

$\mathcal{M}$ | A manifold |

${T}_{x}M$ | The tangent space of $\mathcal{M}$ at x |

$TM$ | The tangent bundle of $\mathcal{M}$ |

${T}^{*}M$ | The cotangent bundle |

$\mathsf{\Gamma}\left(\mathcal{F}\right)$ | The section of the vector bundle $\mathcal{F}$ |

$\mathrm{Exp}$ | The exponential map |

$\mathrm{Log}$ | The inverse exponential map, also denoted as Exp${}^{-1}$ |

∇ | A connection |

${\nabla}^{*}$ | A dual connection |

$\gamma $ | A geodesic, i.e., a curve $\gamma :I\to \mathcal{M}$ such that ${\nabla}_{\gamma \prime}\gamma \prime =0$. |

${\rho}_{g}$ | $\mathcal{M}\times \mathcal{M}\to \mathbb{R}$, the geodesic distance function determined by g, |

$(\mathcal{M},g)$ | A Riemannian manifold equipped with a metric g |

$(\mathcal{M},\mathfrak{M})$ | A smooth manifold of a pair of a topological manifolds $\mathcal{M}$ and an atlas $\mathfrak{M}$ on $\mathcal{M}$ |

## Appendix A. Mathematical Concepts

#### Appendix A.1. Set Theory Concepts

#### Appendix A.1.1. Equivalence Relations

- $x\sim x$ for all $x\in X$.
- $x\sim {x}^{\prime}$ if and only if ${x}^{\prime}\sim x$.
- $x\sim {x}^{\prime}$ and ${x}^{\prime}\sim {x}^{\prime \prime}$ implies $x\sim {x}^{\prime \prime}$.

#### Appendix A.1.2. Equivalence Class

- The equivalence class of $x\in X$, denoted by $\left[x\right]$, means the set $\left\{{x}^{\prime}\right|x\sim {x}^{\prime}\}$. The sets $\left[x\right]$ for all $x\in X$ form a partition of the set X.
- The set of equivalence classes under ∼ can be denoted as $X/\sim $, and it is referred to as the quotient of X with respect to ∼.

#### Appendix A.1.3. Covering

#### Appendix A.2. Topological Concepts

#### Appendix A.2.1. Closed Sets/Interior and Closure of A Set/Limit Points

#### Appendix A.2.2. Continuous Function

#### Appendix A.2.3. Quotient Map

#### Appendix A.2.4. Metric

- $d(x,y)\ge 0$ for all $x,y\in X$, equality holds if and only if $x=y$.
- $d(x,y)=d(y,x)$ for all $x,y\in X$.
- (Triangle inequality) $d(x,y)+d(y,z)\le d(x,z)$, for all $x,y,z\in X$.

#### Appendix A.2.5. Hausdorff Space

#### Appendix A.3. Algebraic Topology Concepts

#### Appendix A.3.1. Orbit Space

- $e\xb7x=x$ for all $x\in X$.
- ${g}_{1}\xb7({g}_{2}\xb7x)=({g}_{1}\xb7{g}_{2})\xb7x$ for all $x\in X$ and ${g}_{1},{g}_{2}\phantom{\rule{3.33333pt}{0ex}}\in G$.

#### Appendix A.3.2. Homotopy

#### Appendix A.3.3. Fundamental Group

#### Appendix A.3.4. Homology

#### Appendix A.3.4.1. Normal Subgroup

#### Appendix A.3.4.2. Abelian Group

#### Appendix A.3.4.3. Commutator Subgroup

#### Appendix A.3.4.4. Homology

#### Appendix A.4. Manifold Concepts

#### Appendix A.4.1. Atlas

#### Appendix A.4.2. Smooth Manifold

#### Appendix A.4.3. Section

#### Appendix A.4.4. Vector Bundle/Fiber Bundle

**Figure A1.**Vector bundle illustration (by Jakob.scholbach at English Wikipedia, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=6082417).

#### Appendix A.4.5. The Tangent Bundle Of A Vector Bundle

#### Appendix A.4.6. Vertical Bundle

#### Appendix A.4.7. Vector Bundle Homomorphism/Isomorphism

#### Appendix A.4.8. Connection

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**Figure 1.**Overall view of this paper. This review is mainly composed of four modules: geometric methods for generic objects; geometric method-based human-related analysis; geometric deep learning for human-related analysis; and generalized geometrics for human-related analysis. Each module has its subsections, each of which is a class of methods based on its categorization standards. HSA, human shape analysis.

**Figure 2.**Main components of Section 2. This section is composed of four modules: set theory concepts; topology concepts developed from set theory; algebraic topology concepts (topology plus algebra); and manifold concepts (a topology that locally resembles Euclidean spaces).

**Figure 3.**Radial projection from a tetrahedron T onto a sphere with center $\widehat{T}$. An example is shown as follows: a point x on a surface of the tetrahedron projected onto its corresponding point $\pi \left(x\right)$ on the sphere with the radial projection function $\pi $.

**Figure 4.**An example of creating a quotient space by gluing. Gluing the boundary of a circle onto a single point. The two-sphere ${S}^{2}$ is obtained by gluing the circle ${S}^{1}$ to a single point.

**Figure 5.**An example of a coordinate chart. The figure illustrates an example of a coordinate chart from U to $\tilde{U}$.

**Figure 6.**Illustration of a tangent space. ${T}_{x}M$ is the tangent space of the manifold $\mathcal{M}$ at point x.

**Figure 7.**Illustration of a tangent bundle of a manifold. The figure illustrates the tangent bundle of a circle (

**a**) viewed from the side and (

**b**) viewed from the top or bottom.

**Figure 8.**Examples of parallel transports. The figure illustrates two examples of parallel transports under Levi–Civita connections on four sampling positions. The transport on the left side is given by the metric $d{s}^{2}=d{r}^{2}+{r}^{2}d{\theta}^{2}$. The transport on the right side is given by the metric $d{s}^{2}=d{r}^{2}+d{\theta}^{2}$.

**Figure 9.**Illustration of the exponential and the logarithmic maps. The example point of g on the manifold $\mathcal{M}$ is mapped to a point on the tangent plane ${T}_{e}M$ using a logarithmic map $Lo{g}_{M}\left(g\right)$. The exponential map $ex{p}_{M}\left(u\right)$ is the reverse of the logarithmic map.

**Figure 10.**Illustration of a topological data analysis (TDA) pipeline. (

**a**) A 3D object (hand) represented as a point cloud. (

**b**) A filter value is applied to the point cloud, and the object is now colored by the values of the filter functions. (

**c**) The data points are binned into overlapping groups. (

**d**) Each bin is clustered and a center of the cluster is calculated, and a network is built by connecting the cluster center sequentially. The figure is originally from [79].

**Figure 11.**Three kernel-based distance visualized on human models. Visualized distances between the reference point (pointed with red arrows in the first column of each sub-group) and other points on the model. On the left, the reference point is the right writs, in the middle the belly, and on the right the chest. The first row shows the results from the heat kernel, the second row shows the results form the wave kernel, and the third row shows the results of the proposed kernel in [95]. Dark blue shows small distances; red represents large distances. ©2014 IEEE. Reprinted, with permission, from R. Litman, and A. M. Bronstein, Learning Spectral Descriptors for Deformable Shape Correspondence, in IEEE Trans. Pattern Anal. Mach. Intell., 2014, 36, 170–180.

**Figure 12.**Heat kernel signature (HKS), wave kernel signature (WKS), and learned spectral descriptors for point matching between human models. Correspondences computed on TOSCA shapes with geodesic distance distortion below $10\%$ of the shape diameter using the heat kernel signature, wave kernel signature, and learned spectral descriptor (from left to right) [95]. ©2014 IEEE. Reprinted, with permission, from R. Litman, and A. M. Bronstein, Learning Spectral Descriptors for Deformable Shape Correspondence, in IEEE Trans. Pattern Anal. Mach. Intell., 2014, 36, 170–180.

**Figure 13.**An action trajectory in R3DGfeature space. One point on the action trajectory is an R3DG feature of a pose [103]. Reprinted from Comput. Vis. Image Underst., Vol. 152, R. Vemulapalli, F. Arrate, and R. Chellappa, R3DG features: Relative 3D geometry-based skeletal representations for human action recognition, 155–166, Copyright 2016, with permission from Elsevier.

**Figure 14.**Illustrations of the differences between extrinsic CNN and intrinsic CNN. Intrinsic methods (right) work on the manifold rather than its Euclidean realization. The figure is originally from [120]. Reproduced with permission from Michael Bronstein, NIPS Proceedings; published by Neural Information Processing Systems Foundation, Inc., 2016.

**Figure 15.**A Training Mesh Example with Its Multiple segmentations. To ensure smooth descriptors, the authors in [126] defined a classification problem for multiple segmentations of the human body. Points on the boundary might be assigned to nearby classes in different segmentation. ©2016 IEEE. Reprinted, with permission, from L. Wei, Q. Huang, D. Ceylan, E. Vouga, and H. Li, Dense Human Body Correspondences Using Convolutional Networks, in Proceedings of the European Conference on Computer Vision, Amsterdam, The Netherlands, 11–14 October 2016, 1544–1553.

**Figure 16.**Spatial construction of geometric CNN. K(K = 2 in the example) scales are considered. ${\mathsf{\Omega}}_{k}$ is defined as a partition of ${\mathsf{\Omega}}_{k-1}$ into ${d}_{k}$ clusters. Each layer of the network transforms a ${f}_{k-1}$-dimensional signal indexed by ${\mathsf{\Omega}}_{k-1}$ into a ${f}_{k}$-dimensional signal indexed by ${\mathsf{\Omega}}_{k}$. The figure is originally from [127].

**Figure 17.**Visualized local geodesic polar coordinates. Left: examples of local geodesic patches, center and right: examples of angular weights and radial weights, ${v}_{\theta}$ and ${v}_{\rho}$, respectively (red denotes larger weights) [128]. ©2015 IEEE. Reprinted, with permission, from J. Masci, D. Boscaini, M. M. Bronstein, and P. Vandergheynst, Geodesic Convolutional Neural Networks on Riemannian Manifolds, in Proceedings of the IEEE Workshop on 3D Representation and Recognition, Santiago, Chile, 17 December 2015, 832–840.

**Figure 18.**Architecture of the proposed dRNNmodel. In the memory cell, the input gate ${\mathbf{i}}_{t}$ and the forget gate ${\mathbf{f}}_{t}$ are controlled by the derivative of states (DoS) $\frac{{d}^{\left(n\right)}{s}_{t-1}}{d{t}^{\left(n\right)}}$ at $t-1$, and the output gate ${\mathbf{o}}_{t}$ is controlled by the DoS $\frac{{d}^{\left(n\right)}{s}_{t}}{d{t}^{\left(n\right)}}$ at t [141]. ©2015 IEEE. Reprinted, with permission, from V. Veeriah, N. Zhuang, and G. Qi, Differential Recurrent Neural Networks for Action Recognition, in Proceedings of the IEEE International Conference on Computer Vision, Región Metropolitana, Chile, 11–18 December 2015, 4041–4049.

**Figure 19.**Examples from the Kidsdataset. The figure is originally from [94].

**Figure 20.**Contents from the H3D dataset. The figure is originally from the website [149].

**Figure 21.**Examples from the Partial Shape Dataset. The figure is originally from the website [18].

**Figure 23.**Contents from the RGB-D Human Tracking Dataset. The figure is originally from the RGB-D Human Tracking Dataset website [152].

**Figure 24.**Sample Images from the URfall dataset. The figure was captured from the demo video on the UR Fall Dataset website [154].

**Figure 25.**The figure shows exemplary point-to-point maps from one human body model to another. The overall performance of the proposed geometric method (right) is working better than the compared SHOT(left) method on the entire shape [83]. Republished with permission of ACM, from ACM Trans. Graph., E. Corman and M. Ovsjanikov, Vol. 38, 2019; permission conveyed through Copyright Clearance Center, Inc.

**Figure 26.**The figure shows exemplary results on partial symmetries of human body models. The partial human body models are obtained by removing certain body parts, and the removed body parts are marked in semitransparent dark gray. The experiments are carried out under various regularization coefficients (the horizontal axis) and various body part sizes (the vertical axis). Symmetric body parts are marked with the same color. Discarded body parts are marked in light gray [84]. Reprinted by permission from SPRINGER NATURE: Springer Nature, Int. J. Comput. Vis., Full and Partial Symmetries of Non-rigid Shapes, D. Raviv, A. M. Bronstein, M. M. Bronstein, R. Kimmel, Copyright 2010.

**Figure 27.**The figure shows exemplary shape recognition results. The first column denotes the query shape, and the second to the fourth columns show the three closest matches [86]. Reprinted from Pattern Recognition, Vol. 45, D. Smeets, J. Hermans, D. Vandermeulen, P. Suetens, Isometric Deformation Invariant 3D Shape Recognition, 2817–2831, Copyright 2012, with permission from Elsevier.

**Figure 28.**The proposed method produces a good approximation to the full simulation while being 60-times faster. The figure is originally from [102]. Reproduced with permission from Jernej Barbic, ACM Transactions on Graphics; published by ACM Digital Library, 2016.

Applications | Year | Methods | Validation Datasets | Accuracy (%) or Error (cm) |
---|---|---|---|---|

Human Shape Analysis | 2016 | Dense correspondence-based method [126] | FAUST | 2–2.35 cm |

CMUMocap | $89.46\%$ | |||

Human Pose Related | 2017 | SkeletonNet [140] | NTURGB+D | $81.16\%$ |

Analysis | SBUKinect interaction | $93.47\%$ | ||

2011 | Spatio temporal manifold model-based method [111] | Mocap | $90.00\%$ | |

2012 | Bi-lingual Hankelets [45] | IXMAS | $90.57\%$ | |

2012 | Graph matching-based method [105] | KTH | $89.3\%$ | |

2013 | Directed acyclic graph kernel-based method [107] | UCFSport | $85.2\%$ | |

2014 | Fully-convolutional network-based method [113] | PASCAL VOC 2011 | $62.7\%$ | |

MSRAction3D | $92.46\%$ | |||

2014 | Lie group-based method [109] | UTKinect-Action | $97.08\%$ | |

Florence3D-Action | $90.88\%$ | |||

2014 | Shape matching-based method [94] | TOSCA | $90.00\%$ | |

2015 | Deep deconvolution network-based method [114] | PASCAL VOC 2012 | $72.5\%$ | |

KTH-1 | $93.96\%$ | |||

2015 | Differential recurrent neural network-based method | KTH-2 | $92.12\%$ | |

[141] | MSR Action3D | $92.03\%$ | ||

2016 | 3D DCNN-based method [26] | MSR Action3D | $98.14\%$ | |

Weizmann | $98.88\%$ | |||

2016 | Convolutional neural random fields [133] | Youtube | $94.4\%$ | |

UCF50 | $86.5\%$ | |||

WBJR | $95.70\%$ | |||

NTURGB+D | $81.60\%$ | |||

SBUInteraction | $93.3\%$ | |||

2016 | Enhanced-LSTM-based method [142] | UT-Kinect | $95.00\%$ | |

Berkeley MHAD | $100.00\%$ | |||

MSRAction3D | $94.80\%$ | |||

HDM05 | $88.0\pm 6.3\%$ | |||

Human action related | 2016 | Gram matrix-based method [104] | MSR-Action3D | $96.97\%$ |

Analysis | MHAD | $100\%$ | ||

UTKinect | $100\%$ | |||

MSR Action3D | $85.86\%$ | |||

2016 | Local joint structure and body part locations | UTKinect-Action | $96.49\%$ | |

Feature-based method [134] | Florence3D-Action | $87.47\%$ | ||

MSR Action3D | $94.77\%$ | |||

2016 | Motionlet-graph-based method [108] | Florence 3D Actions | $91.63\%$ | |

UTKinect Action | $97.44\%$ | |||

Florence3D | $92.16\%$ | |||

G3D | $92.12\%$ | |||

2016 | Relative 3D geometry-based method [103] | MSR Action3D | $90.69\%$ | |

MSRPairs | $94.33\%$ | |||

UTKinect-Action | $97.20\%$ | |||

Florence3D | $91.40\%$ | |||

2016 | Rolling map-based method [110] | MSRPairs | $94.67\%$ | |

G3D | $90.94\%$ | |||

2016 | Segmental spatiotemporal CNN-based method [139] | 50 Salads | $72.00\%$ | |

JIGSAWS | $74.22\%$ | |||

2017 | LSTM and CNN-based method [136] | NTU RGB+D | $87.40\%$ | |

2017 | Geometric feature pooling-based method [136] | HOIactivity dataset | $89.6\%$ | |

2017 | Scene flow to action map [27] | ChaLearn LAP IsoGD | $36.27\%$ | |

Multi-modal and multi-view and interactive dataset | $91.2\%$ | |||

2017 | Spatiotemporal feature-based method [143] | MSRAction3D | $93.81\%$ | |

UTKinect-Action | $97.47\%$ |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Gong, W.; Zhang, B.; Wang, C.; Yue, H.; Li, C.; Xing, L.; Qiao, Y.; Zhang, W.; Gong, F.
A Literature Review: Geometric Methods and Their Applications in Human-Related Analysis. *Sensors* **2019**, *19*, 2809.
https://doi.org/10.3390/s19122809

**AMA Style**

Gong W, Zhang B, Wang C, Yue H, Li C, Xing L, Qiao Y, Zhang W, Gong F.
A Literature Review: Geometric Methods and Their Applications in Human-Related Analysis. *Sensors*. 2019; 19(12):2809.
https://doi.org/10.3390/s19122809

**Chicago/Turabian Style**

Gong, Wenjuan, Bin Zhang, Chaoqi Wang, Hanbing Yue, Chuantao Li, Linjie Xing, Yu Qiao, Weishan Zhang, and Faming Gong.
2019. "A Literature Review: Geometric Methods and Their Applications in Human-Related Analysis" *Sensors* 19, no. 12: 2809.
https://doi.org/10.3390/s19122809