# HTNet: Human Topology Aware Network for 3D Human Pose Estimation

###### Abstract

3D human pose estimation errors would propagate along the human body topology
and accumulate at the end joints of limbs. Inspired by the backtracking
mechanism in automatic control systems, we design an Intra-Part Constraint
module that utilizes the parent nodes as the reference to build topological
constraints for end joints at the part level. Further considering the
hierarchy of the human topology, joint-level and body-level dependencies are
captured via graph convolutional networks and self-attentions, respectively.
Based on these designs, we propose a novel Human Topology aware Network
(HTNet), which adopts a channel-split progressive strategy to sequentially
learn the structural priors of the human topology from multiple semantic
levels: joint, part, and body. Extensive experiments show that the proposed
method improves the estimation accuracy by 18.7% on the end joints of limbs
and achieves state-of-the-art results on Human3.6M and MPI-INF-3DHP datasets.
Code is available at https://github.com/vefalun/HTNet.

Index Terms—  3D Human Pose Estimation, Human Topology, Error Accumulation,
Hierarchical Structure

##  1 Introduction

3D human pose estimation (HPE) from a monocular image is a challenging task,
which has been widely applied in the sub-tasks of human analysis, such as
action recognition [1] and person re-identification [2]. Benefiting from the
effective 2D HPE framework [3], most recent works focus on the 2D-to-3D
lifting pipeline [4], which firstly estimates 2D poses from a single image and
then lifts them to 3D keypoints. Unlike image-based tasks, the 2D-to-3D pose
lifting task takes inherently sparse and structural 2D joint coordinates as
inputs. Therefore, it is critical to take full advantage of the structural
priors of the human topology.

Fig. 1:  (a) Distribution of estimation errors; (b) Joints with different
PDoFs; (c) Physiological explanation of error accumulation at the end joints
(e.g., wrist):
$\vec{\bm{\varepsilon}}=\bm{\vec{\varepsilon}}_{\textit{3}}+\bm{\vec{\varepsilon}}_{\textit{2}}$.

Recently, many works [5, 6, 7] have focused on the most related local topology
by modeling the correlations among body joints via Graph Convolutional
Networks (GCNs), while others [8, 9, 10] have focused on the less related
global contexts via the Multi-head Self-Attention (MSA) of Transformer.
However, the skeleton representations of the human body cannot be sufficiently
captured by these methods due to the complex topological relationships among
joints, leading to dramatically wrong estimation, especially at the end joints
of limbs. As shown in Fig. 1 (a), the previous state-of-the-art model [6]
suffers from significant estimation errors on joints with high PDoFs, and here
we define the Part Degree of Freedom (PDoF) of joints via the distance to the
torso (see Fig. 1 (b)). To address these issues, we explore the human topology
from the following two aspects:

(i) Error accumulation: Since the human body is a linkage structure that limb
joints highly depend on their parent nodes [11] shown in Fig. 1 (c), the
estimation errors would accumulate from the central hip in the torso (root
joint) to the end joints of limbs. In automatic control systems, backtracking
to the previous points with fewer errors and leveraging their kinematics
priors can effectively alleviate the problem of error accumulation [12, 13].
Inspired by it, an Intra-Part Constraint (IPC) is designed to take intra-part
parent joints as the reference to constrain the joints with higher PDoFs.

Fig. 2:  Overview of the proposed HTNet. The HTNet consists of $M$ stacked
Hierarchical Mixers. Each mixer consists of three modules (LJC, IPC, and GBI),
which can extract features at joint, part, and body levels.

(ii) Hierarchical structure: The Joint motion is closely linked to the
hierarchical organization of human topology, which includes joint [5], part
[14, 15], and body [9] levels. Driven by this natural hierarchy, we present a
novel Human Topology aware Network (HTNet) that learns human topology
representations at multiple levels (see Fig. 2). Specifically, HTNet consists
of alternating hierarchical mixers, each composed of three modules. At the
joint level, we design a Local Joint-level Connection (LJC) based on GCN to
model the physical connections between adjacent joints; At the part level, the
IPC in (i) provides the constraints for intra-part joints, such that they have
similar athletic trends; At the body level, the Global Body-level Interaction
(GBI) based on MSA extracts global features among inter-part joints. Notably,
the hierarchical mixer adopts a channel-split progressive design, which
achieves a win-win scenario by providing more expressive features from various
levels while keeping a small model size.

In summary, the main contributions are as follows:

  * •

We propose a Human Topology aware Network (HTNet) with a channel-split
progressive design to learn human topology dependencies at joint, part, and
body levels.

  * •

To alleviate the error accumulation, we design an Intra-Part Constraint (IPC)
module that utilizes topological constraints of parent nodes to reduce errors
of end joints.

  * •

Extensive experiments demonstrate the effectiveness of HTNet, which achieves
state-of-the-art results on both Human3.6M and MPI-INF-3DHP benchmark
datasets.

##  2 Methodology

###  2.1 Overview

The overview of HTNet is depicted in Fig. 2. Given the 2D coordinates
$X{\in}\mathbb{R}^{N\times 2}$, we firstly map $X$ to a high dimension
${X}^{\prime}{\in}\mathbb{R}^{N\times C}$ via the patch embedding, where $N$
is the number of joints and $C$ is the channel dimensions. Then, we embed
${X}^{\prime}$ with a learnable positional matrix
$E_{pos}{\in}\mathbb{R}^{N\times C}$ to obtain the embedded features
$X^{\ell}$, where $\ell$ is the index of hierarchical mixers. Next, the
$X^{\ell}$ is split into three parts: $X^{\ell}_{\mbox{{\tiny LJC}}}$,
$X^{\ell}_{\mbox{{\tiny IPC}}}$, and $X^{\ell}_{\mbox{{\tiny GBI}}}$, which
have equal dimensions $C^{\prime}{=}C/3$ and are fed into corresponding
modules: LJC, IPC, GBI. These modules construct the human topology from
multiple semantic levels: joint, part, and body. Finally, we aggregate
hierarchical representations and use a linear layer as the regression head to
produce the 3D coordinates $Y{\in}\mathbb{R}^{N\times 3}$. Each module and the
structure of HTNet will be introduced in the following sections.

###  2.2 Local Joint-level Connection

Local Joint-level Connection (LJC) is a GCN-based architecture [6]. The graph-
structured human skeleton can be defined as $G{=}(V,A)$, where $V$ is a set of
$N$ joints and $A{\in}\left\\{0,1\right\\}^{N\times N}$ is an adjacency matrix
representing the connection relations between joints. Given the input
$X^{\ell}_{\mbox{{\tiny LJC}}}{\in}\mathbb{R}^{N\times C^{\prime}}$, features
of neighboring joints can be aggregated to $Y^{\ell}_{\mbox{{\tiny LJC}}}$ by
GCN:

$\begin{array}[]{l}\mbox{{GCN}}(X^{\ell}_{\mbox{{\tiny
LJC}}})=\tilde{D}^{-\frac{1}{2}}\tilde{A}\tilde{D}^{-\frac{1}{2}}X^{\ell}_{\mbox{{\tiny
LJC}}}W,\\\ Y^{\ell}_{\mbox{{\tiny LJC}}}=X^{\ell}_{\mbox{{\tiny
LJC}}}+\mbox{{GCN}}(\sigma(\mbox{{GCN}}(X^{\ell}_{\mbox{{\tiny
LJC}}}))),\end{array}$ (1)

where $\tilde{A}{=}A{+}I$, $\tilde{D}$ is the diagonal node degree matrix, $W$
is the weight matrix, $\sigma$ denotes the GELU activation function.

###  2.3 Intra-Part Constraint

To alleviate the error accumulation, we design an Intra-Part Constraint (IPC)
module (see Fig. 3), which aims to conduct the constraint among intra-part
joints with different PDoFs.

Given the input $\tilde{X}^{\ell}_{\mbox{{\tiny IPC}}}=X^{\ell}_{\mbox{{\tiny
IPC}}}+Y^{\ell}_{\mbox{{\tiny LJC}}}$, topological constraints performs in two
sets of joints: (i) $X^{\ell}_{\textit{1}}{\in}{\mathbb{R}^{8\times
C^{\prime}}}$ consists of 2-PDoF and 3-PDoF joints; (ii)
$X^{\ell}_{\textit{2}}{\in}{\mathbb{R}^{12\times C^{\prime}}}$ consists of
1-PDoF, 2-PDoF, and 3-PDoF joints. Next,
$X^{\ell}_{\textit{j}},j{\in}\\{1,2\\}$ are fed into two convolution layers to
generate limb features $\mathcal{F}^{\ell}_{j}$. Then, a channel MLP [16] is
adopted to aggregate information between different channels for each limb
feature:

$\begin{array}[]{l}\mathcal{F}^{\ell}_{j}=\sigma(\mbox{{Conv}}_{j}(X^{\ell}_{j})),j\in\\{1,2\\},\\\\[2.84544pt]
\mathcal{\tilde{F}}^{\ell}_{j}=\mathcal{F}^{\ell}_{j}+\mbox{{MLP}}(\mbox{{LN}}(\mathcal{F}^{\ell}_{j})),\end{array}$
(2)

where $\mathcal{\tilde{F}}^{\ell}_{j}$ are aggregated limb features,
$LN(\cdot)$ denotes Layer Normalization, $\mbox{{Conv}}_{\textit{1}}$ and
$\mbox{{Conv}}_{\textit{2}}$ are convolution layers with kernel sizes of 2 and
3, respectively.

Fig. 3:  Structure of Intra-Part Constraint (IPC) module.

Based on the above $\mathcal{\tilde{F}}^{\ell}_{\textit{j}}$, we construct two
topological constraints $\mathcal{R}_{j}$ in $X^{\ell}_{\textit{j}}$: (i) In
$\mathcal{R}_{1}$, 3-PDoF joints in $X^{\ell}_{\textit{1}}$ are replaced with
$\mathcal{\tilde{F}}^{\ell}_{\textit{1}}$; (ii) In $\mathcal{R}_{2}$, 3-PDoF
and 2-PDoF joints in $X^{\ell}_{\textit{2}}$ are replaced with
$\mathcal{\tilde{F}}^{\ell}_{\textit{2}}$. Then, the unprocessed joints are
filled into the replaced $X^{\ell}_{j}$, and $Y^{\ell}_{\mbox{{\tiny IPC}}}$,
the final output of IPC, can be represented as follows:

$Y^{\ell}_{\mbox{{\tiny IPC}}}=\tilde{X}^{\ell}_{\mbox{{\tiny
IPC}}}+\mathcal{R}_{1}(\tilde{X}^{\ell}_{\mbox{{\tiny
IPC}}},\mathcal{\tilde{F}}^{\ell}_{1})+\mathcal{R}_{2}(\tilde{X}^{\ell}_{\mbox{{\tiny
IPC}}},\mathcal{\tilde{F}}^{\ell}_{2}).$ (3)

Since the limb features $\mathcal{\tilde{F}}^{\ell}_{j}$ are the motion
representation of limbs, which contains both high-PDoF joints and their parent
joints. Therefore, replacing the high-PDoF joints with
$\mathcal{\tilde{F}}^{\ell}_{j}$ can form topological constraints and produce
reasonable 3D pose estimations to mitigate the error accumulation.

###  2.4 Global Body-level Interaction

Global Body-level Interaction (GBI) module is built by the self-attention of
Transformer, which can capture global contexts across the whole human body
[10, 17]. Given $\tilde{X}^{\ell}_{\mbox{{\tiny GBI}}}=X^{\ell}_{\mbox{{\tiny
GBI}}}+Y^{\ell}_{\mbox{{\tiny IPC}}}$ as input, the GBI module can be
formulated as:

$\begin{array}[]{l}H_{i}=\mbox{{Softmax}}({Q^{\ell}{K^{\ell}}^{T}}{/}{\sqrt{C^{\prime}}})V^{\ell},i\in\\{1,...,h\\}\\\\[1.42271pt]
\mbox{{MSA}}(\tilde{X}^{\ell}_{\mbox{{\tiny
GBI}}})=\mbox{Concat}(H_{1},H_{2},...,H_{h})W_{out},\\\\[1.42271pt]
\tilde{Y}^{\ell}_{\mbox{{\tiny GBI}}}=\tilde{X}^{\ell}_{\mbox{{\tiny
GBI}}}+\mbox{{LN}}(\mbox{{MSA}}(\tilde{X}^{\ell}_{\mbox{{\tiny
GBI}}})),\end{array}$ (4)

where $h$ is the number of attention heads, $Q^{\ell},K^{\ell},V^{\ell}$ are
query, key, and value matrices, which are calculated from
$\tilde{X}^{\ell}_{\mbox{{\tiny GBI}}}$ by linear transformations,
$\tilde{Y}^{\ell}_{\mbox{{\tiny GBI}}}$ is the output of the GBI module.

###  2.5 Network Structure

Although hierarchical representations of human topology can be learned with
LJC, IPC and GBI, it is challenging to design a connection structure for such
three modules: the series structure (i.e., three modules are connected
sequentially) will increase the model size, and the parallel structure (i.e.,
three modules divide the channels equally and work in parallel) lacks feature
interactions among various levels.

Inspired by Res2Net [18], we design the hierarchical mixer with a channel-
split progressive structure. Specifically, channels are split into three parts
and fed into LJC, IPC, and GBI. Meanwhile, the output of the previous module
is added to the input of the next module as residual-like connections for
learning the human topology from local to global. Then, outputs of the above
three modules are concatenated to generate $Y^{\ell}{\in}\mathbb{R}^{N\times
C}$, and $Y^{\ell}$ is fed to a channel MLP block:

$\begin{array}[]{l}Y^{\ell}=\mbox{Concat}(Y^{\ell}_{\mbox{{\tiny
LJC}}},Y^{\ell}_{\mbox{{\tiny IPC}}},Y^{\ell}_{\mbox{{\tiny GBI}}}),\\\
\tilde{Y}^{\ell}=Y^{\ell}+\mbox{{MLP}}(LN(Y^{\ell})).\end{array}$ (5)

Such a process can aggregate features from three different levels and obtain a
more expressive representation.

##  3 Experiments

###  3.1 Datasets and Evaluation Metrics

Human3.6M [19] is the largest indoor dataset for 3D HPE. It has 3.6 million
images and 11 professional actors. Following [6, 17], Mean Per Joint Position
Error (MPJPE) and Procrustes MPJPE (P-MPJPE) are adopted as metrics.

MPI-INF-3DHP [20] consists of 1.3 million images from indoor and outdoor
scenes. There are three different scenes in its test set: studio with a green
screen (GS), studio without a green screen (noGS), and outdoor scene
(Outdoor). Following [6, 17, 21], MPJPE, Percentage of Correct Keypoint (PCK),
and Area Under Curve (AUC) are adopted as metrics.

###  3.2 Implementation Details

We implement our method using Pytorch and train the model for 30 epochs with
batch size 512. The proposed HTNet consists of 3 stacked hierarchical mixers.
Note that the channel dimension of inputs should be divisible by 24 (e.g.,
240, 360) because there are eight heads in the MSA and three split channels in
hierarchical mixers. The $L_{2}$ loss is utilized to minimize the errors
between predictions and ground truth.

Method | P1 (CPN) | P2 (CPN) | P1 (GT)
---|---|---|---
Martinez et al. [4] | 62.9 | 47.7 | 45.5
Ci et al. [22] | 52.7 | 42.2 | 36.3
Liu et al. [21] | 52.4 | 41.2 | 37.8
Xu et al. [23] | 51.9 | - | 35.8
Zhao et al. [17] | 51.8 | - | 35.2
Cai et al. [5]$(\dagger)$ | 50.6 | 40.2 | 38.1
Zeng et al. [24] | 49.9 | 39.4 | 36.4
Zou et al. [6]$(\dagger)$ | 49.4 | 39.1 | 37.4
HTNet (Ours) | 48.9 | 39.0 | 34.0
HTNet (Ours) $(\dagger)$ | 47.6 | 38.6 | 31.9
(a) Quantitative comparison on Human3.6M.

Method | GS$\uparrow$ | noGS$\uparrow$ | Outdoor$\uparrow$ | PCK$\uparrow$ | AUC$\uparrow$
---|---|---|---|---|---
Martinez et al. [4] | 49.8 | 42.5 | 31.2 | 42.5 | 17.0
Mehta et al. [20] | 70.8 | 62.3 | 58.5 | 64.7 | 31.7
Ci et al. [22] | 74.8 | 70.8 | 77.3 | 74.0 | 36.7
Zhou et al. [25] | 75.6 | 71.3 | 80.3 | 75.3 | 38.0
Zeng et al. [24] | - | - | 80.3 | 77.6 | 43.8
Liu et al. [26] | 77.6 | 80.5 | 80.1 | 79.3 | 45.8
Zeng et al. [27] | - | - | 84.6 | 82.1 | 46.2
Xu et al. [23] | 81.5 | 81.7 | 75.2 | 80.1 | 45.8
Zou et al. [6] | 86.4 | 86.0 | 85.7 | 86.1 | 53.7
HTNet (Ours) | 86.9 | 86.2 | 85.9 | 86.7 | 54.1
(b) Quantitative comparison on MPI-INF-3DHP.

Method | Frame | Param | MPJPE
---|---|---|---
Pavllo et al. [28] | 9 | 4.4M | 49.8
Cai et al. [5] | 7 | 5.1M | 48.8
Zheng et al. [9] | 9 | 9.6M | 49.9
Li et al. [10] | 9 | 18.9M | 47.8
Chen et al.[29] | 9 | 18.2M | 46.3
HTNet-S (Ours) | 9 | 3.0M | 47.2
Pavllo et al. [28] | 27 | 8.6M | 48.8
Liu et al. [26] | 27 | 5.7M | 48.5
Zheng et al. [9] | 27 | 9.6M | 47.0
HTNet-L (Ours) | 27 | 10.1M | 46.1
(c) Comparison with temporal methods.

Table 1: (a) Quantitative comparison on Human3.6M under Protocol #1 (MPJPE)
and Protocol #2 (P-MPJPE). The 2D keypoints detected by CPN and the ground
truth of 2D poses are used as inputs. $(\dagger)$ \- adopts the same
refinement module as [5, 6]. (b) Quantitative comparison on MPI-INF-3DHP. (c)
Quantitative comparison with temporal methods on Human3.6M.

###  3.3 Method Comparison

Comparison on Human3.6M. We compare HTNet with state-of-the-art methods on
Human3.6M. As shown in Tab. 1 (a), the 2D keypoints from CPN [3] are used as
inputs, and our model achieves the best results under both MPJPE (47.6mm) and
P-MPJPE (38.6mm). Besides, using the ground truth 2D joints as inputs, HTNet
also performs best, outperforming GraFormer [17] by $9.3\%$ (31.9mm vs.
35.2mm).

Comparison on MPI-INF-3DHP. To evaluate the generalization capability of our
approach, we train HTNet on the Human3.6M and test it on the MPI-INF-3DHP
directly. As shown in Tab. 1 (b), HTNet achieves the best performance on all
scenes, which verifies the strong generalization of our method in unseen
environments.

Comparison with Temporal Methods. To explore the portability of HTNet in
video-based 3D HPE, we compare with some methods [5, 9, 10, 26, 28, 29] with
similar frames as inputs, and Tab. 1 (c) shows that HTNet-S ($C{=}240$) can
achieve competitive performance under MPJPE (47.2mm) with much fewer
parameters. Notably, we find that the channel dimension will be the bottleneck
to the performance gains. Thus, HTNet-L is built with larger dimensions
($C{=}720$) and performs the best (46.1mm). The above experiments prove that
our HTNet can work well with video sequence inputs.

| LJC |  I PC |  GBI | Param | MPJPE
---|---|---|---|---|---
Baseline |  |  | ✓ | 2.2M | 52.2
| ✓ |  |  | 2.6M | 50.4
| ✓ |  | ✓ | 2.5M | 50.2
|  | ✓ | ✓ | 3.4M | 51.8
| ✓ | ✓ |  | 3.8M | 49.3
Parallel | ✓ | ✓ | ✓ | 3.0M | 50.0
Serial | ✓ | ✓ | ✓ | 7.2M | 49.2
HTNet | ✓ | ✓ | ✓ | 3.0M | 48.9

Table 2: Ablation study for components and structures.

Fig. 4: Ablation study for the effect of IPC.

###  3.4 Ablation Study

Tab. 2 shows the results of our method under different components and
structures on the Human3.6M dataset. For a fair comparison, we maintain the
consistency of the parameters by keeping the same dimension channels
($C{=}240$).

Impact of Model Components. As shown in the top part of Tab. 2, HTNet with
only a single-level module cannot achieve satisfactory performance, while the
combination of all proposed modules performs the best via learning
representations from various levels. Notably, IPC cannot work individually due
to no operations on 0-PDoF and 1-PDoF joints. To further investigate the
influence of IPC, we categorize limb joints by PDoFs and calculate the average
MPJPE of joints in each category in Fig. 4. Compared with the baseline (the
HTNet with only GBI), the average MPJPE of all joints decreased by 3.8%
(50.2mm vs. 52.2mm) via introducing LJC. By further integrating IPC into
HTNet, the MPJPE would decreased by 6.3% (48.9mm vs. 52.2mm), while MPJPE on
2-PDoF and 3-PDoF joints noticeably reduces by $15.5\%$ and $18.7\%$,
respectively. Such a significant reduction in the estimation errors of end
joints can be attributed to the number of topological constraints they obtain
shown in Sec. 2.3: (i) 3-PDoF joints are constrained by both 1-PDoF and 2-PDoF
joints; (ii) 2-PDoF joints are only constrained by 1-PDoF joints; (iii) 1-PDoF
joints are not subject to any constraints.

Impact of Model Structures. As for the structures (middle part of Tab. 2), the
serial structure exhibits competitive performance (49.2mm) due to the local-
to-global learning; the parallel structure can reduce parameters from 7.2M to
3.0M due to the channel-split structure. The channel-split progressive
structure of HTNet adopts residual connections and combines the advantages of
these two designs, which performs the best (48.9mm) and maintains a small
model size (3.0M).

Fig. 5:  Qualitative comparison on Human3.6M.

###  3.5 Visualization

Fig. 5 provides qualitative comparisons on Human3.6M between HTNet and the
state-of-the-art approach, i.e., MGCN [6]. It can be seen that our method is
capable of producing more precise 3D keypoints at the end of limbs, which
further proves the effectiveness of our method.

##  4 Conclusion

This paper presents a Human Topology aware Network (HTNet), which takes full
advantage of human structural priors for 3D HPE. To address the error
accumulation, we design an Intra-Part Constraint (IPC) module that utilizes
the topological constraints from intra-part parent nodes to reduce the errors
of end joints. Based on the IPC, the hierarchical mixer is further designed to
learn joint-part-body representations via a channel-split progressive
structure, allowing the HTNet to efficiently build hierarchical
representations of the human topology. Extensive experiments show that the
proposed HTNet achieves state-of-the-art performance. We hope our work can
inspire more researchers on skeleton-based tasks, e.g., action recognition,
and 3D human mesh reconstruction.

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