Original: P ROACTIVE M ULTI -C AMERA C OLLABORATION FOR 3D H UMAN P OSE E STIMATION
Revised: P ROACTIVE M ULTI -C AMERA C OLLABORATION FOR 3D H UMAN P OSE E STIMATION

Original: Anonymous authors
Revised: Anonymous authors

Original: Paper under double-blind review
Revised: Paper under double-blind review

Original: A BSTRACT
Revised: A BSTRACT

Original: For human motion capture (MoCap), particularly outdoors, the fixed-viewpoint multi-camera solutions are susceptible to dynamic occlusions and constrained in capture space.
Revised: For human motion capture (MoCap), particularly outdoors, the fixed-viewpoint multi-camera solutions are susceptible to dynamic occlusions and constrained in capture space.

Original: While an active camera approach aims to proactively control the camera poses to find optimal viewpoints for 3D reconstruction.
Revised: While an active camera approach aims to proactively control the camera poses to find optimal viewpoints for 3D reconstruction.

Original: This work introduces a multi-agent reinforcement learning (MARL) scheme to proactive Multi-Camera
Revised: This work introduces a multi-agent reinforcement learning (MARL) scheme to proactive Multi-Camera

Original: Collaboration for 3D Human Pose Estimation (MCC-HPE) in dynamic human crowds.
Revised: Collaboration for 3D Human Pose Estimation (MCC-HPE) in dynamic human crowds.

Original: At its core is a novel Collaborative Triangulation Contribution Reward (CTCR) that incentivizes agents according to their weighted average marginal contribution to the 3D reconstruction.
Revised: At its core is a novel Collaborative Triangulation Contribution Reward (CTCR) that incentivizes agents according to their weighted average marginal contribution to the 3D reconstruction.

Original: CTCR improves convergence and alleviates the multi-agent credit assignment issue resulted from using 3D reconstruction accuracy as the shared reward.
Revised: CTCR improves convergence and alleviates the multi-agent credit assignment issue resulted from using 3D reconstruction accuracy as the shared reward.

Original: To better capture environment dynamics and to encourage anticipatory behaviors for occlusion avoidance, we jointly train our model with multiple world dynamics learning tasks.
Revised: To better capture environment dynamics and to encourage anticipatory behaviors for occlusion avoidance, we jointly train our model with multiple world dynamics learning tasks.

Original: We evaluate our proposed method in four photo-realistic UE4 environments to ensure validity and generalizability.
Revised: We evaluate our proposed method in four photo-realistic UE4 environments to ensure validity and generalizability.

Original: The empirical results show that our methods steadily outperform the fixed and active baselines in different scenarios with various numbers of cameras and humans.
Revised: The empirical results show that our methods steadily outperform the fixed and active baselines in different scenarios with various numbers of cameras and humans.

Original:  I NTRODUCTION
Revised:  I NTRODUCTION

Original: Marker-less motion capture (MoCap) has broad commercial applications in many areas such as cinematography, medical research, virtual reality (VR), sports, and etc .
Revised: Marker-less motion capture (MoCap) has broad commercial applications in many areas such as cinematography, medical research, virtual reality (VR), sports, and etc .

Original: Their successes can be partly attributed to recent developments in 3D Human pose estimation (HPE) techniques
Revised: Their successes can be partly attributed to recent developments in 3D Human pose estimation (HPE) techniques

Original: (Tu et al., 2020; Iskakov et al., 2019; Qiu et al., 2019; Jafarian et al., 2019; Pavlakos et al., 2017b; Dong et al., 2019; Lin & Lee, 2021b).
Revised: (Tu et al., 2020; Iskakov et al., 2019; Qiu et al., 2019; Jafarian et al., 2019; Pavlakos et al., 2017b; Dong et al., 2019; Lin & Lee, 2021b).

Original: A straightforward implementation to solve multi-views 3D HPE is to use fixed cameras.
Revised: A straightforward implementation to solve multi-views 3D HPE is to use fixed cameras.

Original: Although being a convenient solution, it is less effective against dynamic occlusions.
Revised: Although being a convenient solution, it is less effective against dynamic occlusions.

Original: Moreover, fixed camera solutions confine tracking targets within a constrained space, therefore less applicable to outdoor MoCap.
Revised: Moreover, fixed camera solutions confine tracking targets within a constrained space, therefore less applicable to outdoor MoCap.

Original: On the contrary, active cameras such as ones mounted on drones can maneuver proactively against incoming occlusions.
Revised: On the contrary, active cameras such as ones mounted on drones can maneuver proactively against incoming occlusions.

Original: Owing to its remarkable flexibility, the active approach has thus attracted overwhelming interest (Tallamraju et al., 2020;
Revised: Owing to its remarkable flexibility, the active approach has thus attracted overwhelming interest (Tallamraju et al., 2020;

Original: Ho et al., 2021; Nägeli et al., 2018; Xu et al., 2017; Kiciroglu et al., 2019; Zhou et al., 2018;
Revised: Ho et al., 2021; Nägeli et al., 2018; Xu et al., 2017; Kiciroglu et al., 2019; Zhou et al., 2018;

Original: Saini et al., 2022; Cheng et al., 2018; Zhang et al., 2021).
Revised: Saini et al., 2022; Cheng et al., 2018; Zhang et al., 2021).

Original: Previous works have demonstrated the effectiveness of using active cameras for 3D HPE on a single target in indoor (Kiciroglu et al., 2019; Cheng et al., 2018), clean landscapes (Tallamraju et al., 2020; Nägeli et al., 2018;
Revised: Previous works have demonstrated the effectiveness of using active cameras for 3D HPE on a single target in indoor (Kiciroglu et al., 2019; Cheng et al., 2018), clean landscapes (Tallamraju et al., 2020; Nägeli et al., 2018;

Original: Zhou et al., 2018;
Revised: Zhou et al., 2018;

Original: Saini et al., 2022) or landscapes with scattered static obstacles (Ho et al., 2021).
Revised: Saini et al., 2022) or landscapes with scattered static obstacles (Ho et al., 2021).

Original: However, to our best knowledge, we have not seen any existing work
Revised: However, to our best knowledge, we have not seen any existing work

Original: [Figure]
Revised: [Figure]

Original: that experimented with multiple ( n > 3) active cameras to conduct 3D HPE in human crowd .
Revised: that experimented with multiple ( n > 3) active cameras to conduct 3D HPE in human crowd .

Original: There are two key challenges : First , frequent human-to-human interactions lead to random dynamic occlusions .
Revised: There are two key challenges : First , frequent human-to-human interactions lead to random dynamic occlusions .

Original: Different from previous works that only consider clean landscapes or static obstacles, dynamic scenes require frequent adjustments of cameras’ viewpoints for occlusion avoidance while keeping an overall good team formation for multi-view reconstruction.
Revised: Different from previous works that only consider clean landscapes or static obstacles, dynamic scenes require frequent adjustments of cameras’ viewpoints for occlusion avoidance while keeping an overall good team formation for multi-view reconstruction.

Original: Therefore, it is challenging to achieve optimality with a fixed camera formation or a hand-crafted control policy.
Revised: Therefore, it is challenging to achieve optimality with a fixed camera formation or a hand-crafted control policy.

Original: In addition, the complex behavioral pattern of a human crowd makes the occlusion patterns less comprehensible and predictable, further increasing the difficulty in control.
Revised: In addition, the complex behavioral pattern of a human crowd makes the occlusion patterns less comprehensible and predictable, further increasing the difficulty in control.

Original: Second , as the size of a camera team grows, the multi-agent credit assignment issue becomes prominent which hinders policy learning of the camera agents.
Revised: Second , as the size of a camera team grows, the multi-agent credit assignment issue becomes prominent which hinders policy learning of the camera agents.

Original: Concretely, as a team effort, multi-view 3D HPE requires inputs from multiple cameras to generate an accurate reconstruction.
Revised: Concretely, as a team effort, multi-view 3D HPE requires inputs from multiple cameras to generate an accurate reconstruction.

Original: Having more camera agents participate in a reconstruction introduces more redundancy.
Revised: Having more camera agents participate in a reconstruction introduces more redundancy.

Original: Though it reduces the susceptibility to reconstruction failure caused by dynamic occlusions, it consequently weakens the association between the individual performance and the reconstruction accuracy of the team, which likely leads to the “lazy agent” problem (Sunehag et al., 2017).
Revised: Though it reduces the susceptibility to reconstruction failure caused by dynamic occlusions, it consequently weakens the association between the individual performance and the reconstruction accuracy of the team, which likely leads to the “lazy agent” problem (Sunehag et al., 2017).

Original: A shared reward risks disincentivizing some individual cameras on exploring better viewpoints due to an adequate accuracy already being attained by their teammates alone.
Revised: A shared reward risks disincentivizing some individual cameras on exploring better viewpoints due to an adequate accuracy already being attained by their teammates alone.

Original: We introduce a proactive multi-camera collaboration framework based on multi-agent reinforcement learning (MARL) for real-time distributive adjustments of multi-camera formation for 3D HPE in a human crowd.
Revised: We introduce a proactive multi-camera collaboration framework based on multi-agent reinforcement learning (MARL) for real-time distributive adjustments of multi-camera formation for 3D HPE in a human crowd.

Original: In our approach, multiple camera agents perform seamless collaboration for successful reconstructions of 3D human poses.
Revised: In our approach, multiple camera agents perform seamless collaboration for successful reconstructions of 3D human poses.

Original: Additionally, it is a decentralized framework which offers flexibility over the size of formation and eliminates dependency to a control hierarchy or a centralized entity.
Revised: Additionally, it is a decentralized framework which offers flexibility over the size of formation and eliminates dependency to a control hierarchy or a centralized entity.

Original: In regards of the first challenge, we argue the utmost importance of the model’s capability to anticipate human motions and future states of the environment.
Revised: In regards of the first challenge, we argue the utmost importance of the model’s capability to anticipate human motions and future states of the environment.

Original: To model these properties into the state representations, we incorporate World Dynamics Learning into the training of our model, i.e ., learning with five auxiliary tasks to predict target’s position, pedestrians’ positions, self state, teammates’ states and team reward.
Revised: To model these properties into the state representations, we incorporate World Dynamics Learning into the training of our model, i.e ., learning with five auxiliary tasks to predict target’s position, pedestrians’ positions, self state, teammates’ states and team reward.

Original: To tackle the second challenge, we further introduce the Collaborative Triangulation Contribution
Revised: To tackle the second challenge, we further introduce the Collaborative Triangulation Contribution

Original: Reward (CTCR) , which incentivizes each agent according to its characteristic contribution to a 3D reconstruction.
Revised: Reward (CTCR) , which incentivizes each agent according to its characteristic contribution to a 3D reconstruction.

Original: Inspired by the Shapley Value (Rapoport, 1970), CTCR computes the average weighted marginal contribution to the 3D reconstruction for any given agent over all possible coalitions that contain it.
Revised: Inspired by the Shapley Value (Rapoport, 1970), CTCR computes the average weighted marginal contribution to the 3D reconstruction for any given agent over all possible coalitions that contain it.

Original: This reward aims to directly associate agents’ levels of participation with their return and guides their policy learning when the team reward alone is insufficient to produce such direct association.
Revised: This reward aims to directly associate agents’ levels of participation with their return and guides their policy learning when the team reward alone is insufficient to produce such direct association.

Original: Moreover, CTCR penalizes occluded camera agents more efficiently than the shared reward, encouraging emergent occlusion avoidance behaviors.
Revised: Moreover, CTCR penalizes occluded camera agents more efficiently than the shared reward, encouraging emergent occlusion avoidance behaviors.

Original: Empirical results show that
Revised: Empirical results show that

Original: CTCR can accelerate convergence and increase reconstruction accuracy.
Revised: CTCR can accelerate convergence and increase reconstruction accuracy.

Original: Furthermore, CTCR is a general approach that can benefit policy learning in active 3D HPE and serve as a new assessment metric for view selection in other multi-view reconstruction tasks.
Revised: Furthermore, CTCR is a general approach that can benefit policy learning in active 3D HPE and serve as a new assessment metric for view selection in other multi-view reconstruction tasks.

Original: In experiments, we build photo-realistic environments based on Unreal Engine 4 (UE4) and UnrealCV (Qiu et al., 2017) for training and testing.
Revised: In experiments, we build photo-realistic environments based on Unreal Engine 4 (UE4) and UnrealCV (Qiu et al., 2017) for training and testing.

Original: Our environments can simulate realistic-behaving crowds with assurances of high fidelity and customizability.
Revised: Our environments can simulate realistic-behaving crowds with assurances of high fidelity and customizability.

Original: We train the agents on a Blank environment and validate the generalizability on three unseen scenarios with different landscapes, levels of illumination, human appearances, and various quantities of cameras and humans.
Revised: We train the agents on a Blank environment and validate the generalizability on three unseen scenarios with different landscapes, levels of illumination, human appearances, and various quantities of cameras and humans.

Original: The empirical results show that our method can achieve more accurate and stable 3D pose estimates than off-the-shelf passive- and active-camera baselines.
Revised: The empirical results show that our method can achieve more accurate and stable 3D pose estimates than off-the-shelf passive- and active-camera baselines.

Original: To help facilitate more fruitful research on this topic, we will open-source our environments that are integrated with OpenAI Gym-API (Brockman et al., 2016) and together with a dedicated visualization tool.
Revised: To help facilitate more fruitful research on this topic, we will open-source our environments that are integrated with OpenAI Gym-API (Brockman et al., 2016) and together with a dedicated visualization tool.

Original: Here we summarize the key contributions of our work:
Revised: Here we summarize the key contributions of our work:

Original: • We formulate active 3D human pose estimation in a human crowd problem as a Dec-POMDP, and proposed a novel multi-camera ( n ≥ 3) collaboration framework.
Revised: • We formulate active 3D human pose estimation in a human crowd problem as a Dec-POMDP, and proposed a novel multi-camera ( n ≥ 3) collaboration framework.

Original: • We propose CTCR to improve credit assignment in multi-camera collaboration and demonstrate notable improvements in reconstruction accuracy compared to both passive and active baselines.
Revised: • We propose CTCR to improve credit assignment in multi-camera collaboration and demonstrate notable improvements in reconstruction accuracy compared to both passive and active baselines.

Original: • We introduce five auxiliary tasks called to help the model learn environment dynamics, further enhancing the model’s ability to handle highly dynamic scenes.
Revised: • We introduce five auxiliary tasks called to help the model learn environment dynamics, further enhancing the model’s ability to handle highly dynamic scenes.

Original: • We contribute high-fidelity environments built for simulating realistic-
Revised: • We contribute high-fidelity environments built for simulating realistic-

Original: looking human crowds with authentic behaviors, along with visualization software for frame-by-frame video analysis.
Revised: looking human crowds with authentic behaviors, along with visualization software for frame-by-frame video analysis.

Original:  R ELATED W ORK
Revised:  R ELATED W ORK

Original: 3D Human Pose Estimation (HPE)
Revised: 3D Human Pose Estimation (HPE)

Original: Recent works demonstrated recovering 3 D human pose from a single monocular image (Ma et al., 2021;
Revised: Recent works demonstrated recovering 3 D human pose from a single monocular image (Ma et al., 2021;

Original: Pavlakos et al., 2017a; Martinez et al., 2017; Kanazawa et al., 2018; Pavlakos et al., 2018; Sun et al., 2018; Ci et al., 2019; Zeng et al., 2020; Ci et al., 2020) or monocular video (Mehta et al., 2017; Hossain & Little, 2018;
Revised: Pavlakos et al., 2017a; Martinez et al., 2017; Kanazawa et al., 2018; Pavlakos et al., 2018; Sun et al., 2018; Ci et al., 2019; Zeng et al., 2020; Ci et al., 2020) or monocular video (Mehta et al., 2017; Hossain & Little, 2018;

Original: Pavllo et al., 2019; Kocabas et al., 2020).
Revised: Pavllo et al., 2019; Kocabas et al., 2020).

Original: Another line of work utilized multi-camera systems (i.e. triangulation) to eliminate ambiguity and provide redundancy to visibility (Qiu et al., 2019; Jafarian et al., 2019; Pavlakos et al., 2017b;
Revised: Another line of work utilized multi-camera systems (i.e. triangulation) to eliminate ambiguity and provide redundancy to visibility (Qiu et al., 2019; Jafarian et al., 2019; Pavlakos et al., 2017b;

Original: Dong et al., 2019; Lin & Lee, 2021b; Tu et al., 2020; Iskakov et al., 2019).
Revised: Dong et al., 2019; Lin & Lee, 2021b; Tu et al., 2020; Iskakov et al., 2019).

Original: However, these multi-view methods are limited to the indoor laboratory environment with fixed cameras.
Revised: However, these multi-view methods are limited to the indoor laboratory environment with fixed cameras.

Original: This work presents an active camera system with multiple mobile cameras for mocap in outdoor scenes.
Revised: This work presents an active camera system with multiple mobile cameras for mocap in outdoor scenes.

Original: Proactive Motion
Revised: Proactive Motion

Original: Capture
Revised: Capture

Original: Few previous works studied proactive motion capture with a single mobile camera (Zhou et al., 2018; Cheng et al., 2018; Kiciroglu et al., 2019).
Revised: Few previous works studied proactive motion capture with a single mobile camera (Zhou et al., 2018; Cheng et al., 2018; Kiciroglu et al., 2019).

Original: In comparison, more works studied the control of a multi-camera team.
Revised: In comparison, more works studied the control of a multi-camera team.

Original: Among them, many are based on optimization with various system designs, including marker-based (Nägeli et al., 2018), RGBD-based (Xu et al., 2017), two-stage system (Saini et al., 2019; Tallamraju et al., 2019), hierarchical system (Ho et al., 2021), etc .
Revised: Among them, many are based on optimization with various system designs, including marker-based (Nägeli et al., 2018), RGBD-based (Xu et al., 2017), two-stage system (Saini et al., 2019; Tallamraju et al., 2019), hierarchical system (Ho et al., 2021), etc .

Original: It is important to note that all the above methods deal with static occlusion sources or clean landscapes.
Revised: It is important to note that all the above methods deal with static occlusion sources or clean landscapes.

Original: Also, the common similarity shared by these works is the use of hand-crafted optimization objectives and some fixed-form camera formations.
Revised: Also, the common similarity shared by these works is the use of hand-crafted optimization objectives and some fixed-form camera formations.

Original: These factors resulted in poor adaptability to dynamic scenes saturated with uncertainties.
Revised: These factors resulted in poor adaptability to dynamic scenes saturated with uncertainties.

Original: Recently, RL-based methods received more attention due to their potential for dynamic formation adjustments.
Revised: Recently, RL-based methods received more attention due to their potential for dynamic formation adjustments.

Original: These works focused on active 3D HPE in the Gazebo simulation (Tallamraju et al., 2020) or Panoptic dome (Joo et al., 2015; Pirinen et al., 2019;
Revised: These works focused on active 3D HPE in the Gazebo simulation (Tallamraju et al., 2020) or Panoptic dome (Joo et al., 2015; Pirinen et al., 2019;

Original: Gärtner et al., 2020) for active view selection.
Revised: Gärtner et al., 2020) for active view selection.

Original: Among them, AirCapRL (Tallamraju et al., 2020) shares similarities with our work.
Revised: Among them, AirCapRL (Tallamraju et al., 2020) shares similarities with our work.

Original: However, it is restricted to coordinating between two cameras in clean landscapes without occlusion.
Revised: However, it is restricted to coordinating between two cameras in clean landscapes without occlusion.

Original: We study the collaboration between more cameras and resolve the credit assignment issue with novel CTCR incentives.
Revised: We study the collaboration between more cameras and resolve the credit assignment issue with novel CTCR incentives.

Original: Meanwhile, we consider a more challenging scenario with multiple distracting humans as dynamic occlusions, which requires dedicated algorithms to handle.
Revised: Meanwhile, we consider a more challenging scenario with multiple distracting humans as dynamic occlusions, which requires dedicated algorithms to handle.

Original: Multi-Camera Collaboration Many works in computer vision have studied multi-camera collaboration and designed active camera systems accordingly.
Revised: Multi-Camera Collaboration Many works in computer vision have studied multi-camera collaboration and designed active camera systems accordingly.

Original: Earlier works (Qureshi & Terzopoulos, 2007)(Collins et al., 2003; Matsuyama et al., 2012) focused on developing a network of pan-tilezoom (PTZ) cameras.
Revised: Earlier works (Qureshi & Terzopoulos, 2007)(Collins et al., 2003; Matsuyama et al., 2012) focused on developing a network of pan-tilezoom (PTZ) cameras.

Original: Owing to recent advances in MARL algorithms (Lowe et al., 2017; Sunehag et al., 2017; Rashid et al., 2018; Wang et al., 2020; Yu et al., 2021), many works have formulated multi-camera collaboration as a multi-agent learning problem and solved it using MARL algorithms accordingly (Li et al., 2020; Xu et al., 2020; Wenhong et al., 2022;
Revised: Owing to recent advances in MARL algorithms (Lowe et al., 2017; Sunehag et al., 2017; Rashid et al., 2018; Wang et al., 2020; Yu et al., 2021), many works have formulated multi-camera collaboration as a multi-agent learning problem and solved it using MARL algorithms accordingly (Li et al., 2020; Xu et al., 2020; Wenhong et al., 2022;

Original: Fang et al., 2022; Sharma et al., 2022).
Revised: Fang et al., 2022; Sharma et al., 2022).

Original: However, most works focus on the target tracking problem, whereas this work attempts to solve the task of 3D HPE.
Revised: However, most works focus on the target tracking problem, whereas this work attempts to solve the task of 3D HPE.

Original: Compared with tracking, 3D HPE has more strict criteria for optimal view selections due to correlations across multiple views, which requires stronger collaboration between cameras.
Revised: Compared with tracking, 3D HPE has more strict criteria for optimal view selections due to correlations across multiple views, which requires stronger collaboration between cameras.

Original: To our best knowledge, this work is the first to experiment with various camera agents ( n ≥ 3) to learn multi-camera collaboration strategies for active 3D HPE.
Revised: To our best knowledge, this work is the first to experiment with various camera agents ( n ≥ 3) to learn multi-camera collaboration strategies for active 3D HPE.

Original:  P ROACTIVE M ULTI -C AMERA C OLLABORATION
Revised:  P ROACTIVE M ULTI -C AMERA C OLLABORATION

Original: This section will explain the formulation of multi-camera collaboration in 3D HPE as a Dec-POMDP.
Revised: This section will explain the formulation of multi-camera collaboration in 3D HPE as a Dec-POMDP.

Original: Then we will describe our proposed solutions for modeling the virtual environment’s complex dynamics and strengthening credit assignment in the multi-camera collaboration task.
Revised: Then we will describe our proposed solutions for modeling the virtual environment’s complex dynamics and strengthening credit assignment in the multi-camera collaboration task.

Original: 3. P ROBLEM F ORMULATION
Revised: 3. P ROBLEM F ORMULATION

Original: We formulate the multi-cameras 3D HPE problem as a Decentralized Partially-Observable Markov
Revised: We formulate the multi-cameras 3D HPE problem as a Decentralized Partially-Observable Markov

Original: Decision Process (Dec-POMDP), where each camera is considered as an agent which is decentralized controlled and has partial observability over the environment.
Revised: Decision Process (Dec-POMDP), where each camera is considered as an agent which is decentralized controlled and has partial observability over the environment.

Original: Formally, a Dec-POMDP is defined as ⟨S , O , A n , n, P, r, γ ⟩ , where S denotes the global state space of the environment, including all human states and camera states in our problem.
Revised: Formally, a Dec-POMDP is defined as ⟨S , O , A n , n, P, r, γ ⟩ , where S denotes the global state space of the environment, including all human states and camera states in our problem.

Original: o i ∈
Revised: o i ∈

Original: O denotes the agent
Revised: O denotes the agent

Original: i ’s local observation, i.e ., the RGB image observed by camera i .
Revised: i ’s local observation, i.e ., the RGB image observed by camera i .

Original: A denotes the action space of an agent and A n represents the joint action space of all n agents.
Revised: A denotes the action space of an agent and A n represents the joint action space of all n agents.

Original: P : S
Revised: P : S

Original: ×
Revised: ×

Original: A n → S is the transition probability function
Revised: A n → S is the transition probability function

Original: P ( s t +1 | s t , a t ) , in which a t ∈
Revised: P ( s t +1 | s t , a t ) , in which a t ∈

Original: A n is a joint action by all n agents.
Revised: A n is a joint action by all n agents.

Original: At each timestep t , every agent obtains a local view o ti from the environment s t and then pre-process o ti to form i -th agent’s local observation ˜ o
Revised: At each timestep t , every agent obtains a local view o ti from the environment s t and then pre-process o ti to form i -th agent’s local observation ˜ o

Original: ti .
Revised: ti .

Original: The agent performs action a ti ∼ π ti | ˜ o
Revised: The agent performs action a ti ∼ π ti | ˜ o

Original: ti and receives its reward r ( s t , a t ) .
Revised: ti and receives its reward r ( s t , a t ) .

Original: γ ∈ (0 , 1] is the discount factor used to calculate the cumulative discounted reward G ( t ) =
Revised: γ ∈ (0 , 1] is the discount factor used to calculate the cumulative discounted reward G ( t ) =

Original: (cid:80) t ′ ≥ t γ t ′ − t r
Revised: (cid:80) t ′ ≥ t γ t ′ − t r

Original: t ′ ) .
Revised: t ′ ) .

Original: In a cooperative team, the objective is to learn a group of decentralized policies { π i ( a ti | ˜ o ti ) } ni =1 that maximizes E ( s, a ) ∼ π [ G ( t )] .
Revised: In a cooperative team, the objective is to learn a group of decentralized policies { π i ( a ti | ˜ o ti ) } ni =1 that maximizes E ( s, a ) ∼ π [ G ( t )] .

Original: For convenience, we let i means the agent index, (cid:74) n (cid:75) =
Revised: For convenience, we let i means the agent index, (cid:74) n (cid:75) =

Original: { 1 , . . . , n } is the set for all agents, and − i
Revised: { 1 , . . . , n } is the set for all agents, and − i

Original: = (cid:74) n (cid:75) \ { i } are all agents except agent i .
Revised: = (cid:74) n (cid:75) \ { i } are all agents except agent i .

Original: Observation Camera agents have partial observability over the environment.
Revised: Observation Camera agents have partial observability over the environment.

Original: The pre-processed observation ˜ o i =
Revised: The pre-processed observation ˜ o i =

Original: ( p i , ξ i , ξ − i ) of the camera agent i consists of: (1) p i , a set of states of visible humans to agent i , containing information including the detected human bounding box in the 2 D local view, the 3D positions and orientations of all visible humans measured in both local coordinate frame of camera i and world coordinates; (2) own camera pose ξ i showing the camera’s position and orientation in world coordinates; (3) peer cameras poses ξ − i showing their positions and orientations in world coordinates and are obtained via multi-agent communication.
Revised: ( p i , ξ i , ξ − i ) of the camera agent i consists of: (1) p i , a set of states of visible humans to agent i , containing information including the detected human bounding box in the 2 D local view, the 3D positions and orientations of all visible humans measured in both local coordinate frame of camera i and world coordinates; (2) own camera pose ξ i showing the camera’s position and orientation in world coordinates; (3) peer cameras poses ξ − i showing their positions and orientations in world coordinates and are obtained via multi-agent communication.

Original: Action Space
Revised: Action Space

Original: The action space of each camera agent consists of the velocity of 3 D egocentric translation ( x, y, z ) and velocity of 2 D pitch-yaw rotation ( θ, ψ ) .
Revised: The action space of each camera agent consists of the velocity of 3 D egocentric translation ( x, y, z ) and velocity of 2 D pitch-yaw rotation ( θ, ψ ) .

Original: To reduce the exploration space for state-action mapping, the agent’s action space is discretized into three levels across all five dimensions.
Revised: To reduce the exploration space for state-action mapping, the agent’s action space is discretized into three levels across all five dimensions.

Original: At each timestep, the camera agent can move its position by [+ δ, 0 , − δ ] in ( x, y, z ) directions and rotate about pitch-yaw axes by [+ η, 0 , − η ] degrees.
Revised: At each timestep, the camera agent can move its position by [+ δ, 0 , − δ ] in ( x, y, z ) directions and rotate about pitch-yaw axes by [+ η, 0 , − η ] degrees.

Original: 3. F RAMEWORK
Revised: 3. F RAMEWORK

Original: This section will describe the technical framework that constitutes our camera agents, which contains a Perception Module and a Controller Module.
Revised: This section will describe the technical framework that constitutes our camera agents, which contains a Perception Module and a Controller Module.

Original: The Perception Module maps the original RGB images taken by the camera to numerical observations.
Revised: The Perception Module maps the original RGB images taken by the camera to numerical observations.

Original: The Controller Module takes the numerical observations and correspondingly outputs the controls.
Revised: The Controller Module takes the numerical observations and correspondingly outputs the controls.

Original: Fig.
Revised: Fig.

Original: 2 illustrates this framework.
Revised: 2 illustrates this framework.

Original: Perception Module The perception module executes a procedure consisting of four sequential stages: (1) 2 D HPE.
Revised: Perception Module The perception module executes a procedure consisting of four sequential stages: (1) 2 D HPE.

Original: The agent performs 2 D human detection and pose estimation on the observed
Revised: The agent performs 2 D human detection and pose estimation on the observed

Original: RGB image with the YOLOv3 (Redmon & Farhadi, 2018) detector and the HRNet-w32 (Sun et al., 2019) pose estimator, respectively.
Revised: RGB image with the YOLOv3 (Redmon & Farhadi, 2018) detector and the HRNet-w32 (Sun et al., 2019) pose estimator, respectively.

Original: Both models are pre-trained on the COCO dataset, (Lin et al., 2014) and their parameters are kept frozen during policy learning of camera agents to ensure crossscene generalization.
Revised: Both models are pre-trained on the COCO dataset, (Lin et al., 2014) and their parameters are kept frozen during policy learning of camera agents to ensure crossscene generalization.

Original: (2) Person ReID.
Revised: (2) Person ReID.

Original: A ReID model (Zhong et al., 2018) is used to distinguish people in a scene.
Revised: A ReID model (Zhong et al., 2018) is used to distinguish people in a scene.

Original: For simplicity, an appearance dictionary of all to-be-appeared people is built in advance following (Gärtner et al., 2020).
Revised: For simplicity, an appearance dictionary of all to-be-appeared people is built in advance following (Gärtner et al., 2020).

Original: At test time, the ReID network computes features for all detected people and identifies different people by comparing features to the pre-built appearance dictionary.
Revised: At test time, the ReID network computes features for all detected people and identifies different people by comparing features to the pre-built appearance dictionary.

Original: (3) Multi-agent Communication.
Revised: (3) Multi-agent Communication.

Original: Detected 2 D human pose, IDs, and own camera pose are broadcasted to other agents.
Revised: Detected 2 D human pose, IDs, and own camera pose are broadcasted to other agents.

Original: (4) 3 D human pose reconstruction.
Revised: (4) 3 D human pose reconstruction.

Original: 3 D human pose is finally reconstructed via local triangulation after receiving other agents’ communications.
Revised: 3 D human pose is finally reconstructed via local triangulation after receiving other agents’ communications.

Original: Human position and orientation that are parts of p ti can then be calculated from the reconstructed human pose.
Revised: Human position and orientation that are parts of p ti can then be calculated from the reconstructed human pose.

Original: The whole process is illustrated in Appendix Fig.
Revised: The whole process is illustrated in Appendix Fig.

Original: Controller Module The controller module consists of a state encoder E and an actor network
Revised: Controller Module The controller module consists of a state encoder E and an actor network

Original: A .
Revised: A .

Original: The state encoder E takes ˜ o ti as input, encoding the temporal dynamics of the environment via
Revised: The state encoder E takes ˜ o ti as input, encoding the temporal dynamics of the environment via

Original: LSTM.
Revised: LSTM.

Original: The future states of the target, pedestrians, and cameras are modeled using Mixture Density
Revised: The future states of the target, pedestrians, and cameras are modeled using Mixture Density

Original: Network (MDN) (Bishop, 1994) to account for uncertainty.
Revised: Network (MDN) (Bishop, 1994) to account for uncertainty.

Original: During model inference, it computestarget position prediction, and then the ( ϕ, µ, σ ) parameters of target prediction MDN are used as a part of the inputs to the actor network to enhance feature encoding. Please refer to Section 3.4 for more details regarding training the MDN.
Revised: During model inference, it computes

Original: [Equation]
Revised: [Equation]

Original: Human Trajectory 
Revised: Human Trajectory Prediction

Original: Prediction

Original: [Equation]
Revised: [Equation]

Original: where p tgt and p pd refer to the state of the target and the pedestrian, respectively.
Revised: where p tgt and p pd refer to the state of the target and the pedestrian, respectively.

Original: The actor network A consists of 2 fully-connected layers that output the action, a ti =
Revised: The actor network A consists of 2 fully-connected layers that output the action, a ti =

Original: A ( E (˜ o ti , h t − 1 i )) .
Revised: A ( E (˜ o ti , h t − 1 i )) .

Original: 3. R EWARD S TRUCTURE
Revised: 3. R EWARD S TRUCTURE

Original: To alleviate the credit assignment issue that arises in multi-camera collaboration, we propose the
Revised: To alleviate the credit assignment issue that arises in multi-camera collaboration, we propose the

Original: Collaborative Triangulation Contribution Reward (CTCR).
Revised: Collaborative Triangulation Contribution Reward (CTCR).

Original: We start by defining a base reward that reflects the reconstruction accuracy of the triangulated pose generated by the camera team.
Revised: We start by defining a base reward that reflects the reconstruction accuracy of the triangulated pose generated by the camera team.

Original: Then we explain how our CTCR is computed based on this base team reward.
Revised: Then we explain how our CTCR is computed based on this base team reward.

Original: Reconstruction Accuracy as A Team Reward To directly reflect the reconstruction accuracy, the reward function negatively correlates with the pose estimation error (Mean Per Joint Position Error,
Revised: Reconstruction Accuracy as A Team Reward To directly reflect the reconstruction accuracy, the reward function negatively correlates with the pose estimation error (Mean Per Joint Position Error,

Original: MPJPE) of the multi-camera triangulation.
Revised: MPJPE) of the multi-camera triangulation.

Original: Formally,
Revised: Formally,

Revised: [Equation]

Original: [Equation]
Revised: [Equation]

Original: Where X denotes a set of cameras that participate in the triangulation.
Revised: Where X denotes a set of cameras that participate in the triangulation.

Original: Gemen( · ) = 2( · / c ) 2 ( · / c ) 2 +4 , is the
Revised: Gemen( · ) = 2( · / c ) 2 ( · / c ) 2 +4 , is the

Original: Geman-McClure smoothing (Barron, 2019) function used to stabilize policy updates.
Revised: Geman-McClure smoothing (Barron, 2019) function used to stabilize policy updates.

Original: Empirically we set c = 50mm in our experiments.
Revised: Empirically we set c = 50mm in our experiments.

Original: In the context of our MAPPO baseline, X represents the entire camera team, and each camera receives a shared team reward r ( X ) , from which the credit assignment issue arises.
Revised: In the context of our MAPPO baseline, X represents the entire camera team, and each camera receives a shared team reward r ( X ) , from which the credit assignment issue arises.

Original: Intuitively, when one camera is occluded, all cameras receive the same reduced reward.
Revised: Intuitively, when one camera is occluded, all cameras receive the same reduced reward.

Original: It is hard to tell who the culprit is.
Revised: It is hard to tell who the culprit is.

Original: To deal with this issue, we introduce CTCR.
Revised: To deal with this issue, we introduce CTCR.

Original: Collaborative Triangulation Contribution Reward (CTCR) CTCR computes each agent’s individual reward based on its marginal contribution to the collaborative multi-view triangulation.
Revised: Collaborative Triangulation Contribution Reward (CTCR) CTCR computes each agent’s individual reward based on its marginal contribution to the collaborative multi-view triangulation.

Original: Please see Fig.
Revised: Please see Fig.

Original: 3 for a rundown of computing CTCR for a 3-cameras team.
Revised: 3 for a rundown of computing CTCR for a 3-cameras team.

Original: The contribution of agent i can be measured by:
Revised: The contribution of agent i can be measured by:

Original: [Equation]
Revised: [Equation]

Original: Where n denotes the total number of agents.
Revised: Where n denotes the total number of agents.

Original: S denotes all the subsets of (cid:74) n (cid:75) not containing agent i .
Revised: S denotes all the subsets of (cid:74) n (cid:75) not containing agent i .

Original: | S | !
Revised: | S | !

Original: ( n −| S |− 1)!
Revised: ( n −| S |− 1)!

Original: n !
Revised: n !

Original: is the normalization term.
Revised: is the normalization term.

Original: [ r ( S ∪ { i } ) − r ( S )] means the marginal contribution of agent i .
Revised: [ r ( S ∪ { i } ) − r ( S )] means the marginal contribution of agent i .

Original: Note that (cid:80) i ∈ (cid:74) n (cid:75) φ r
Revised: Note that (cid:80) i ∈ (cid:74) n (cid:75) φ r

Original: ( i ) =
Revised: ( i ) =

Original: r ( (cid:74) n (cid:75) ) .
Revised: r ( (cid:74) n (cid:75) ) .

Original: We additionally multiply a constant n to rescale the 
Revised: We additionally multiply a constant n to rescale the [Figure]

Original: CTCR to have the same scale as the team reward.
Revised: CTCR to have the same scale as the team reward.

Original: Specially, in the 2-cameras case, the individual
Revised: Specially, in the 2-cameras case, the individual

Original: CTCR should be equivalent to the team reward, i.e ., CTCR
Revised: CTCR should be equivalent to the team reward, i.e ., CTCR

Original: ( i = 1) =
Revised: ( i = 1) =

Original: CTCR( i = 2) =
Revised: CTCR( i = 2) =

Original: r ( { 1 , 2 } ) .
Revised: r ( { 1 , 2 } ) .

Original: [Figure] [Table] [Table]
Revised: For more explanations on CTCR, please refer to Appendix Section G.

Original:  L EARNING M ULTI -C AMERA C OLLABORATION VIA MARL
Revised: 3. L EARNING M ULTI -C AMERA C OLLABORATION VIA MARL

Original: We employ the multi-agent learning variant of PPO (Schulman et al., 2017) called Multi-Agent PPO (MAPPO)
Revised: We employ the multi-agent learning variant of PPO (Schulman et al., 2017) called Multi-Agent PPO (MAPPO)

Original: (Yu et al., 2021) to learn the collaboration strategy.
Revised: (Yu et al., 2021) to learn the collaboration strategy.

Original: Alongside the RL loss, we jointly train the model with five auxiliary tasks that encourage comprehension of the world dynamics and the stochasticity in human behaviors.
Revised: Alongside the RL loss, we jointly train the model with five auxiliary tasks that encourage comprehension of the world dynamics and the stochasticity in human behaviors.

Original: The pseudocode of the learning algorithm can be found in
Revised: The pseudocode of the learning algorithm can be found in

Original: Appendix A.
Revised: Appendix A.

Original: World Dynamics Learning (WDL)
Revised: World Dynamics Learning (WDL)

Original: We use the encoder’s hidden states ( z ti , h ti ) as the basis to model the world.
Revised: We use the encoder’s hidden states ( z ti , h ti ) as the basis to model the world.

Original: Three WDL objectives correspond to modeling agent dynamics : (1) learning the forward dynamics of the camera P 1 ( ξ t +1 i |
Revised: Three WDL objectives correspond to modeling agent dynamics : (1) learning the forward dynamics of the camera P 1 ( ξ t +1 i |

Original: z ti , h ti , a ti ) , (2) prediction of team reward P 2 ( r t | z ti , h ti , a ti ) , (3) prediction of future position of peer agents P 3 ( ξ t +1 − i | z ti , h ti , a ti ) .
Revised: z ti , h ti , a ti ) , (2) prediction of team reward P 2 ( r t | z ti , h ti , a ti ) , (3) prediction of future position of peer agents P 3 ( ξ t +1 − i | z ti , h ti , a ti ) .

Original: Two WDL objectives correspond to modeling human dynamics: (4) prediction of future position of target person P 4 ( p t +1 tgt | z ti , h ti , p t tgt ) , (5) prediction of future position of pedestrians, P 5 ( p t +1 pd | z ti , h ti , p t pd ) .
Revised: Two WDL objectives correspond to modeling human dynamics: (4) prediction of future position of target person P 4 ( p t +1 tgt | z ti , h ti , p t tgt ) , (5) prediction of future position of pedestrians, P 5 ( p t +1 pd | z ti , h ti , p t pd ) .

Original: All the probability functions above are approximated using Mixture Density Networks (MDNs) (Bishop, 1994).
Revised: All the probability functions above are approximated using Mixture Density Networks (MDNs) (Bishop, 1994).

Original: Total Training Objectives L Train =
Revised: Total Training Objectives L Train =

Original: L RL + λ WDL L WDL .
Revised: L RL + λ WDL L WDL .

Original: The L RL is the reinforcement learning loss consisting of PPO-Clipped loss and centralized-critic network loss similar to MAPPO (Yu et al., 2021).
Revised: The L RL is the reinforcement learning loss consisting of PPO-Clipped loss and centralized-critic network loss similar to MAPPO (Yu et al., 2021).

Original: L WDL = − 1 n (cid:80) l λ l (cid:80) i
Revised: L WDL = − 1 n (cid:80) l λ l (cid:80) i

Original: E [log P l ( ·| ˜ o ti , h ti , a ti )] is the world dynamics learning loss that consists of MDN supervised losses on the five prediction tasks mentioned above.
Revised: E [log P l ( ·| ˜ o ti , h ti , a ti )] is the world dynamics learning loss that consists of MDN supervised losses on the five prediction tasks mentioned above.

Original:  E XPERIMENT
Revised:  E XPERIMENT

Original: In this section, we first introduce our novel environment, U NREAL P OSE , used for training and testing the learned policies.
Revised: In this section, we first introduce our novel environment, U NREAL P OSE , used for training and testing the learned policies.

Original: Then we compare our method with various passive multi-camera baselines and perform an ablation study on the effectiveness of the proposed CTCR and WDL objectives.
Revised: Then we compare our method with various passive multi-camera baselines and perform an ablation study on the effectiveness of the proposed CTCR and WDL objectives.

Original: Additionally, we evaluate the effectiveness of the learned policies by comparing them against other active multi-camera methods.
Revised: Additionally, we evaluate the effectiveness of the learned policies by comparing them against other active multi-camera methods.

Original: Lastly, we test our method in four different scenarios to showcase its robustness.
Revised: Lastly, we test our method in four different scenarios to showcase its robustness.

Original: 4. U NREAL P OSE : A V IRTUAL E NVIRONMENT FOR P ROACTIVE H UMAN P OSE E STIMATION
Revised: 4. U NREAL P OSE : A V IRTUAL E NVIRONMENT FOR P ROACTIVE H UMAN P OSE E STIMATION

Original: We built a virtual environment for active HPE based on Unreal Engine 4 (UE4), a powerful 3 D game engine that can provide real-time and photo-realistic renderings provided for making visuallystunning video games.
Revised: We built a virtual environment for active HPE based on Unreal Engine 4 (UE4), a powerful 3 D game engine that can provide real-time and photo-realistic renderings provided for making visuallystunning video games.

Original: The environment handles the interactions between realistic-behaving human crowds and camera agents.
Revised: The environment handles the interactions between realistic-behaving human crowds and camera agents.

Original: Here is a list of characteristics of UnrealPose that we would like to highlight: Realistic :
Revised: Here is a list of characteristics of UnrealPose that we would like to highlight: Realistic :

Original: Diverse generations of human trajectories, built-in collision avoidance, and several scenarios with different human appearance, terrain, and level of illumination.
Revised: Diverse generations of human trajectories, built-in collision avoidance, and several scenarios with different human appearance, terrain, and level of illumination.

Original: Flexibility : extensive configuration in numbers of humans, cameras, or their physical properties, more than
Revised: Flexibility : extensive configuration in numbers of humans, cameras, or their physical properties, more than

Original: MoCap action sequences incorporated.
Revised: MoCap action sequences incorporated.

Original: RL-Ready : integrated with OpenAI Gym API, overhaul the communication module in the UnrealCV (Qiu et al., 2017) plugin with inter-process communication (IPC) mechanism.
Revised: RL-Ready : integrated with OpenAI Gym API, overhaul the communication module in the UnrealCV (Qiu et al., 2017) plugin with inter-process communication (IPC) mechanism.

Original: For more detailed descriptions, please refer to Appendix Section B.
Revised: For more detailed descriptions, please refer to Appendix Section B.

Original: [Figure]

Original: 4. E VALUATION M ETRICS
Revised: 4. E VALUATION M ETRICS

Original: We adopt Mean Per Joint Position Error (MPJPE) between the ground truth and the reconstructed 3 D pose as our primary evaluation metric.
Revised: We adopt Mean Per Joint Position Error (MPJPE) between the ground truth and the reconstructed 3 D pose as our primary evaluation metric.

Original: While cameras making adjustments toward higher-quality perceptions could take several frames to complete or have high peaks in MPJPE that were overlooked  by the mean aggregation.
Revised: While cameras making adjustments toward higher-quality perceptions could take several frames to complete or have high peaks in MPJPE that were overlooked [Figure] [Table] by the mean aggregation.

Original: Hence we additionally use the “success rate” metric to evaluate the robustness and smooth execution of the learned policies.
Revised: Hence we additionally use the “success rate” metric to evaluate the robustness and smooth execution of the learned policies.

Original: The success rate is the ratio of frames in an episode with MPJPE lower than τ .
Revised: The success rate is the ratio of frames in an episode with MPJPE lower than τ .

Original: Formally, SuccessRate( τ ) =
Revised: Formally, SuccessRate( τ ) =

Original: P (MPJPE ≤ τ ) .
Revised: P (MPJPE ≤ τ ) .

Original: This metric is a proxy measure for the integrity of multi-view coordination.
Revised: This metric is a proxy measure for the integrity of multi-view coordination.

Original: One instance of bad coordination may cause partial occlusions or have too many overlapping perceptions due to a bad formation.
Revised: One instance of bad coordination may cause partial occlusions or have too many overlapping perceptions due to a bad formation.

Original: Both will result in a dramatic increase in MPJPE and consequently cause a drop in the success rate.
Revised: Both will result in a dramatic increase in MPJPE and consequently cause a drop in the success rate.

Original: 4. R ESULTS AND A NALYSIS
Revised: 4. R ESULTS AND A NALYSIS

Original: We trained all the learning-based control policies in a mix of 60 instances of the Blank Environment containing 1 to 6 humans (uniformly sampled).
Revised: We trained all the learning-based control policies in a mix of 60 instances of the Blank Environment containing 1 to 6 humans (uniformly sampled).

Original: Each training run has 500,000 steps of environment interactions.
Revised: Each training run has 500,000 steps of environment interactions.

Original: For fair evaluation, we report all of the mean metrics based on the data of a hundred 500-step episodes.
Revised: For fair evaluation, we report all of the mean metrics based on the data of a hundred 500-step episodes.

Original: In all experiments, the cameras and humans interact in a 10m × 10m area.
Revised: In all experiments, the cameras and humans interact in a 10m × 10m area.

Original: Active vs. Passive To show the necessity of proactive camera control, we compare the active camera control methods with three passive methods, i.e ., Fixed Camera, Fixed Camera (RANSAC), and Fixed
Revised: Active vs. Passive To show the necessity of proactive camera control, we compare the active camera control methods with three passive methods, i.e ., Fixed Camera, Fixed Camera (RANSAC), and Fixed

Original: Camera (PlaneSweepPose).
Revised: Camera (PlaneSweepPose).

Original: “Fixed Cameras” denotes that the poses of the cameras are fixed, hanging 3 meters above ground with − 35 ◦ pitch angles (i.e. overseeing the entire area).
Revised: “Fixed Cameras” denotes that the poses of the cameras are fixed, hanging 3 meters above ground with − 35 ◦ pitch angles (i.e. overseeing the entire area).

Original: The placements of these fixed cameras are carefully determined with strong priors, for example, right-angle, triangle, square, and pentagon formations for 2, 3, 4, and 5 cameras, respectively.
Revised: The placements of these fixed cameras are carefully determined with strong priors, for example, right-angle, triangle, square, and pentagon formations for 2, 3, 4, and 5 cameras, respectively.

Original: “RANSAC” denotes the method that uses RANSAC (Fischler & Bolles, 1981) for enhanced triangulation.
Revised: “RANSAC” denotes the method that uses RANSAC (Fischler & Bolles, 1981) for enhanced triangulation.

Original: “PlaneSweepPose” represents the off-the-shelf learning-based method (Lin & Lee, 2021b) for multi-view 3D HPE.
Revised: “PlaneSweepPose” represents the off-the-shelf learning-based method (Lin & Lee, 2021b) for multi-view 3D HPE.

Original: Please refer to the Appendix E.1 for more implementation details.
Revised: Please refer to the Appendix E.1 for more implementation details.

Original: We show the MPJPE(mm) and Success
Revised: We show the MPJPE(mm) and Success

Original: Rate versus a different number of cameras in Fig.
Revised: Rate versus a different number of cameras in Fig.

Original: We observe that all passive baselines are being outperformed by the active approaches due to their inability to adjust camera views against dynamic occlusions.
Revised: We observe that all passive baselines are being outperformed by the active approaches due to their inability to adjust camera views against dynamic occlusions.

Original: The improvement of active approaches is especially significant when the number of cameras is less, i.e. when the camera system has little or no redundancy against occlusions.
Revised: The improvement of active approaches is especially significant when the number of cameras is less, i.e. when the camera system has little or no redundancy against occlusions.

Original: Notably, the MPJPE achieved by our 3-camera control strategy is even lower than the MPJPE from 5 Fixed cameras.
Revised: Notably, the MPJPE achieved by our 3-camera control strategy is even lower than the MPJPE from 5 Fixed cameras.

Original: This suggests that proactive strategies can help reduce the number of cameras necessary for deployment.
Revised: This suggests that proactive strategies can help reduce the number of cameras necessary for deployment.

Original: The Effectiveness of CTCR and WDL We also perform ablation studies on the two proposed modules (CTCR and WDL) to analyze their benefits to performance.
Revised: The Effectiveness of CTCR and WDL We also perform ablation studies on the two proposed modules (CTCR and WDL) to analyze their benefits to performance.

Original: We take “MAPPO” as the baseline for comparison, which is our method but trained instead by a shared global reconstruction reward and the absence of any world dynamics modeling.
Revised: We take “MAPPO” as the baseline for comparison, which is our method but trained instead by a shared global reconstruction reward and the absence of any world dynamics modeling.

Original: Fig.
Revised: Fig.

Original: 5 shows the consistent performance gap between the “MAPPO” baseline and our methods (MAPPO + CTCR).
Revised: 5 shows the consistent performance gap between the “MAPPO” baseline and our methods (MAPPO + CTCR).

Original: This explains the increasing difficulty in credit assignments with more cameras.
Revised: This explains the increasing difficulty in credit assignments with more cameras.

Original: The proposed CTCR mitigates such an issue  by computing the weighted marginal contribution of each camera.
Revised: The proposed CTCR mitigates such an issue [Figure] [Figure] by computing the weighted marginal contribution of each camera.

Original: Also, CTCR promotes faster convergence.
Revised: Also, CTCR promotes faster convergence.

Original: Training curves are shown in Appendix Fig.
Revised: Training curves are shown in Appendix Fig.

Original: Training with WDL objectives further improves the MPJPE metric for our 2-Camera model by approx.
Revised: Training with WDL objectives further improves the MPJPE metric for our 2-Camera model by approx.

Original: However, its supporting effect[Figure] [Figure] gradually weakens with the increasing number of cameras.
Revised: However, its supporting effect gradually weakens with the increasing number of cameras.

Original: We argue that is caused by the more complex dynamics involved with more cameras simultaneously interacting in the same environment.
Revised: We argue that is caused by the more complex dynamics involved with more cameras simultaneously interacting in the same environment.

Original: Notably, we observe that the agents trained with WDL are of better generalization in unseen scenes, as shown in Fig.
Revised: Notably, we observe that the agents trained with WDL are of better generalization in unseen scenes, as shown in Fig.

Original: Ablation Study within the WDL Objectives We perform a detailed ablation study regarding the effect of each WDL sub-task on the model performance.
Revised: Ablation Study within the WDL Objectives We perform a detailed ablation study regarding the effect of each WDL sub-task on the model performance.

Original: As shown in Fig.
Revised: As shown in Fig.

Original: 6, we can observe that the MPJPE metric gradually decreases as we incorporate more WDL losses.
Revised: 6, we can observe that the MPJPE metric gradually decreases as we incorporate more WDL losses.

Original: This aligns with our assumptions that training the model with world dynamics learning objectives will promote the model’s ability to capture a better representation of future states, which in turn increases performance.
Revised: This aligns with our assumptions that training the model with world dynamics learning objectives will promote the model’s ability to capture a better representation of future states, which in turn increases performance.

Original: Our method (full, + RLPred + TgtPred + PdPred + Merge) additionally demonstrates the importance of incorporating information regarding the target’s future state into the encoder’s output features.
Revised: Our method (full, + RLPred + TgtPred + PdPred + Merge) additionally demonstrates the importance of incorporating information regarding the target’s future state into the encoder’s output features.

Original: Predicting the target’s future states should not only be used as an auxiliary task but should also directly influence the inference process of the actor model.
Revised: Predicting the target’s future states should not only be used as an auxiliary task but should also directly influence the inference process of the actor model.

Original: Moreover, “Ours” method suffers less performance drop from increasing the number of pedestrians.
Revised: Moreover, “Ours” method suffers less performance drop from increasing the number of pedestrians.

Original: In contrast, the accuracy of the baselines drops dramatically as the number of pedestrians increases.
Revised: In contrast, the accuracy of the baselines drops dramatically as the number of pedestrians increases.

Original: We argue that the proposed WDL objectives can improve the model’s generalizability.
Revised: We argue that the proposed WDL objectives can improve the model’s generalizability.

Original: Versus Other Active Methods To show the effectiveness of the learned policies, we further compare our method with other active multi-camera formation control methods in 3-cameras BlankEnv.
Revised: Versus Other Active Methods To show the effectiveness of the learned policies, we further compare our method with other active multi-camera formation control methods in 3-cameras BlankEnv.

Original: (1) “MAPPO” (Yu et al., 2021) and (2) AirCapRL (Tallamraju et al., 2020) are two learningbased methods, built on PPO (Schulman et al., 2017).
Revised: (1) “MAPPO” (Yu et al., 2021) and (2) AirCapRL (Tallamraju et al., 2020) are two learningbased methods, built on PPO (Schulman et al., 2017).

Original: The main difference between these two methods is the reward shaping technique, i.e ., AirCapRL additionally employs multiple carefullydesigned rewards (Tallamraju et al., 2020) for learning.
Revised: The main difference between these two methods is the reward shaping technique, i.e ., AirCapRL additionally employs multiple carefullydesigned rewards (Tallamraju et al., 2020) for learning.

Original: We also program a (3) rule-based fixed formation control method (keeping an equilateral triangle, spread by 120 ◦ ) to track and surround the target person.
Revised: We also program a (3) rule-based fixed formation control method (keeping an equilateral triangle, spread by 120 ◦ ) to track and surround the target person.

Original: Results are shown in Table 1.
Revised: Results are shown in Table 1.

Original: Interestingly, these three baselines achieve similar  reconstruction performance.
Revised: Interestingly, these three baselines achieve similar [Figure] reconstruction performance.

Original: Our method notably outperforms them, indicating a more effective multicamera collaboration strategy for 3D HPE.
Revised: Our method notably outperforms them, indicating a more effective multicamera collaboration strategy for 3D HPE.

Original: For example, our method learns a spatially spread-out formation while automatically adjusting to avoid impending occlusion.
Revised: For example, our method learns a spatially spread-out formation while automatically adjusting to avoid impending occlusion.

Original: [Figure]

Original: Generalize to Various Scenarios We train the control policies in BlankEnv while testing them in three other realistic environments (SchoolGym, UrbanStreet, and Wilderness) to evaluate their generalization capability in unseen scenarios.
Revised: Generalize to Various Scenarios We train the control policies in BlankEnv while testing them in three other realistic environments (SchoolGym, UrbanStreet, and Wilderness) to evaluate their generalization capability in unseen scenarios.

Original: Fig.
Revised: Fig.

Original: 7 shows that our method consistently outperforms baseline methods with lower variance in MPJPE during the evaluations in three test environments.
Revised: 7 shows that our method consistently outperforms baseline methods with lower variance in MPJPE during the evaluations in three test environments.

Original: Note that we report the results in the BlankEnv as a reference.
Revised: Note that we report the results in the BlankEnv as a reference.

Original: Qualitative Analysis In Figure 8, we show six examples of the emergent camera formations under our trained policies using the proposed method (CTCR + WDL).
Revised: Qualitative Analysis In Figure 8, we show six examples of the emergent camera formations under our trained policies using the proposed method (CTCR + WDL).

Original: The camera agents learn to spread out and ascent above humans to avoid occlusions and collision.
Revised: The camera agents learn to spread out and ascent above humans to avoid occlusions and collision.

Original: Their placements in an emergent formation are not assigned by other entities but rather determined by the decentralized control policies themselves based on observations.
Revised: Their placements in an emergent formation are not assigned by other entities but rather determined by the decentralized control policies themselves based on observations.

Original: For more vivid examples of emergent formations, please refer to the project website for the demo videos.
Revised: For more vivid examples of emergent formations, please refer to the project website for the demo videos.

Revised: 2 For more analysis on the behavior mode of the our 3-, 4and 5-camera models, please refer to Appendix Section H.

Original:  C ONCLUSION AND D ISCUSSION
Revised:  C ONCLUSION AND D ISCUSSION

Original: To the best of our knowledge, this paper presents the first active multi-camera system targeting the 3 D reconstruction in a dynamic crowd.
Revised: To the best of our knowledge, this paper presents the first active multi-camera system targeting the 3 D reconstruction in a dynamic crowd.

Original: It is also the first study regarding active 3D HPE that promptly experimented with multi-camera collaborations at different scales and scenarios.
Revised: It is also the first study regarding active 3D HPE that promptly experimented with multi-camera collaborations at different scales and scenarios.

Original: We propose CTCR to alleviate the multi-agent credit assignment issue when the camera team scales and identifies multiple auxiliary tasks that are helpful for representation learning of complex dynamics.
Revised: We propose CTCR to alleviate the multi-agent credit assignment issue when the camera team scales and identifies multiple auxiliary tasks that are helpful for representation learning of complex dynamics.

Original: As a final note, we have decided to open-source our UE4 virtual environment and the visualization software.
Revised: As a final note, we have decided to open-source our UE4 virtual environment and the visualization software.

Original: Limitation Admittedly, a couple of aspects of this work have room for improvement.
Revised: Limitation Admittedly, a couple of aspects of this work have room for improvement.

Original: Firstly, the camera agents received the positions for their teammates via non-disrupting broadcasts of information, which may be prone to packet losses during deployment.
Revised: Firstly, the camera agents received the positions for their teammates via non-disrupting broadcasts of information, which may be prone to packet losses during deployment.

Original: One idea is to incorporate a specialized protocol for multi-agent communication into our pipeline, such as TarMAC (Das et al., 2019),
Revised: One idea is to incorporate a specialized protocol for multi-agent communication into our pipeline, such as TarMAC (Das et al., 2019),

Original: I2C (Ding et al., 2020), or ToM2C(Wang et al., 2022).
Revised: I2C (Ding et al., 2020), or ToM2C(Wang et al., 2022).

Original: Secondly, intended initially to reduce the communication bandwidth (for example, to eliminate the need for image transmission between cameras), the current pipeline comprises a Human Re-Identification module requiring a pre-scan memory on all to-be-appeared human subjects.
Revised: Secondly, intended initially to reduce the communication bandwidth (for example, to eliminate the need for image transmission between cameras), the current pipeline comprises a Human Re-Identification module requiring a pre-scan memory on all to-be-appeared human subjects.

Original: For some out-of-distribution humans’ appearances, the current ReID module may not be able to recognize.
Revised: For some out-of-distribution humans’ appearances, the current ReID module may not be able to recognize.

Original: Though A CTIVE 3DP OSE can accommodate a more sophisticated ReID module to resolve this shortcoming.
Revised: Though A CTIVE 3DP OSE can accommodate a more sophisticated ReID module to resolve this shortcoming.

Original: Lastly, we assume near-perfect calibrations for a group of active and mobile cameras, which is difficult to sustain in practice.
Revised: Lastly, we assume near-perfect calibrations for a group of active and mobile cameras, which is difficult to sustain in practice.

Original:  E THICS D ISCUSSION
Revised:  E THICS D ISCUSSION

Original: There are many great benefits brought by the advances in active 3D HPE technologies, for example, biomechanical analysis in sports and automated video-assisted coach (AVAC).
Revised: There are many great benefits brought by the advances in active 3D HPE technologies, for example, biomechanical analysis in sports and automated video-assisted coach (AVAC).

Original: However in reality, misusing these technologies through repressive surveillance may lead to privacy infringements and human rights violations.
Revised: However in reality, misusing these technologies through repressive surveillance may lead to privacy infringements and human rights violations.

Original: We condemn these malicious acts and advocate fair uses of our virtual environment U NREAL P OSE and all other 3D HPE technologies.
Revised: We condemn these malicious acts and advocate fair uses of our virtual environment U NREAL P OSE and all other 3D HPE technologies.

Original: For maximum safety compliance in the experiments involving human-machine interactions, we have introduced safety-related features to minimize the probability of collision (Appendix Section F).
Revised: For maximum safety compliance in the experiments involving human-machine interactions, we have introduced safety-related features to minimize the probability of collision (Appendix Section F).

Original:  R EPRODUCIBILITY S TATEMENT
Revised:  R EPRODUCIBILITY S TATEMENT

Original: We will publicly release the project upon official publishing of this work.
Revised: We will publicly release the project upon official publishing of this work.

Original: The release will include the
Revised: The release will include the

Original: U NREAL P OSE environment, RL LIB training scripts, and the visualization tool.
Revised: U NREAL P OSE environment, RL LIB training scripts, and the visualization tool.

Original: The UE4 binaries and the pre-trained models used in our experiments will also be available for download.
Revised: The UE4 binaries and the pre-trained models used in our experiments will also be available for download.

Original: The RL LIB library is specifically chosen as the base architecture of the implementation of our MARL algorithm.
Revised: The RL LIB library is specifically chosen as the base architecture of the implementation of our MARL algorithm.

Original: This is to ensure cross-platform compatibility, scalability, maintainability and transparency.
Revised: This is to ensure cross-platform compatibility, scalability, maintainability and transparency.

Original: B U NREAL P OSE : A CCESSORIES AND M ISCELLANEOUS I TEMS
Revised: B U NREAL P OSE : A CCESSORIES AND M ISCELLANEOUS I TEMS

Original: Our UnrealPose virtual environment supports different active vision tasks, such as active human pose estimation and active tracking.
Revised: Our UnrealPose virtual environment supports different active vision tasks, such as active human pose estimation and active tracking.

Original: This environment also supports various settings ranging from single-target single-camera settings to multi-target multi-camera settings.
Revised: This environment also supports various settings ranging from single-target single-camera settings to multi-target multi-camera settings.

Original: Here we provide a more detailed description of the three key characteristics of UnrealPose:
Revised: Here we provide a more detailed description of the three key characteristics of UnrealPose:

Original: Realistic The built-in navigation system governs the collision avoidance movements of virtual humans against dynamic obstacles.
Revised: Realistic The built-in navigation system governs the collision avoidance movements of virtual humans against dynamic obstacles.

Original: In the meantime, it also ensures diverse generations of walking trajectories.
Revised: In the meantime, it also ensures diverse generations of walking trajectories.

Original: These features enable the users to simulate a realistic-looking crowd exhibiting socially acceptable behaviors.
Revised: These features enable the users to simulate a realistic-looking crowd exhibiting socially acceptable behaviors.

Original: We have also provided several pre-set scenes, e.g ., school gym, wilderness, urban crossing, and etc .
Revised: We have also provided several pre-set scenes, e.g ., school gym, wilderness, urban crossing, and etc .

Original: These scenes have notable differences in illuminations, terrains, and crowd appearances to reflect the dramatically different-looking scenarios in real-life.
Revised: These scenes have notable differences in illuminations, terrains, and crowd appearances to reflect the dramatically different-looking scenarios in real-life.

Original: Extensive Configuration
Revised: Extensive Configuration

Original: The environment can be configured with different numbers of humans and cameras and swapped across other scenarios with ease, which we demonstrated in Fig 4(a-d).
Revised: The environment can be configured with different numbers of humans and cameras and swapped across other scenarios with ease, which we demonstrated in Fig 4(a-d).

Original: Besides simulating walking human crowds, the environment incorporates over 100 Mocap action sequences with smooth animation interpolations to enrich the data variety for other MoCap tasks.
Revised: Besides simulating walking human crowds, the environment incorporates over 100 Mocap action sequences with smooth animation interpolations to enrich the data variety for other MoCap tasks.

Original: RL-Ready We use the UnrealCV (Qiu et al., 2017) plugin as the medium to acquire images and annotations from the environment.
Revised: RL-Ready We use the UnrealCV (Qiu et al., 2017) plugin as the medium to acquire images and annotations from the environment.

Original: The original UnrealCV plugin suffers from unstable data transfer and unexpected disconnections under high CPU workloads.
Revised: The original UnrealCV plugin suffers from unstable data transfer and unexpected disconnections under high CPU workloads.

Original: To ensure fast and reliable data acquisition for large-scale MARL experiments, we overhauled the communication module in the UnrealCV plugin with inter-process communication (IPC) mechanism, which eliminates the aforementioned instabilities.
Revised: To ensure fast and reliable data acquisition for large-scale MARL experiments, we overhauled the communication module in the UnrealCV plugin with inter-process communication (IPC) mechanism, which eliminates the aforementioned instabilities.

Original: B. V ISUALIZATION T OOL
Revised: B. V ISUALIZATION T OOL

Original: We provide a visualization tool to facilitate per-frame analysis of the learned policy and reconstruction results (shown in Fig. 9).
Revised: We provide a visualization tool to facilitate per-frame analysis of the learned policy and reconstruction results (shown in Fig. 9).

Original: The main interface consists of four parts: (1) Live 2D views from all cameras.
Revised: The main interface consists of four parts: (1) Live 2D views from all cameras.

Original: (2) 3D spatial view of camera positions and reconstructions.
Revised: (2) 3D spatial view of camera positions and reconstructions.

Original: (3) Plot of statistics.
Revised: (3) Plot of statistics.

Original: (4) Frame control bar.
Revised: (4) Frame control bar.

Original: This visualization tool supports different numbers of humans and cameras.
Revised: This visualization tool supports different numbers of humans and cameras.

Original: Meanwhile, it is written in Python to support easy customization.
Revised: Meanwhile, it is written in Python to support easy customization.

Original: B. L ICENSE
Revised: B. L ICENSE

Original: All assets used in the environment are commercially-available and obtained from the UE4 Marketplace.
Revised: All assets used in the environment are commercially-available and obtained from the UE4 Marketplace.

Original: The environment and tools developed in this work are licensed under Apache License 2.0.
Revised: The environment and tools developed in this work are licensed under Apache License 2.0.

Original: C O BSERVATION P ROCESSING
Revised: C O BSERVATION P ROCESSING

Original: Fig.10 shows the pipeline of the observation processing.
Revised: Fig.10 shows the pipeline of the observation processing.

Original: Each camera observes an RGB image and detects the 2 D human poses and IDs via the Perception Module described in the main paper.
Revised: Each camera observes an RGB image and detects the 2 D human poses and IDs via the Perception Module described in the main paper.

Original: The camera pose, 2 D human poses and IDs are then broadcast to other cameras for multi-view 3 D triangulation.
Revised: The camera pose, 2 D human poses and IDs are then broadcast to other cameras for multi-view 3 D triangulation.

Original: The human position is calculated as the median of the reconstructed joints.
Revised: The human position is calculated as the median of the reconstructed joints.

Original: Human orientation is calculated from the cross product of the reconstructed shoulder and spine.
Revised: Human orientation is calculated from the cross product of the reconstructed shoulder and spine.

Original: D I MPLEMENTATION D ETAILS D. T RAINING D ETAILS
Revised: D I MPLEMENTATION D ETAILS D. T RAINING D ETAILS

Original: All control policies are trained in the BlackEnv scene.
Revised: All control policies are trained in the BlackEnv scene.

Original: At the testing stage, we apply zeroshot transfer for the learned policies to three realistic scenes: SchoolGym , UrbanStreet , and
Revised: At the testing stage, we apply zeroshot transfer for the learned policies to three realistic scenes: SchoolGym , UrbanStreet , and

Original: Wilderness .
Revised: Wilderness .

Original: To simulate a dynamic human crowd that performs high random behaviors, we sample arbitrary goals for each human and employ the built-in navigation system to generate collision-free trajectories.
Revised: To simulate a dynamic human crowd that performs high random behaviors, we sample arbitrary goals for each human and employ the built-in navigation system to generate collision-free trajectories.

Original: Each human walks at a random speed.
Revised: Each human walks at a random speed.

Original: To ensure the generalization across a different number of humans, we train our RL policy with a mixture of environments of 1 to 6 humans.
Revised: To ensure the generalization across a different number of humans, we train our RL policy with a mixture of environments of 1 to 6 humans.

Original: The learning rate is set to 5 × 10 − 4 with scheduled decay during the training phase.
Revised: The learning rate is set to 5 × 10 − 4 with scheduled decay during the training phase.

Original: The annealing schedule for the learning rate is detailed in Table.
Revised: The annealing schedule for the learning rate is detailed in Table.

Original: The maximum episode length is 500 steps, discounted factor γ is 0 .and
Revised: The maximum episode length is 500 steps, discounted factor γ is 0 .and

Original: the GAE horizon is 25 steps.
Revised: the GAE horizon is 25 steps.

Original: Each sampling iteration produces a training batch with the size of 1 , 500 steps, then we perform 16 iterations on every training batch with 4 SGD mini-batch updates for each iteration.
Revised: Each sampling iteration produces a training batch with the size of 1 , 500 steps, then we perform 16 iterations on every training batch with 4 SGD mini-batch updates for each iteration.

Original: Table.
Revised: Table.

Original: 2 shows the common training hyper-parameters shared between the baseline models (MAPPO) and all of our methods.
Revised: 2 shows the common training hyper-parameters shared between the baseline models (MAPPO) and all of our methods.

Original: Table.
Revised: Table.

Original: 4 shows the hyperparameters for the WDL module.
Revised: 4 shows the hyperparameters for the WDL module.

Original: [Table]
Revised: [Table]

Original: Rate
Revised: Rate

Original: [Table]
Revised: [Table]

Original: lr
Revised: lr

Original: [Table]
Revised: [Table]

Original: ) [(0, 5E-4), (200E3, 5E-4), (200E3, 1E-4), (400E3, 1E4), (600E3, 5E-5), (600E3, 5E-5)]
Revised: ) [(0, 5E-4), (200E3, 5E-4), (200E3, 1E-4), (400E3, 1E4), (600E3, 5E-5), (600E3, 5E-5)]

Original: [Table]
Revised: [Table]

Original: Size
Revised: Size

Original: [Table]
Revised: [Table]

Original: Layers [128, 128, 128]
Revised: Layers [128, 128, 128]

Original: Value Network Hidden Layers [128]
Revised: Value Network Hidden Layers [128]

Original: Actor Network Hidden Layers [128]
Revised: Actor Network Hidden Layers [128]

Original: D. D IMENSIONS OF F EATURE T ENSORS IN THE C ONTROLLER M ODULE
Revised: D. D IMENSIONS OF F EATURE T ENSORS IN THE C ONTROLLER M ODULE

Original: Table 3 serves as a complementary description for Eqn. 1, 2, 3, 4.
Revised: Table 3 serves as a complementary description for Eqn. 1, 2, 3, 4.

Original: The table shows the dimensions of the feature tensors used in the controller module.
Revised: The table shows the dimensions of the feature tensors used in the controller module.

Original: “B” denotes the batch size.
Revised: “B” denotes the batch size.

Original: In the current model design, the dimension of local observation is adjusted based on the maximum number of camera agents ( N _ cam max ) and the maximum number of observable humans ( N _ human max ) in an environment.
Revised: In the current model design, the dimension of local observation is adjusted based on the maximum number of camera agents ( N _ cam max ) and the maximum number of observable humans ( N _ human max ) in an environment.

Original: In our experiments, N _ human max has been set to 7.
Revised: In our experiments, N _ human max has been set to 7.

Original: The observation pre-processor will zero-pad each observation to a length equal N _ human max × 18 if the current environment instance has less than N _ human max humans.
Revised: The observation pre-processor will zero-pad each observation to a length equal N _ human max × 18 if the current environment instance has less than N _ human max humans.

Original: “9” and “18” correspond to the feature length for a camera and a human, respectively.
Revised: “9” and “18” correspond to the feature length for a camera and a human, respectively.

Original: The MDN of the Target Prediction module has 16 Gaussian components, in which each component outputs ( ϕ, µ x , σ x , µ y , σ y ) and ϕ is the weight parameter of a component.
Revised: The MDN of the Target Prediction module has 16 Gaussian components, in which each component outputs ( ϕ, µ x , σ x , µ y , σ y ) and ϕ is the weight parameter of a component.

Original: The current implementation of MDN only predicts the x-y location of a human, which is a simplification since the z coordinate of a simulated human barely changes across an episode compared to the x and y coordinates.
Revised: The current implementation of MDN only predicts the x-y location of a human, which is a simplification since the z coordinate of a simulated human barely changes across an episode compared to the x and y coordinates.

Original: The dimension of an MDN output has a length of 80 and the exact prediction is produced by ϕ -weighted averaging.
Revised: The dimension of an MDN output has a length of 80 and the exact prediction is produced by ϕ -weighted averaging.

Original: In Eqn. 4, { ( ϕ, µ, σ ) } MDN tgt is an encoded feature produced by passing the MDN output to a 2-layer MLP that has an output dimension of 128.
Revised: In Eqn. 4, { ( ϕ, µ, σ ) } MDN tgt is an encoded feature produced by passing the MDN output to a 2-layer MLP that has an output dimension of 128.

Original: [Table]
Revised: [Table]

Original: D. C OMPUTATIONAL R ESOURCES
Revised: D. C OMPUTATIONAL R ESOURCES

Original: We used 15 Ray workers for each experiment to ensure consistency in the training procedure.
Revised: We used 15 Ray workers for each experiment to ensure consistency in the training procedure.

Original: Each worker carries a Gym vectorized environment consisting of 4 actual environment instances.
Revised: Each worker carries a Gym vectorized environment consisting of 4 actual environment instances.

Original: Each worker demands approximately 3 .
Revised: Each worker demands approximately 3 .

Original: 7 GB of VRAM.
Revised: 7 GB of VRAM.

Original: We run each experiment with 8 NVIDIA RTX 2080 Ti GPUs.
Revised: We run each experiment with 8 NVIDIA RTX 2080 Ti GPUs.

Original: Depending on the number of camera agents, the total training hours required for an experiment to run 500 k steps will vary between 4 to 12 hours.
Revised: Depending on the number of camera agents, the total training hours required for an experiment to run 500 k steps will vary between 4 to 12 hours.

Original: [Table]
Revised: [Table]

Original: Hyperparameter 
Revised: Hyperparameter Our

Original: Our Methods
Revised: Methods

Original: Prediction Loss Coefficient ( λ WDL ) 1.
Revised: Prediction Loss Coefficient ( λ WDL ) 1.

Original: Camera Prediction Coefficient 1.
Revised: Camera Prediction Coefficient 1.

Original: Other Camera Prediction Coefficient 1.
Revised: Other Camera Prediction Coefficient 1.

Original: Reward Prediction Coefficient 1.
Revised: Reward Prediction Coefficient 1.

Original: Human Prediction Coefficient 1.
Revised: Human Prediction Coefficient 1.

Original: Pedestrian Prediction Coefficient 0.
Revised: Pedestrian Prediction Coefficient 0.

Original: MDN: Hidden Layers [128, 128]
Revised: MDN: Hidden Layers [128, 128]

Original: MDN: Number of Gaussian Distributions
Revised: MDN: Number of Gaussian Distributions

Original: D. T RAINING C URVE
Revised: D. T RAINING C URVE

Original: Fig.
Revised: Fig.

Original: 11 shows the training curves of our method and the baseline method.
Revised: 13 shows the training curves of our method and the baseline method.

Original: We can find that our methods converge faster and improve reconstruction accuracy than the baseline method.
Revised: We can find that our methods converge faster and improve reconstruction accuracy than the baseline method.

Revised: D. T OTAL I NFERENCE T IME

Revised: Our solution can run in real-time.

Revised: Table 5 reports the inference time for each module of the proposed

Revised: Active3DPose pipeline.

Revised: [Table]

Original: E A DDITIONAL E XPERIMENT R ESULTS E. B ASELINE — F IXED -C AMERAS
Revised: E A DDITIONAL E XPERIMENT R ESULTS E. B ASELINE — F IXED -C AMERAS

Original: In addition to the triangulation and RANSAC baselines introduced in the main text, we compare and elaborate on two more baselines that use fixed cameras: (1) fixed cameras with RANSAC-based triangulation and temporal smoothing (TS) (2) an off-shelf 3D pose estimator PlaneSweepPose (Lin & Lee, 2021a).
Revised: In addition to the triangulation and RANSAC baselines introduced in the main text, we compare and elaborate on two more baselines that use fixed cameras: (1) fixed cameras with RANSAC-based triangulation and temporal smoothing (TS) (2) an off-shelf 3D pose estimator PlaneSweepPose (Lin & Lee, 2021a).

Original: In the temporal smoothing baseline
Revised: In the temporal smoothing baseline

Original: [Table]
Revised: [Table]

Original: we applied a low-pass filter (Casiez et al., 2012) and temporal fusion where the algorithm will fill in any missing keypoints in the current frame with the detected keypoints from the last frame.
Revised: we applied a low-pass filter (Casiez et al., 2012) and temporal fusion where the algorithm will fill in any missing keypoints in the current frame with the detected keypoints from the last frame.

Original: In the PlaneSweep baseline, as per the official instructions
Revised: In the PlaneSweep baseline, as per the official instructions

Original: [Table]
Revised: [Table]

Original: we train three separate models (3 cams to 5 cams) with the same camera setup as in our testing scenarios.
Revised: we train three separate models (3 cams to 5 cams) with the same camera setup as in our testing scenarios.

Original: We have tested the trained models in different scenarios and reported the MPJPE results in Table5, 6, 7 and 8.
Revised: We have tested the trained models in different scenarios and reported the MPJPE results in Table 6, 7, 8 and 9.

Original: Note that, this off-shelf pose estimator performs better than the Fixed-Camera Baseline (Triangulation) but still underperforms compared to our active method.
Revised: Note that, this off-shelf pose estimator performs better than the Fixed-Camera Baseline (Triangulation) but still underperforms compared to our active method.

Original: Fig.
Revised: Fig.

Original: 12 illustrates the formations of the fixed camera baselines.
Revised: 12 illustrates the formations of the fixed camera baselines.

Original: [Table] [Table]
Revised: [Table] [Table]

Original: [Table] [Table]
Revised: [Table] [Table]

Original: Camera placements for all fixed-camera baselines are shown in Fig.
Revised: Camera placements for all fixed-camera baselines are shown in Fig.

Original: These formations are carefully designed not to disadvantage the fixed-camera baselines on-purpose.
Revised: These formations are carefully designed not to disadvantage the fixed-camera baselines on-purpose.

Original: Especially for the 5-cameras pentagon formation, which helps the fixed-camera baseline to obtain satisfactory performance on the 5-camera setting as shown in Tables 5,6,7 and 
Revised: Especially for the 5-cameras pentagon formation, which helps the fixed-camera baseline to obtain satisfactory performance on the 5-camera setting as shown in Tables 6,7,8 and 9. [Figure] [Figure]

Original: [Figure]
Revised: [Table]

Revised: E. O UR M ETHOD E NHANCED WITH RANSAC- BASED T RIANGULATION

Original: RANSAC is a generic technique that can be used to improve triangulation performance.
Revised: RANSAC is a generic technique that can be used to improve triangulation performance.

Original: In this experiment, we also train and test our model with RANSAC.
Revised: In this experiment we also train and test our model with RANSAC.

Original: The final result (Table 9) shows a further improvement on our original triangulation version [Equation] [Equation]
Revised: The final result (Table 11) shows a further improvement on our original triangulation version.

Original: [Equation]
Revised: [Table]

Original: F G ENERATING S AFE AND S MOOTH T RAJECTORIES F. C OLLISION A VOIDANCE
Revised: F G ENERATING S AFE AND S MOOTH T RAJECTORIES F. C OLLISION A VOIDANCE

Original: In order to generate safe trajectories, in this section, we introduce and evaluate two different ways to enforce collision avoidance between cameras and humans.
Revised: In order to generate safe trajectories, in this section, we introduce and evaluate two different ways to enforce collision avoidance between cameras and humans.

Original: Obstacle Collision Avoidance (OCA)
Revised: Obstacle Collision Avoidance (OCA)

Original: OCA resembles a feed-forward PID controller on the final control outputs before execution.
Revised: OCA resembles a feed-forward PID controller on the final control outputs before execution.

Original: Concretely, OCA adds a constant reverse quantity to the control output if it detects any surrounding objects within its safety range.
Revised: Concretely, OCA adds a constant reverse quantity to the control output if it detects any surrounding objects within its safety range.

Original: This “detouring” mechanism safeguards the cameras from possible collisions and prevents them from making dangerous maneuvers.
Revised: This “detouring” mechanism safeguards the cameras from possible collisions and prevents them from making dangerous maneuvers.

Original: Action-Masking (AM) AM also resembles a feed-forward controller but is instead embedded into the forward step of the deep-learning model.
Revised: Action-Masking (AM) AM also resembles a feed-forward controller but is instead embedded into the forward step of the deep-learning model.

Original: At each step, AM module first identifies the dangerous actions among all possible actions, then modifies the probabilities (output by the policy model) of choosing the hazardous actions to be zero so that the learning-based control policy will never pick them.
Revised: At each step, AM module first identifies the dangerous actions among all possible actions, then modifies the probabilities (output by the policy model) of choosing the hazardous actions to be zero so that the learning-based control policy will never pick them.

Original: Note that AM must be trained with the MARL policy model.
Revised: Note that AM must be trained with the MARL policy model.

Original: We proposed the minimum Camera-Human distance (in which the scope includes the target and the pedestrians) as the safety metric.
Revised: We proposed the minimum Camera-Human distance (in which the scope includes the target and the pedestrians) as the safety metric.

Original: It measures the distance between the closest human and the camera at a timestep.
Revised: It measures the distance between the closest human and the camera at a timestep.

Original: Fig.
Revised: Fig.

Original: 13 shows the histograms of Min Camera-Human distance sampled over five episodes of 500 steps.
Revised: 14 shows the histograms of Min Camera-Human distance sampled over five episodes of 500 steps.

Original: F. T RAJECTORY S MOOTHING
Revised: F. T RAJECTORY S MOOTHING

Original: Exponential Moving Average (EMA)
Revised: Exponential Moving Average (EMA)

Original: To generate smooth trajectories, we introduce EMA to smooth the outputs of our learned policy model.
Revised: To generate smooth trajectories, we introduce EMA to smooth the outputs of our learned policy model.

Original: EMA is a common technique used in smoothing time-series data.
Revised: EMA is a common technique used in smoothing time-series data.

Original: In our case, the smoothing operator is defined as :
Revised: In our case, the smoothing operator is defined as :

Original: [Equation]
Revised: [Equation]

Original: Where a t is the action (or control signal) output by the model at the current step, ˆ a t − 1 is the smoothed action from the last step and η is the smoothing factor.
Revised: Where a t is the action (or control signal) output by the model at the current step, ˆ a t − 1 is the smoothed action from the last step and η is the smoothing factor.

Original: A smaller η results in greater smoothness.
Revised: A smaller η results in greater smoothness.

Original: ˆ a t is the smoothed action that the camera will execute.
Revised: ˆ a t is the smoothed action that the camera will execute.

Original: F. R OBUSTNESS OF THE L EARNED P OLICY
Revised: F. R OBUSTNESS OF THE L EARNED P OLICY

Original: In this section, we evaluate the robustness of our model on different external perturbations to the control signal.
Revised: In this section, we evaluate the robustness of our model on different external perturbations to the control signal.

Original: In conclusion, our model shows resilience against the delay effect and random noise.
Revised: In conclusion, our model shows resilience against the delay effect and random noise.

Original: Delay EMA also brings a delay effect while smoothing the generated trajectory.
Revised: Delay EMA also brings a delay effect while smoothing the generated trajectory.

Original: The level of smoothing positively correlates with a larger delay factor.
Revised: The level of smoothing positively correlates with a larger delay factor.

Original: Here, we evaluate our model’s robustness to the EMA simulated delay.
Revised: Here, we evaluate our model’s robustness to the EMA simulated delay.

Original: Random Action Noise Control devices in real-life are inevitably affected by errors.
Revised: Random Action Noise Control devices in real-life are inevitably affected by errors.

Original: For example, the control signal of a controller may be over-damped or may overshoot.
Revised: For example, the control signal of a controller may be over-damped or may overshoot.

Original: We simulated this type of random error by multiplying the output action by a uniformly-sampled noise.
Revised: We simulated this type of random error by multiplying the output action by a uniformly-sampled noise.

Original: In Table 10, we intend to observe the effects of EMA delay and random action noise on the reconstruction accuracy of our model, marked as “Vanilla”.
Revised: In Table 12, we intend to observe the effects of EMA delay and random action noise on the reconstruction accuracy of our model, marked as “Vanilla”.

Original: [Table]
Revised: [Table]

Revised: G M ORE E XPLANATIONS ON CTCR

Revised: Figure 3 is an example of how to plug numbers into Eq.

Revised: 6 to compute CTCR for each of the three cameras.

Revised: There is a breakdown of Eq.

Revised: 6 just below it.

Revised: But just in case if it seems too obscure, here is a more intuitive description of Eq.

Revised: The CTCR is incentivized by the Shapley Value, so the main idea is that the overall optimality needs to also account for the optimality of every possible sub-formation.

Revised: In the context of an active HPE task, for a camera agent to receive the highest CTCR possible, its current position and view must be optimal both in terms of its current formation and any sub-formation possible.

Revised: Note: Game theory folks like to call a group of collaborating players a “coalition”.

Revised: Here we apply the same concept but to a group of cameras, so we used the more initiative term “formation” instead.

Revised: Eq.

Revised: 6 can be further breakdown as follows:

Revised: [Equation]

Revised: where [ n ] = 1 , r ( S ) computes the reconstruction accuracy of the formation S .

Revised: And [ r ( S ∪ { i } ) − r ( S )] computes the marginal improvement after adding the camera i to sub-formation S .

Revised: So this equation means we iterate over all possible S and compute the marginal contribution of camera i and average over all possible combinations of ( S, i ) .

Revised: Suppose we have a 3-cameras formation, similarly shown in Figure 3.

Revised: So n = 3 , the number of cameras.

Revised: Let’s name these cameras (1,2,3), and let’s say we only care about Camera 1 for now.

Revised: Since we are computing the average marginal contribution for Camera 1, we are looking for those formations that do not have Camera 1 because we want to see how much of an increase in performance resulted from the addition of Camera 1 to those formations.

Revised: For all possible formations denoted by the set [ n ] , four formations satisfy this condition, S ⊆

Revised: [ n ] \ { i } −→ S ∈ ( ∅ , 2 , 3 , 23) .

Revised: The binomial coefficient (cid:0) n − 1 | S | (cid:1) for a 2-camera sub-formation in a 3-cameras case is (cid:0) 22 (cid:1) , which makes sense because there exists only one unique combination that does not contain Camera 1, which is sub-formation 23 .

Revised: r (23) computes the reconstruction accuracy of the formation 23 and r (23 ∪ { 1 } ) computes the reconstruction accuracy after adding Camera 1 to sub-formation 23 .

Revised: Their difference gives us the marginal contribution of Camera 1.

Revised: As we sum over all subsets S of [ n ] not containing

Revised: Camera 1, and then divide by (cid:0) n − 1 | S | (cid:1) and the number of cameras n , we have the average marginal contribution of Camera 1 ( φ r (1)) to the collaborative triangulated reconstruction.

Revised: Further multiplying this term by n , you have the CTCR 1 as shown in Eq.

Revised: H A NALYSIS ON THE MODE OF BEHAVIOR OF THE PROPOSED METHODS

Revised: Here in Figure 15 we provide statistics and analysis on the behaviour mode of the agents controlled by our 3-, 4- and 5-camera policies, respectively.

Revised: We are interested in understanding the characteristics of the emergent formations learned by our model.

Revised: Hence we proposed three quantitative measures to understand the topology of the emergent formations: (1) the min-angle between the cameras’ orientation and the per-frame-mean of the min-camera angle, (2) the camera’s pitch angle, and (3) the camera-human distance.

Revised: Hence we provide rigorous definitions as follows:

Revised: [Equation]

Revised: -frame

Revised: [Equation]

Revised: of

Revised: [Equation]

Revised: camera

Revised: [Equation]

Revised: In simpler terms, min-camera angle( i ) finds the minimum angle between camera i and any other camera j .

Revised: “per-frame-mean of min-camera angle” is the mean of min-camera angle( i ) for all camera i in one frame.

Revised: A positive camera’s pitch angle means looking upward, and a negative camera’s pitch angle means looking downward.

Revised: The camera-human distance measures the distance between the target human and the given camera.

Revised: Regarding the distance between cameras and humans, the camera agents actively adjust their position relative to the target human.

Revised: The cameras learn to keep a camera-human distance between 2m and 3m. It is neither too distant from the target human nor too close, violating the safety constraint.

Revised: The camera agents surround the target at an appropriate distance to have a better resolution on the 2D views.

Revised: In the meantime, as the safe-distance constraint is enforced during training, the camera agents are prohibited from aggressively minimizing the camera-human distance.

Revised: The histograms for the camera’s pitch angle suggest that the cameras mostly maintain negative pitch angles.

Revised: Their preferred strategy is to hover over the humans and capture images at a higher altitude.

Revised: This is likely because of emergent occlusion avoidance.

Revised: The cameras also emerge to fly at an even level with the humans (where the pitch angle approximately equals 0) to capture more accurate 2D poses of the target human.

Revised: This propensity is apparent from the peaks at x=0 angles in the histograms.

Revised: A relatively wide distribution of the pitch angle histogram suggests that the camera formation is spread out in the 3D space and dynamic adjustments of flying heights and pitch angles by the camera agents.

Revised: For the average angle between the cameras’ orientations, this statistic shows that the cameras in various formations will maintain reasonable non-zero spatial angles between each other.

Revised: Therefore, their camera views are less likely to coincide and provide more diverse perspectives to generate a more reliable 3D triangulation.

Revised: [Figure]