Original: On Coordinate Decoding for Keypoint Estimation Tasks
Revised: On Coordinate Decoding for Keypoint Estimation Tasks

Original: Anonymous Author(s)
Revised: Anonymous Author(s)

Original: AfﬁliationAddress email
Revised: AfﬁliationAddress email

Original:  Scope of Reproducibility
Revised:  Scope of Reproducibility

Original: A series of 2D (and 3D) keypoint estimation tasks are built upon heatmap coordinate representation, i.e. a probabilitymap that allows for learnable and spatially aware encoding and decoding of keypoint coordinates on grids, even allowingfor sub-pixel coordinate accuracy.
Revised: A series of 2D (and 3D) keypoint estimation tasks are built upon heatmap coordinate representation, i.e. a probabilitymap that allows for learnable and spatially aware encoding and decoding of keypoint coordinates on grids, even allowingfor sub-pixel coordinate accuracy.

Original: In this report, we aim to reproduce the ﬁndings of DARK [1] that investigated the 2Dheatmap representation by highlighting the importance of the encoding of the ground truth heatmap and the decoding ofthe predicted heatmap to keypoint coordinates.
Revised: In this report, we aim to reproduce the ﬁndings of DARK [1] that investigated the 2Dheatmap representation by highlighting the importance of the encoding of the ground truth heatmap and the decoding ofthe predicted heatmap to keypoint coordinates.

Original: The authors claim that a) a more principled distribution-aware coordinatedecoding method overcomes the limitations of the standard techniques widely used in the literature, and b) , that thereconstruction of heatmaps from ground-truth coordinates by generating accurate and continuous (non-quantized)heatmap distributions lead to unbiased model training, contrary to the standard coordinate encoding process thatquantizes the keypoint coordinates on the resolution of the input image grid.
Revised: The authors claim that a) a more principled distribution-aware coordinatedecoding method overcomes the limitations of the standard techniques widely used in the literature, and b) , that thereconstruction of heatmaps from ground-truth coordinates by generating accurate and continuous (non-quantized)heatmap distributions lead to unbiased model training, contrary to the standard coordinate encoding process thatquantizes the keypoint coordinates on the resolution of the input image grid.

Original: Methodology
Revised: Methodology

Original: To reproduce DARK, we thoroughly studied and followed the ofﬁcial implementation provided by the authors.
Revised: To reproduce DARK, we thoroughly studied and followed the ofﬁcial implementation provided by the authors.

Original: Wepartially used the publicly available code and integrated it to a model development kit to accelerate the implementationand execution of our experiments.
Revised: Wepartially used the publicly available code and integrated it to a model development kit to accelerate the implementationand execution of our experiments.

Original: We conducted the experiments on a recent human pose and depth dataset aiming tovalidate the claimed concepts on different a different setting than the one originally used and assessed.
Revised: We conducted the experiments on a recent human pose and depth dataset aiming tovalidate the claimed concepts on different a different setting than the one originally used and assessed.

Original: Our experimentswere conducted on an Nvidia 2080{+
 Ti+} 12 GB GPU with an average training time of 20 hours.
Revised: Our experimentswere conducted on an Nvidia {+
 Ti+} 12 GB GPU with an average training time of 20 hours.

Original: Results
Revised: Results

Original: We were able to reproduce the ﬁndings of the original work.
Revised: We were able to reproduce the ﬁndings of the original work.

Original: The proposed distribution-aware sub-pixel coordinatedecoding improves the keypoint estimation performance, outperforming existing, standard decoding techniques.
Revised: The proposed distribution-aware sub-pixel coordinatedecoding improves the keypoint estimation performance, outperforming existing, standard decoding techniques.

Original: Theelimination of coordinate quantization after re-scaling to the down-scaled input image resolution before the coordinateencoding (heatmap reconstruction), indeed leads to unbiased model training.
Revised: Theelimination of coordinate quantization after re-scaling to the down-scaled input image resolution before the coordinateencoding (heatmap reconstruction), indeed leads to unbiased model training.

Original: Going a step beyond, we assess theperformance of other sub-pixel decoding approaches, such as Center of Mass [2, 3], which also show increasedperformance.
Revised: Going a step beyond, we assess theperformance of other sub-pixel decoding approaches, such as Center of Mass [2, 3], which also show increasedperformance.

Original:  What was easy
Revised:  What was easy

Original: The DARK paper is well-structured and -presented aiding reproducibility.
Revised: The DARK paper is well-structured and -presented aiding reproducibility.

Original: Further, the ofﬁcial code of the paper ispublicly available, ensuring that the method and its results are reproducible.
Revised: Further, the ofﬁcial code of the paper ispublicly available, ensuring that the method and its results are reproducible.

Original: Given that DARK serves as a modelagnostic head that relies on post-inference processing only during testing, it is overall straightforward to implement andverify its effectiveness.
Revised: Given that DARK serves as a modelagnostic head that relies on post-inference processing only during testing, it is overall straightforward to implement andverify its effectiveness.

Original: What was difﬁcult
Revised: What was difﬁcult

Original: A potential issue has to do with the availability of new datasets, beyond the ones used in the paper, that providecoordinates in higher resolutions.
Revised: A potential issue has to do with the availability of new datasets, beyond the ones used in the paper, that providecoordinates in higher resolutions.

Original: Communication with original authors
Revised: Communication with original authors

Original: No communication was required, as the implementation was openly available and the veriﬁcation is straightforward.
Revised: No communication was required, as the implementation was openly available and the veriﬁcation is straightforward.

Revised: Submitted to ML Reproducibility Challenge 2020.

Revised: Do not distribute.

Original:  Introduction
Revised:  Introduction

Original: Keypoint coordinate estimation in N − dimensional grids is a common task related to a variety of computer visiondomains such as human and object pose estimation, face tracking, crowd scene analysis and beyond.
Revised: Keypoint coordinate estimation in N − dimensional grids is a common task related to a variety of computer visiondomains such as human and object pose estimation, face tracking, crowd scene analysis and beyond.

Original: For moderndata-driven methods, the heatmap representation, i.e. a N -dimensional probability distribution (Gaussian in most cases)centred at each keypoint coordinates, is considered the de facto coordinate representation for keypoint estimation.
Revised: For moderndata-driven methods, the heatmap representation, i.e. a N -dimensional probability distribution (Gaussian in most cases)centred at each keypoint coordinates, is considered the de facto coordinate representation for keypoint estimation.

Original: Heatmap representations enable the use of efﬁcient fully N -dimensional convolutional networks, learning dense spatialfeatures around the ground-truth location, and lending to a more natural way of estimation coordinates.
Revised: Heatmap representations enable the use of efﬁcient fully N -dimensional convolutional networks, learning dense spatialfeatures around the ground-truth location, and lending to a more natural way of estimation coordinates.

Original: Despite the popularity of heatmap coordinate representation, DARK is the ﬁrst research work that investigates heatmapsin depth, meaning that the authors explore and assess the standard coordinate-to-heatmap encoding and the heatmap-tocoordinate decoding techniques present in the literature, and formulate and assess a novel approach for distribution-awarecoordinate representation.
Revised: Despite the popularity of heatmap coordinate representation, DARK is the ﬁrst research work that investigates heatmapsin depth, meaning that the authors explore and assess the standard coordinate-to-heatmap encoding and the heatmap-tocoordinate decoding techniques present in the literature, and formulate and assess a novel approach for distribution-awarecoordinate representation.

Original:  Scope of reproducibility
Revised:  Scope of reproducibility

Original: We aim to reproduce the Distribution-Aware coordinate Representation of Keypoints (DARK) [1] method to assess itsbeneﬁts in keypoint coordinate estimation.
Revised: We aim to reproduce the Distribution-Aware coordinate Representation of Keypoints (DARK) [1] method to assess itsbeneﬁts in keypoint coordinate estimation.

Original: In particular, we reproduce and assess DARK in 2D human pose estimationwith the use of state-of-the-art fully convolutional networks, such as Stacked Hourglass [4] and HRNet [5], similarly tothe original work.
Revised: In particular, we reproduce and assess DARK in 2D human pose estimationwith the use of state-of-the-art fully convolutional networks, such as Stacked Hourglass [4] and HRNet [5], similarly tothe original work.

Original: A recent dataset, HUMAN4D [6], including multi-view depth data and 3D poses captured with theuse of a high-quality VICON Motion Capture [6] setup, is used to train our models from scratch.
Revised: A recent dataset, HUMAN4D [6], including multi-view depth data and 3D poses captured with theuse of a high-quality VICON Motion Capture [6] setup, is used to train our models from scratch.

Original: In a nutshell, the main claims of DARK paper, and those that we seek to validate, are summarised below:
Revised: In a nutshell, the main claims of DARK paper, and those that we seek to validate, are summarised below:

Original: • Claim #1: Efﬁcient Taylor-expansion based coordinate decoding improves coordinate estimation accuracy.
Revised: • Claim #1: Efﬁcient Taylor-expansion based coordinate decoding improves coordinate estimation accuracy.

Original: • Claim #2: Unbiased sub-pixel centred coordinate encoding results in optimal supervision and upgraded modelperformance.
Revised: • Claim #2: Unbiased sub-pixel centred coordinate encoding results in optimal supervision and upgraded modelperformance.

Original:  Methodology
Revised:  Methodology

Original: Our approach in reproducing the work was to carefully re-implement every single step of the approach, following thepresented methodology as well as studying the code of the ofﬁcial repository of the authors 1 .
Revised: Our approach in reproducing the work was to carefully re-implement every single step of the approach, following thepresented methodology as well as studying the code of the ofﬁcial repository of the authors 1 .

Original: Beyond that, the code thatwe used as is from the authors’ implementation is the Taylor-expansion based coordinate decoding.
Revised: Beyond that, the code thatwe used as is from the authors’ implementation is the Taylor-expansion based coordinate decoding.

Original: The rest of theimplementation for all our experiments was developed in a model development kit [7], oriented towards reproduction.
Revised: The rest of theimplementation for all our experiments was developed in a model development kit [7], oriented towards reproduction.

Original: The code and its documentation are submitted and published along with this report.
Revised: The code and its documentation are submitted and published along with this report.

Original: 3.1 Models
Revised: 3.1 Models

Original: Following the original paper, we selected and used the following models for predicting coordinate heatmap distributionsin images:
Revised: Following the original paper, we selected and used the following models for predicting coordinate heatmap distributionsin images:

Original: • Stacked Hourglass (SH) [4] ; with feature maps of 128 width and 4 stages and 18 output heatmap layers.• HRNet [5] ; with feature maps of 32 width and 4 stages and 18 output heatmap layers.
Revised: • Stacked Hourglass (SH) [4] ; with feature maps of 128 width and 4 stages and 18 output heatmap layers.• HRNet [5] ; with feature maps of 32 width and 4 stages and 18 output heatmap layers.

Original: The 2nd, 3rd and 4thstages contain 1 exchange block containing 4 residual units each.
Revised: The 2nd, 3rd and 4thstages contain 1 exchange block containing 4 residual units each.

Original: 3.2 Coordinate representation
Revised: 3.2 Coordinate representation

Original: 3.2.1 Coordinate decoding
Revised: 3.2.1 Coordinate decoding

Original: We consider a heatmap H j that encodes the coordinates of each j − joint 2D position as predicted by our trained models.
Revised: We consider a heatmap H j that encodes the coordinates of each j − joint 2D position as predicted by our trained models.

Original: In our experiments, we decode the coordinate from H j with 4 different decoding methods.
Revised: In our experiments, we decode the coordinate from H j with 4 different decoding methods.

Original: In the following description,
Revised: In the following description,

Original: N u and N v are the width and height of the heatmap, and p
Revised: N u and N v are the width and height of the heatmap, and p

Original: ∈ Ω represents
Revised: ∈ Ω represents

Original: a pixel coordinate in the heatmap domain Ω
Revised: a pixel coordinate in the heatmap domain Ω

Original: • ArgMax ; by directly using the maximal activation location m by:
Revised: • ArgMax ; by directly using the maximal activation location m by:

Original: [Equation] [Equation]
Revised: [Equation] [Equation]

Original: • Standard ; by slightly shifting (sub-pixel shifting)
Revised: • Standard ; by slightly shifting (sub-pixel shifting)

Original: the estimated coordinates between the maximal m andsecond maximal s activation by:
Revised: the estimated coordinates between the maximal m andsecond maximal s activation by:

Original: [Equation]
Revised: [Equation]

Original: This method constitutes one of the standard coordinate decoding techniques that predicts the maximal activation
Revised: This method constitutes one of the standard coordinate decoding techniques that predicts the maximal activation

Original: with a greedy sub-pixel shifting (0.25 pixels) towards the second maximal activation in the heatmap space Ω .
Revised: with a greedy sub-pixel shifting (0.25 pixels) towards the second maximal activation in the heatmap space Ω .

Original: • Taylor-expansion (DARK) ; exploring the distribution structure of the predicted heatmap to infer the underlying
Revised: • Taylor-expansion (DARK) ; exploring the distribution structure of the predicted heatmap to infer the underlying

Original: maximum activation assuming the predicted heatmap signal follows a 2D Gaussian distribution, similarly tothe ground-truth heatmap during supervision by:
Revised: maximum activation assuming the predicted heatmap signal follows a 2D Gaussian distribution, similarly tothe ground-truth heatmap during supervision by:

Original: [Equation]
Revised: [Equation]

Original: where D (cid:48) ( m ) and D (cid:48)(cid:48) ( m ) denote the ﬁrst and second derivative (i
Revised: where D (cid:48) ( m ) and D (cid:48)(cid:48) ( m ) denote the ﬁrst and second derivative (i

Original: e. Hessian) of the predicted heatmap afterapplying logarithmic transformation.
Revised: e. Hessian) of the predicted heatmap afterapplying logarithmic transformation.

Original: • CoM ; considering heatmap H j as a 2D grid of point masses determined by the corresponding heatmap pixelvalues, we calculate one single 2D point whose mass is the total mass of the grid by:
Revised: • CoM ; considering heatmap H j as a 2D grid of point masses determined by the corresponding heatmap pixelvalues, we calculate one single 2D point whose mass is the total mass of the grid by:

Original: [Equation]
Revised: [Equation]

Original: where ◦ denotes element-wise multiplication.
Revised: where ◦ denotes element-wise multiplication.

Original: CoM constitutes by nature a sub-pixel coordinate decodingmethod that is not evaluated in the original paper.
Revised: CoM constitutes by nature a sub-pixel coordinate decodingmethod that is not evaluated in the original paper.

Original: 3.2.2 Coordinate encoding
Revised: 3.2.2 Coordinate encoding

Original: The second claim is about coordinate encoding where the existing standard methods down-sample the original inputimages into the model input resolution, quantizing the keypoint coordinates accordingly ( w/ quant ).
Revised: The second claim is about coordinate encoding where the existing standard methods down-sample the original inputimages into the model input resolution, quantizing the keypoint coordinates accordingly ( w/ quant ).

Original: Thus, the groundtruth heatmaps reconstructed based on the quantized coordinates are erroneous leading to sub-optimal supervision anddegraded model performance.
Revised: Thus, the groundtruth heatmaps reconstructed based on the quantized coordinates are erroneous leading to sub-optimal supervision anddegraded model performance.

Original: Instead, DARK authors propose the heatmap generation placing the heatmap centre at the unbiased, non-quantizedkeypoint coordinate ( w/o quant ), claiming that, independently of the network architecture and the coordinate decodingmethod, the models perform consistently better.
Revised: Instead, DARK authors propose the heatmap generation placing the heatmap centre at the unbiased, non-quantizedkeypoint coordinate ( w/o quant ), claiming that, independently of the network architecture and the coordinate decodingmethod, the models perform consistently better.

Original: 3.3 Datasets3.3.1 HUMAN4D
Revised: 3.3 Datasets3.3.1 HUMAN4D

Original: We investigate the beneﬁts that DARK introduces in heatmap-based keypoint estimation by conducting our experimentson a recent dataset, HUMAN4D, that contains, among other data, pose annotated depth maps captured with the use ofrecent consumer-grade depth sensing devices.
Revised: We investigate the beneﬁts that DARK introduces in heatmap-based keypoint estimation by conducting our experimentson a recent dataset, HUMAN4D, that contains, among other data, pose annotated depth maps captured with the use ofrecent consumer-grade depth sensing devices.

Original: Beyond the experimentation on a dataset different from the ones used inthe original work, the rationale behind this selection is twofold:
Revised: Beyond the experimentation on a dataset different from the ones used inthe original work, the rationale behind this selection is twofold:

Original: • The dataset provides the original 3D poses allowing for their projection as non-quantized 2D coordinates onthe 2D depth map grids and, thereby, enabling the comparison between w/ quant and w/o quant coordinateencoding.•
Revised: • The dataset provides the original 3D poses allowing for their projection as non-quantized 2D coordinates onthe 2D depth map grids and, thereby, enabling the comparison between w/ quant and w/o quant coordinateencoding.•

Original: The training and evaluation of baseline pose estimation data-driven models on depth data which are relativelylimited in comparison with models trained on color data.
Revised: The training and evaluation of baseline pose estimation data-driven models on depth data which are relativelylimited in comparison with models trained on color data.

Original: The activities included are the following: running , jumping_jack , bending , punching_n_kicking , basketball_dribbling ,laying_down , sitting_down , sitting_on_a_stool , talking , object_dropping_n_picking , stretching_n_talking , walking_n_talking , watching_scary_movie and in-ﬂight_safety_announcement .
Revised: The activities included are the following: running , jumping_jack , bending , punching_n_kicking , basketball_dribbling ,laying_down , sitting_down , sitting_on_a_stool , talking , object_dropping_n_picking , stretching_n_talking , walking_n_talking , watching_scary_movie and in-ﬂight_safety_announcement .

Original: 3.3.2 Preparation
Revised: 3.3.2 Preparation

Original: With the use of HUMAN4D 3D poses, we project the joint 3D positions to the 2D depth map grids to obtain the 2Dnon-quantized poses.
Revised: With the use of HUMAN4D 3D poses, we project the joint 3D positions to the 2D depth map grids to obtain the 2Dnon-quantized poses.

Original: Using the single-person part of the HUMAN4D dataset, clipping the ﬁrst 100 frames from eachsequence (to exclude T-Pose calibration frames) and sub-sampling the remaining part of the sequence, we create a set of98 , 864 single-view samples from 14 single-person activities, including all 4 depth maps per multi-view frame.
Revised: Using the single-person part of the HUMAN4D dataset, clipping the ﬁrst 100 frames from eachsequence (to exclude T-Pose calibration frames) and sub-sampling the remaining part of the sequence, we create a set of98 , 864 single-view samples from 14 single-person activities, including all 4 depth maps per multi-view frame.

Original: We use the data of the ﬁrst three subjects performing all the activities for training, while we split the activities performedby the fourth subject (unseen) in two halves for validation and testing.
Revised: We use the data of the ﬁrst three subjects performing all the activities for training, while we split the activities performedby the fourth subject (unseen) in two halves for validation and testing.

Original: We decide to split the data that way in orderto assess the models on an unseen subject with different body structure, also keeping different activities between thevalidation and testing sets to provide fair conclusions with respect to the models’ performance.
Revised: We decide to split the data that way in orderto assess the models on an unseen subject with different body structure, also keeping different activities between thevalidation and testing sets to provide fair conclusions with respect to the models’ performance.

Original: The training, validationand testing data sets consist of 73 , 248 , 12 , 236 and 13 , 380 samples, respectively.
Revised: The training, validationand testing data sets consist of 73 , 248 , 12 , 236 and 13 , 380 samples, respectively.

Original: Finally, beyond the application of center cropping on depth maps from 320 × 180 to 320 × 160 ( 10 px from top andbottom) to better ﬁt to the multi-stage models, no further pre-processing steps were applied on the original data of thedataset.
Revised: Finally, beyond the application of center cropping on depth maps from 320 × 180 to 320 × 160 ( 10 px from top andbottom) to better ﬁt to the multi-stage models, no further pre-processing steps were applied on the original data of thedataset.

Original: 3.4 Hyperparameters
Revised: 3.4 Hyperparameters

Original: All the models are trained for 30 epochs, picking for testing the best performing ones based on validation metrics acrossthe epochs.
Revised: All the models are trained for 30 epochs, picking for testing the best performing ones based on validation metrics acrossthe epochs.

Original: Given that our aim is to assess the heatmap coordinate representation, not purely the effectiveness of themodels in pose estimation, we use constant and common training hyperparameters for the various models, withoutfurther investigation for ﬁnetuning.
Revised: Given that our aim is to assess the heatmap coordinate representation, not purely the effectiveness of themodels in pose estimation, we use constant and common training hyperparameters for the various models, withoutfurther investigation for ﬁnetuning.

Original: To this end, both for SH and HRNet , we used the Adam optimizer with a learningrate of 2 e − 3 , betas of values 0 .
Revised: To this end, both for SH and HRNet , we used the Adam optimizer with a learningrate of 2 e − 3 , betas of values 0 .

Original: 9 and 0 . 999 , without weight decay.
Revised: 9 and 0 . 999 , without weight decay.

Original: The seed remained constant during all models’training, equal to 1314, ensuring reproducibility.
Revised: The seed remained constant during all models’training, equal to 1314, ensuring reproducibility.

Original: We used simple MSE loss as in the original work that easily drove allmodels to convergence.
Revised: We used simple MSE loss as in the original work that easily drove allmodels to convergence.

Original: 3.5 Experimental setup and code
Revised: 3.5 Experimental setup and code

Original: [Figure]
Revised: [Figure]

Original: As already noted, carefully following the authors’ description and code, we built our implementation upon moai[7], a PyTorch Model Development Kit for rapid development of Deep Learning workﬂows 2 .
Revised: As already noted, carefully following the authors’ description and code, we built our implementation upon moai[7], a PyTorch Model Development Kit for rapid development of Deep Learning workﬂows 2 .

Original: In this framework,we implemented our models as well as the heatmap coordinate encoding and decoding operations with the use of aconﬁguration ﬁle that allows for the deﬁnition and conﬁguration of the various components and hyperparameters.
Revised: In this framework,we implemented our models as well as the heatmap coordinate encoding and decoding operations with the use of aconﬁguration ﬁle that allows for the deﬁnition and conﬁguration of the various components and hyperparameters.

Original: Similarly to DARK paper, we report the following standard pose estimation metrics:
Revised: Similarly to DARK paper, we report the following standard pose estimation metrics:

Original: RMSE : represents the square root of the squared differences between estimated and ground truth keypoint coordinatesin pixels.
Revised: RMSE : represents the square root of the squared differences between estimated and ground truth keypoint coordinatesin pixels.

Original: PCKh : considers an estimated keypoint location correct only if the euclidean distance error is lower than a percentagethreshold α of the euclidean distance between the head body part segment, i.e. from neck to head joint positions.
Revised: PCKh : considers an estimated keypoint location correct only if the euclidean distance error is lower than a percentagethreshold α of the euclidean distance between the head body part segment, i.e. from neck to head joint positions.

Original: In ourexperiments, we use PCKh-0.1 and PCKh-0.5 with α = 10% and α = 50% , respectively.
Revised: In ourexperiments, we use PCKh-0.1 and PCKh-0.5 with α = 10% and α = 50% , respectively.

Original: 3.6 Computational requirements
Revised: 3.6 Computational requirements

Original: The training of the models was executed on a workstation machine with the hardware speciﬁcations ﬁgured in Table 1.
Revised: The training of the models was executed on a workstation machine with the hardware speciﬁcations ﬁgured in Table 1.

Original: [Table]
Revised: [Table]

Original:  Results
Revised:  Results

Original: Our experimental results validate both claims of DARK [1], as presented in Table 2.
Revised: Our experimental results validate both claims of DARK [1], as presented in Table 2.

Original: In particular, w/o quant modelsoutperform the corresponding w/ quant ones, while DARK coordinate decoding method shows the best performancecompared to the other competitive decoding methods.
Revised: In particular, w/o quant modelsoutperform the corresponding w/ quant ones, while DARK coordinate decoding method shows the best performancecompared to the other competitive decoding methods.

Original: 4.1 Results reproducing original paper
Revised: 4.1 Results reproducing original paper

Original: The results presented in Table 2 support both claims of the paper, allowing the reader to easily study and relativelyassess the coordinate decoding and encoding achievements of each method
Revised: The results presented in Table 2 support both claims of the paper, allowing the reader to easily study and relativelyassess the coordinate decoding and encoding achievements of each method

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

Original: As mentioned above, our main aim is to highlight the effectiveness of the distribution-aware heatmap representation,instead of assessing the performance and comparison between the models.
Revised: As mentioned above, our main aim is to highlight the effectiveness of the distribution-aware heatmap representation,instead of assessing the performance and comparison between the models.

Original: Nevertheless, in our experiments, a generalcomment could be that SH_4S performs better than HRNet_4S almost in all combinations.
Revised: Nevertheless, in our experiments, a generalcomment could be that SH_4S performs better than HRNet_4S almost in all combinations.

Original: 4.1.1 Taylor-expansion coordinate decoding - Claim # 
Revised: 4.1.1 Taylor-expansion coordinate decoding - Claim #

Original: Assessing the various coordinate decoding methods we implemented and evaluated, as presented in Sec.
Revised: Assessing the various coordinate decoding methods we implemented and evaluated, as presented in Sec.

Original: 3.2.1, Claim #1is fully supported since the Taylor-expansion coordinate decoding does improve the coordinate estimation performance.
Revised: 3.2.1, Claim #1is fully supported since the Taylor-expansion coordinate decoding does improve the coordinate estimation performance.

Original: Considering the predicted heatmap as a Gaussian heatmap and applying Taylor-expansion coordinate decoding shows remarkable results against the rest of the methods.
Revised: Considering the predicted heatmap as a Gaussian heatmap and applying Taylor-expansion coordinate decoding shows remarkable results against the rest of the methods.

Original: In particular, as shown in Table 2, DARK decoding performs betterin all experiments for all metrics, with the only exception the RMSE error in “ SH_4S (w/o quant) + CoM " experiment.
Revised: In particular, as shown in Table 2, DARK decoding performs better inall experiments for all metrics, with the only exception the RMSE error in “ SH_4S (w/o quant) + CoM " experiment.

Revised: Inthat case, DARK is more accurate than CoM, but CoM exhibits a smaller average error.

Revised: This means that DARK suffersfrom larger outliers than CoM, a partly reasonable case given their nature.

Revised: CoM uses the entire heatmap to reach aconsensus about the coordinate, while DARK uses local heatmap statistics around the maximum activation, but is moresusceptible to heatmap noise.

Original: 4.1.2 Non-quantized coordinate encoding - Claim #
Revised: When applying DARK, a low-pass Gaussian ﬁlter is ﬁrst used, which is standard practisebefore the application of derivative extraction, in order to suppress noise and capture only the signal’s high frequencyinformation. However, this might not always be the case in out-of-distribution data predictions. When the predictionsfollow the underlying assumptions of DARK, namely a 2D Gaussian distribution, its ﬁner-grained localisation willbe effective. In the case of distribution noise, the globalised nature of CoM will be more robust.

Revised: Evidently, the SHexperiment is one such case, but nonetheless, DARK’s accuracy indicates that it still offers favourable behaviour.

Revised: 4.1.2 Non-quantized coordinate encoding - Claim #2

Original: Observing again the results in Table 2 from another perspective, we can assess the validity of Claim #2, i.e. that thecoordinate quantization before heatmap generation results in inaccurate and biased ground-truth signals that reduce themodel performance.
Revised: Observing again the results in Table 2 from another perspective, we can assess the validity of Claim #2, i.e. that thecoordinate quantization before heatmap generation results in inaccurate and biased ground-truth signals that reduce themodel performance.

Original: Indeed, for both architectures, SH and HRNet , and for every coordinate decoding method, w/oquant models show higher PCKh accuracy and lower RMSE errors, totally supporting the second claim of the authors.
Revised: Indeed, for both architectures, SH and HRNet , and for every coordinate decoding method, w/oquant models show higher PCKh accuracy and lower RMSE errors, totally supporting the second claim of the authors.

Original: 4.2 Results beyond original paper
Revised: 4.2 Results beyond original paper

Original: [Figure] An experiment we conducted, beyond the experiments of the present paper, is the comparison between DARK andspatial coordinate regression methods for keypoint estimation, such as Center of Mass (CoM) [2, 3].
Revised: An experiment we conducted, beyond the experiments of the present paper, is the comparison between DARK andspatial coordinate regression methods for keypoint estimation, such as Center of Mass (CoM) [2, 3].

Original: 4.2.1 DARK against Center of Mass
Revised: 4.2.1 DARK against Center of Mass

Original: Observing Table 2, DARK obviously outperforms CoM almost in all experiments.
Revised: Observing Table 2, DARK obviously outperforms CoM almost in all experiments.

Original: Nevertheless, it is worth-notingthat focusing on the results of the best performing model, as shown in Table 3, CoM demonstrates comparably to
Revised: Nevertheless, it is worth-notingthat focusing on the results of the best performing model, as shown in Table 3, CoM demonstrates comparably to

Original: DARK.
Revised: DARK.

Original: Especially in RMSE, which is a continuous metric, CoM presents lower errors than DARK, while, generally, itsperformance is higher when decoding heatmaps predicted by SH_4S .
Revised: Especially in RMSE, which is a continuous metric, CoM presents lower errors than DARK, while, generally, itsperformance is higher when decoding heatmaps predicted by SH_4S .

Original: [Table]
Revised: [Table]

Original:  Discussion
Revised:  Discussion

Original: Summarizing the present reproduction study, we conclude that the DARK paper introduces a novel, simple, lightweightand highly effective method for heatmap coordinate encoding/decoding that boosts the keypoint estimation accuracy.
Revised: Summarizing the present reproduction study, we conclude that the DARK paper introduces a novel, simple, lightweightand highly effective method for heatmap coordinate encoding/decoding that boosts the keypoint estimation accuracy.

Original: DARK outperforms standard greedy sub-pixel coordinate decoding methods.
Revised: DARK outperforms standard greedy sub-pixel coordinate decoding methods.

Original: Furthermore, it shows higher accuracythan spatial coordinate regression methods, such as CoM, which also shows lower erroneous predictions than standardmethods.
Revised: Furthermore, it shows higher accuracythan spatial coordinate regression methods, such as CoM, which also shows lower erroneous predictions than standardmethods.

Original: On top of those, DARK can be considered a signiﬁcant improvement for multi-person pose estimation.
Revised: On top of those, DARK can be considered a signiﬁcant improvement for multi-person pose estimation.

Original: Thatis due to the fact that spatial coordinate regression methods, though highly effective and fully differentiable, struggle inthe regression of more than one keypoint location when more than one heatmap in the same heatmap layer, i.e. speciﬁcjoint, are present in the same predicted layer, a common case in multi-person datasets.
Revised: Thatis due to the fact that spatial coordinate regression methods, though highly effective and fully differentiable, struggle inthe regression of more than one keypoint location when more than one heatmap in the same heatmap layer, i.e. speciﬁcjoint, are present in the same predicted layer, a common case in multi-person datasets.

Original: With regards to identiﬁed gaps in the present heatmap representation study, we believe that spatial coordinate regressionmethods, such as CoM or MoM (median of mass) [8], should have been taken into account, benchmarked and reportedin this paper.
Revised: With regards to identiﬁed gaps in the present heatmap representation study, we believe that spatial coordinate regressionmethods, such as CoM or MoM (median of mass) [8], should have been taken into account, benchmarked and reportedin this paper.

Original: Several recent heatmap-based keypoint estimation data-driven methods have been developed with the useof spatial coordinate regression, which beyond its effectiveness, allows the design of end-to-end, fully differentiablearchitectures with direct supervision on the actual task of keypoint estimation, i.e. the coordinate distance error betweenthe predictions and ground-truth.
Revised: Several recent heatmap-based keypoint estimation data-driven methods have been developed with the useof spatial coordinate regression, which beyond its effectiveness, allows the design of end-to-end, fully differentiablearchitectures with direct supervision on the actual task of keypoint estimation, i.e. the coordinate distance error betweenthe predictions and ground-truth.

Original: 5.1 What was easy
Revised: 5.1 What was easy

Original: Implementing most of the code was straightforward as authors provide  source code through GitHub.
Revised: Implementing most of the code was straightforward as authors provide their source code on GitHub.

Original: Apart from that,past GitHub issues were another source of retrieving information, clarifying parts of the paper when needed.
Revised: Apart from that,past GitHub issues were another source of retrieving information, clarifying parts of the paper when needed.

Original: 5.2 What was difﬁcult
Revised: 5.2 What was difﬁcult

Original: All and all, this reproduction study was smooth without bottlenecks, delays or other barriers.
Revised: All and all, this reproduction study was smooth without bottlenecks, delays or other barriers.

Original: A potential difﬁculty canbe considered  the availability of human pose datasets, beyond the ones used in the paper, that provide coordinates inhigher resolutions in order to further investigate the quantization error effects.
Revised: A potential difﬁcultythat can be considered was the availability of human pose datasets, beyond the ones used in the paper, that providecoordinates in higher resolutions, in order to further investigate the quantization error effects.

Original: 5.3 Communication with original authors
Revised: 5.3 Communication with original authors

Original: As implementing the code of the paper was straightforward and the ideas presented in the paper are clear and welldeﬁned, we did not communicate with the authors.
Revised: As implementing the code of the paper was straightforward and the ideas presented in the paper are clear and welldeﬁned, we did not communicate with the authors.