SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Following the coarse-to-fine pipeline, to obtain a coarse motion of each body part, we need to obtain the pose transformation parameters. Previous works [25, 27] use the network to do direct regression but proved to have a poor generalization [28]. We thus follow [28] to use singular value decomposition (SVD) to compute transformation parameters of the bone map with respect to a reference heatmap, which is whitened and has zero mean and identity covariance. However, different from [28], where the bone maps are predicted by the network, we generate the bone map according to keypoint locations  $\pmb{\mu}_k$  and the kinematic tree. Formally, we assume there are  $J$  chains in the kinematic tree and we denote the parent and child node of the kinematic chain  $c_j$  as  $\pmb{\mu}_{jp}$  and  $\pmb{\mu}_{jc}$  respectively. The value of bone map  $\mathbf{B}_j$  at pixel  $\pmb{p}$  of the  $j$ -th kinematic chain can be formulated as
$$
b _ {j} (\boldsymbol {p}) = e ^ {- d _ {j} (\boldsymbol {p}) / \sigma^ {2}}, \tag {6}
$$
where  $\sigma$  is a hyperparameter that controls the thickness of the edge and  $d_{j}$  denotes the distance between the pixel  $\pmb{p}$  and the edge determined by  $\mu_{jp}$  and  $\mu_{jc}$ . Accordingly, the transformation parameters $^2$ $\mathbf{A}$  of  $\mathbf{I}$  can be obtained by
$$
\mathbf {A} _ {j} = \left[ \mathbf {U} _ {j} \mathbf {S} _ {j} ^ {\frac {1}{2}}, \boldsymbol {\mu} _ {j} \right], \text {w h e r e} \underbrace {\mathbf {U} _ {j} \mathbf {S} _ {j} \mathbf {V} _ {j}} _ {\text {S V D}} = \sum_ {\boldsymbol {p} \in \Omega} b _ {j} (\boldsymbol {p}) (\boldsymbol {p} - \boldsymbol {\mu} _ {j}) (\boldsymbol {p} - \boldsymbol {\mu} _ {j}) ^ {T}, \tag {7}
$$
where  $\pmb{\mu}_{j}$  is the mean of  $\pmb{\mu}_{jp}$  and  $\pmb{\mu}_{jc}$ . By Eq. 7, we can get the transformations  $\mathbf{A}^{\mathrm{b}\leftarrow \mathrm{ref}}$  and  $\mathbf{A}^{\mathrm{drv}\leftarrow \mathrm{ref}}$ . Finally, the geometric transformation of bone  $j$  from driving to base image is calculated by  $\mathbf{A}^{\mathrm{drv}\leftarrow \mathrm{b}} = \mathbf{A}^{\mathrm{drv}\leftarrow \mathrm{ref}}(\mathbf{A}^{\mathrm{b}\leftarrow \mathrm{ref}})^{-1}$ .
To generate a dense shift to deform  $\mathbf{I}^{\mathrm{b}}$  to approach  $\mathbf{I}^{\mathrm{drv}}$ , we next convert  $J$  transformation parameters to a fine-grained displacement field along with background transformation parameters. Specifically, with the input of  $\mathbf{I}^{\mathrm{b}}$ ,  $\mathbf{B}^{\mathrm{b}}$  and  $\mathbf{B}^{\mathrm{drv}}$ , an hourglass network outputs  $J + 1$  masks  $\mathbf{M}_j$  indicating one background and  $J$  bones.  $\mathbf{M}_0$  corresponds to the background.  $\mathbf{M}_j(\pmb {p})$  denotes the possibility of  $\pmb{p}$  belonging to the  $j$ -th region when  $j > 0$ . To ensure that the possibilities of every channel sum up to one, softmax is applied across the channels. Then, the displacement field  $\mathbf{D}^{\mathrm{drv}\leftarrow \mathrm{b}}(\pmb {p})\in \mathbb{R}^{2}$ , is generated by
$$
\mathbf {D} ^ {\mathrm {d r v} \leftarrow \mathrm {b}} (\boldsymbol {p}) = \sum_ {j = 0} ^ {J} \mathbf {M} _ {j} (\boldsymbol {p}) \underbrace {\mathbf {A} _ {j} \left[ \begin{array}{l} \boldsymbol {p} \\ 1 \end{array} \right]} _ {\text {E x p a n d}}. \tag {8}
$$
Through region-wise displacement field  $\mathbf{D}^{\mathrm{drv}\leftarrow \mathrm{b}}$ , the network gains insight into the specific locations on the base image that require deformation to match the driving image. Nonetheless, certain regions may be absent in the base image while present in the driving image. To identify these areas in need of inpainting by the network, we add an additional layer after the same hourglass to generate the inpainting map  $\mathbf{C}^{\mathrm{drv}\leftarrow \mathrm{b}}$ .
2We only need to rotate, translate, and scale to realize the transformation between the designed bone maps, which is different from the previous works based on affine transformation.
Generation Module  $\mathcal{G}$  We build  $\mathcal{G}$  with downsampling and upsampling, interconnected through skip connections. Similar to [28], the feature map from the skip connection is warped by displacement field  $\mathbf{D}^{\mathrm{drv}\leftarrow \mathrm{b}}$  and then activated with inpainting map  $\mathbf{C}^{\mathrm{drv}\leftarrow \mathrm{b}}$ . We add the processed feature map to the  $1 - \mathbf{C}^{\mathrm{drv}\leftarrow \mathrm{b}}$  activated feature map of the previous layer, and the sum is passed to the next layer. In this way,  $\mathcal{G}$  can generate driving images through feature warping and limited inpainting from a similar image without the need for extensive rendering.
Perceptual Loss Following [14, 35], we apply a multi-scale perceptual  $\ell_1$  loss with a pre-trained VGG-19 network. Mathematically, the reconstruction loss  $\mathcal{L}_{\mathrm{rec}}$  is formulated as
$$
\mathcal {L} _ {\mathrm {r e c}} = \sum_ {i} | \phi_ {i} (\hat {\mathbf {I}} ^ {\mathrm {d r v}}) - \phi_ {i} (\mathbf {I} ^ {\mathrm {d r v}}) |, \tag {9}
$$
where  $\phi_{i}(\mathbf{I})$  is the intermediate output of  $i$ -th layer of VGG-19.
Training Procedure The overall training of our framework is done in two stages. First is the pretraining on the source domain with supervised learning in Eq. 1 and invariant feature learning in Eq. 2 with weighting hyperparameter  $\lambda_{a}$ :
$$
\mathcal {L} _ {\text {p r e - t r a i n}} = \mathcal {L} _ {\sup } + \lambda_ {a} \mathcal {L} _ {\text {a l i g n}}. \tag {10}
$$
The second stage finetunes in the target domain, with pseudo-labelling from Eq. 3 and geometric reconstruction from Eq. 9, together with supervision from the source domain to avoid over-fitting:
$$
\mathcal {L} _ {\text {f i n e - t u n e}} = \mathcal {L} _ {\sup } + \lambda_ {r} \mathcal {L} _ {\text {r e c}} + \lambda_ {p} \mathcal {L} _ {\text {p s e u d o}}, \tag {11}
$$
where  $\lambda_r$  and  $\lambda_p$  are balancing hyper-parameters. We have a warmstart in the fine-tuning where  $\mathcal{L}_{\mathrm{sup}}$  and  $\mathcal{L}_{\mathrm{pseudo}}$  are first used and then add  $\mathcal{L}_{\mathrm{rec}}$  together to update the overall pipeline.
4.1 Datasets & Evaluation Metric
Hand Pose Datasets. For the source domain, we consider the synthetic dataset RHD [43] with 44k rendered images for training. For the unlabeled target domain, we consider real-world datasets H3D [41] and MVHand [39]; these have  $11\mathrm{k} / 2\mathrm{k}$  and  $42\mathrm{k} / 42\mathrm{k}$  training/testing splits respectively. For H3D, we consider only the subset with one-handed gestures. H3D and MVHand are both multi-view datasets; we treat each viewpoint as a "video" source.
Human Pose Datasets. SURREAL [31] is a synthetic human dataset with 6 million annotations including keypoint locations. Human3.6M [8] annotates 3.6 million real-world indoor human poses. We follow protocol 1, using S1 and S5-S8 for training and S9 and S11 for testing. 3DPW [32] is a challenging outdoor dataset with 24 videos for training and 24 videos for testing. We obtain 2D keypoints by projecting the corresponding 3D ground truth.
Evaluation Metric. The convention of domain adaptive pose estimation works [20, 15] is to evaluate 2D keypoint detection with Percentage of Correct Keypoint (PCK). We report PCK@0.05, which tabulates the percentage of correct predictions within the range of  $5\%$  of the input image size; a higher PCK indicates better performance. For 3D keypoint estimation, we evaluate with mean end-point-error (EPE); a lower EPE indicates better performance.
Our framework is shown in Fig. 1. We use ResNet-101 as the feature extractor  $f_{\mathrm{enc}}$  and deconvolutional layers as the decoder  $f_{\mathrm{dec}}$  to produce a heatmap of size  $2K \times 64 \times 64$  for 2D and depth. Each input image is cropped around the hand or the human and resized to  $256 \times 256$ . The initial learning rate is 1e-4, and we used Adam optimizer and degraded the learning rate with 0.1 at steps 60 and 75. Pre-training is done with a batch size of 64 for 40 epochs; fine-tuning is done with a batch size of 32 for 80 epochs. The hyperparameters  $\lambda_a, \lambda_r, \lambda_p$  are set as 0.1. We compare with state-of-the-art domain adaptation methods: RegDA [12], CC-SSL [20], UniFrame [15], SemiHand [36], and DualNet [18]. Where possible, results are reported directly from the corresponding papers; otherwise, results are based on officially released code. In pre-training, RHD [43] and SURREAL [31] are
Method	RHD→H3D	RHD→MVHand
MCP	PIP	DIP	Fin	All	MCP	PIP	DIP	Fin	All
Source only (Lsup)	67.4	64.2	63.3	54.8	61.8	32.1	70.5	64.6	39.8	52.7
SemiHand [36]	-	-	-	-	67.2	-	-	-	-	56.3
DualNet [18]	-	-	-	-	74.9	-	-	-	-	68.9
CC-SSL [20]	81.5	79.9	74.4	64.0	75.1	-	-	-	-	60.2
RegDA [12]	79.6	74.4	71.2	62.9	72.5	-	-	-	-	60.1
UniFrame[15]	86.7	84.6	78.9	68.1	79.6	45.0	77.7	71.0	57.6	62.9
Ours	89.4	88.3	81.9	73.9	84.1	76.4	76.9	68.7	61.0	70.8
Table 1: Hand 2D keypoint detection. Our method has the best average PCK@0.05 on both datasets and the most significant improvements on MCP and Fin.
Method	SURREAL→Human3.6M	SURREAL→3DPW
Head	Sld	Elb	Wrist	Hip	Knee	Ankle	All	Head	Sld	Elb	Wrist	Hip	Knee	Ankle	All
Source Only	51.3	69.4	75.4	66.4	37.9	77.3	77.7	67.3	40.9	59.2	65.6	64.2	64.4	56.4	39.8	57.9
CC-SSL [20]	-	44.3	68.5	55.2	22.2	62.3	57.8	51.7	41.0	58.5	76.3	67.4	77.6	61.7	47.8	62.5
RegDA [12]	-	73.3	86.4	72.8	54.8	82.0	84.4	75.6	41.8	65.8	73.3	68.1	72.8	65.0	49.3	64.8
UniFrame[15]	63.5	78.1	89.6	81.1	52.6	85.3	87.1	79.0	54.6	68.9	77.5	74.8	75.5	67.8	60.3	70.5
Ours	87.5	89.8	90.1	78.7	69.5	85.4	84.8	83.7	66.6	86.6	77.8	75.8	83.6	71.9	65.3	76.7
Table 2: The comparison on PCK@0.05 for 2D human keypoint detection. We achieve the best average performance on both datasets with the most significant improvements on the head.
used as labeled source dataset  $\mathcal{D}_s$  in hand and human pose estimation, respectively. In fine-tuning, the training sets of H3D [41], MVHand [39], Human3.6M [8] and 3DPW [32] are individually used as unlabeled target dataset  $\mathcal{D}_t$  for each pose adaptation experiment. And we evaluate on the corresponding test set.
Hand Pose. Table 1 shows that for 2D keypoint detection on the hand, our method outperforms the previous best method by  $5.7\%$  and  $12.6\%$  on the H3D and MVHand datasets respectively. For more in-depth analysis, we also report the individual joint results averaged across the fingers i.e., MCP, PIP, DIP,  $\mathrm{Fin}^3$ . Adapting  $RHD \rightarrow H3D$  gives a consistent improvement, with increases of  $3.1\%$  to  $8.5\%$ . On  $RHD \rightarrow MVHand$ , ours still achieves a significant improvement in PCK on MCP, increasing from 45.0 to 76.4.
Table 5 (b) shows that our method is state-of-the-art on 3D hand pose estimation for both  $RHD \rightarrow H3D$  and  $RHD \rightarrow MVHand$ . Especially notable is that we surpass DualNet [18], as we use only RGB images, while they incorporate additional modalities like background masks and depth images.
Human Body Pose. Table 2 shows, for SURREAL  $\rightarrow$  Human3.6M and SURREAL  $\rightarrow$  3DPW that our method outperforms state-of-the-art UniFrame [15] by  $5.9\%$  for Human3.6M and  $8.8\%$  for 3DPW. The biggest improvements come in the head, shoulders, and hips. In particular, we observe the hip problem arising from the gap in annotation convention between SURREAL and Human3.6M, so all methods (including ours) have lower accuracy on the hips. However, we outperform others by  $32.1\%$  on Human3.6M, indicating our geometric reconstruction can help the model less affected by the annotation gap.
Effectiveness of Components. We made two core contributions: geometric reconstruction and integrated pseudo-labelling. We here provide the gain of each component in Table 3 (a).  $\mathcal{L}_{\mathrm{UniFrame}}$  means we use the pseudo-labelling strategy in [15]. The comparison with  $\mathcal{L}_{\mathrm{UniFrame}}$  reveals the effectiveness of integrated pseudo-labelling with a 1.2 PCK improvement. Together with geometric reconstruction, we can further boost the increase to 2.7.  $\mathcal{L}_{\mathrm{heatmap}}$  means that we remove the warping estimation module and purely use heatmaps of both images to reconstruct  $\hat{\mathbf{I}}^{\mathrm{drv}}$ . The results show that using explicit guidance in the generation module could help effectively link reconstruction back to the underlying poses.
<sup>3</sup>Hand joints moving away from the palm: MetaCarpoPhalangeal (MCP), PIP (Proximal InterPhalangeal), DIP (Distal InterPhalangeal) and Fin (Fingertips).
30
before
Hannnnnne
before
Method	RHD \( \rightarrow \) H3D	SURREAL \( \rightarrow \) Human3.6M
\( {\mathcal{L}}_{\text{pre-train }} \)	67.2	69.0
\( + {\mathcal{L}}_{\text{UniFrame }} \)	80.2	79.8
\( + {\mathcal{L}}_{\text{pseudo }} \)	81.4	80.8
\( + {\mathcal{L}}_{\text{heatmap }} \)	81.6	81.2
\( + {\mathcal{L}}_{\text{rec }} \)	84.1	83.7
Figure 2: Comparisons before and after applying geometric reconstruction. Our method can correct the predictions that are on the background (left) and alleviate the annotation gap (right).
(a)
(b)
Table 3: (a) Ablation study on the proposed components and the reconstruction module contributes the most to the final performance. (b) Percentage of correct pseudo-labels in the training set of MVHand dataset. Both strategies saturate but the proposed integrated pseudo-labelling induces more correct labels. (c) Accuracy comparison before and after applying reconstruction loss  $\mathcal{L}_{\mathrm{rec}}$  for a specific set of confident keypoints on Human3.6M training set. After applying  $\mathcal{L}_{\mathrm{rec}}$ , we are able to improve the pseudo-label of those keypoints previously proposed using only  $\mathcal{L}_{\mathrm{pseudo}}$  and  $\mathcal{L}_{\mathrm{sup}}$ .
Keypoint Correction by Geometric Reconstruction. We analyze the impact of geometric reconstruction on confident yet inaccurate keypoints. We first train the model with  $\mathcal{L}_{\mathrm{sup}}$  and  $\mathcal{L}_{\mathrm{pseudo}}$  until convergence, and then save the indices of confident keypoints. Next, the reconstruction loss  $\mathcal{L}_{\mathrm{rec}}$  is added to fine-tune the model. We show the accuracy of the pseudo-labels for the keypoints associated with the saved indices, both before and after adding the reconstruction loss in Table 3 (c). The reconstruction loss obviously improves the confident yet inaccurate keypoints (i.e., head, shoulder and hip), while having a negligible influence on other keypoints. This is because confident yet inaccurate keypoints will cause large reconstruction errors based on image evidence while others will not. Also, we observe that those confident yet inaccurate keypoints tend to be specific keypoints, and speculate it is due to the annotation gap.
The Amount of Correct Pseudo-labels. We select pseudo-labels with high confidence. However, we cannot assure that their accuracy is within PCK@0.05 for effective adaptation. We therefore tabulate the percentage of correct pseudo-labels, whose accuracy is within PCK@0.05, in unlabeled training data aggregated by the last ten epochs. As shown in Table 3 (b), the percentage saturates to  $59\%$  for the pseudo-labelling strategy and to  $72\%$  for the proposed integrated pseudo-labelling. Since the pseudo-labels are explored on training data with augmentations, their accuracy might not align consistently with the accuracy observed on the evaluation set. It is evident that both our approach and Uniframe eventually reach a saturation point for accurate pseudo-labels, but our method involves more usable pseudo-labels and leads to a better result.
Fairness & Stride Strategy. In our method, we need a pair of images with a similar background and the same object (human/hand). In contrast, existing state-of-the-art methods only require a single image during training on the target domain. For a fair comparison, we first consider the most common module to utilize adjacent paired input, i.e., temporal consistency by applying  $\ell_2$  loss on the predicted heatmaps  $\| h_{\pmb{p}}^{i} - h_{\pmb{p}}^{i + 1}\|_{2}$  of two consecutive frames  $\mathbf{I}_i$ ,  $\mathbf{I}_{i + 1}$ . Results in Table 5 (a) show it can only gain marginal improvement. Another consideration is whether the difference between the two poses affects the effectiveness of the reconstruction. We attempted to amplify the pose difference of two images from small to large by adjusting the stride from [0,5] to [30, 50]. As shown in Table 4, our method performs best on [5,15]. This makes sense that degenerately close
Stride	[0,5]	[0,15]	[5,15]	[15,30]	[30,50]
SURREAL→Human3.6M	81.8	83.5	83.7	83.1	82.5
Table 4: Ablation study on frame strides for the task of SURREAL  $\rightarrow$  Human3.6M evaluated by PCK@0.05. We can see that all strides lead to improvement, and our method is robust to the selection of strides within a certain range.
Method	RHD→MVHand	SURREAL→Human3.6M
RegDA[12]	60.7(↑ 0.6)	76.4(↑ 0.8)
UniFrame[15]	63.4(↑ 0.5)	79.3(↑ 0.3)
Ours	70.8	83.7
(a)
Method	RHD→ H3D	RHD→ MVHand
Source only	27.77	21.21
SemiHand[15]	19.19	19.75
DualNet[18]	17.08	16.45
Ours	16.92	16.37
Table 5: (a) We add temporal consistency to ensure equivalence in the input information, which only brings minor improvement. (b) The comparison on EPE (mm) for 3D hand pose. By only improving 2D and applying a simple 3D pseudo-labelling strategy, we beat the state-of-the-art methods.
frames will make the network find the shortcut to self-reconstruction and far frames will make the generation too difficult to have a meaningful perceptual loss on keypoint locations.
Hand Pose. Fig. 2 (left) shows a common case in only using pseudo-labelling, where the fingertip is predicted on the background, although it is near the ground truth location. Applying our geometric reconstruction results in more accurate fingertip predictions. Besides, the wrong prediction of the pinky fingertip falling on the palm can also be rectified via the perceptual loss in our reconstruction module.
Human Body Pose. Fig. 2 (right) shows the comparison of our method on a Human3.6M sample before and after applying geometric reconstruction, where the shoulders are much lower in "before" compared to "GT". One possible cause is the difference in the annotation conventions across datasets, e.g. The annotation of the shoulders in SURREAL is closer to the chest, while Human3.6M localizes them at a reasonable shoulder position (See Supp.). Similar differences due to the annotation gap are reflected in the accuracy of head and hips, as shown in Table 2. Our method, however, can refine the pose prediction by leveraging the correlation between bone map and reconstruction, which is independent of the pose prior learned in the source domain. More analysis can be seen in Supp.
Pseudo-labelling is a common strategy for domain adaptive pose estimation which selects confident predictions to supervise the network. However, the number of accurate labels under this selection will saturate with the progress of training and some of the wrong predictions will remain unchanged. We hereby introduce a novel geometric reconstruction module to relieve this problem that aims to reconstruct the driving image according to keypoint locations and geometric transformations from the base image to the driving image. The incredible improvement especially comes from keypoints that generalize extremely poorly to target domain by only pseudo-labelling. We hope this will inspire future work to explore reconstruction-based methods to bridge the gap between source and target domains.
Acknowledgments This research / project is supported by the Ministry of Education, Singapore, under its MOE Academic Research Fund Tier 2 (STEM RIE2025 MOE-T2EP20220-0015).
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