SlowGuess/NeurIPS_2023_OCR huggingface dataset:
where  $\tilde{v}_i$  is the closest vertex in  $\tilde{V}_i$ ,  $\mathbf{n}_i$  is the normal of  $\tilde{v}_i$ , and  $\cdot$  represents the dot product. The repulsive force is also recorded in the UV space to generate the 2D force map  $M_f$ . Note that it is 0 for vertices that are already outside of the inner garment, for which no collision occurs. Given the forces  $M_f$ , the garment geometry in the rest state  $M_r$  and after draping  $M_d$ , the network  $\mathcal{D}_m$  predicts a vertex displacements map  $D_m = \mathcal{D}_m(M_r, M_d, M_f)$  for the outer garment to resolve intersections, as shown in Fig. 3. We replace the vertex  $\tilde{v}_o \in \tilde{V}_o$  with coordinates  $(x_u, x_v)$  by  $\tilde{v}_o^* = \tilde{v}_o + D_m[x_u, x_v]$ .  $\mathcal{D}_m$  is implemented as a CNN, and it can capture the local geometry and force information of vertices from the input 2D maps. The training of  $\mathcal{D}_m$  is self-supervised by
$$
\mathcal {L} _ {\mathcal {D} _ {m}} = \mathcal {L} _ {p h y} + \lambda_ {g} \mathcal {L} _ {G G c o l} + \lambda_ {r} \mathcal {L} _ {r e g}, \tag {10}
$$
$$
\mathcal {L} _ {G G c o l} = \sum_ {\tilde {\boldsymbol {v}} _ {o} ^ {*}} \max (0, \epsilon - (\tilde {\boldsymbol {v}} _ {o} ^ {*} - \tilde {\boldsymbol {v}} _ {i}) \cdot \mathbf {n} _ {i}) ^ {3}, \mathrm {a n d} \mathcal {L} _ {r e g} = \| \mathcal {D} _ {m} (M _ {r}, M _ {d}, M _ {f}) \| _ {2} ^ {2},
$$
where  $\mathcal{L}_{phy}$  is the physics-based loss of Eq. (8),  $\lambda_{g}$  and  $\lambda_{r}$  are weighting constants, and  $\epsilon$  is a safety margin to avoid collisions.  $\mathcal{L}_{GGcol}$  penalizes the intersections between the outer and underlying garments, and  $\mathcal{L}_{reg}$  is an  $L_{2}$  regularization on the output of  $\mathcal{D}_m$ .
Given a pair of garments, our layering network  $\mathcal{D}_m$  only deforms the outer garment to resolve collisions, leaving the inner one untouched. Given more than 2 overlapping garments, the process can be iterated to layer them in any desired order over a body, as detailed in the Supplementary Material.
Figure 3: Multi-layer Draping. The network  $\mathcal{D}_m$  uses the garment geometry and forces encoded in the input UV maps to resolve garment intersections for multilayered draping.
Figure 4: Comparison between UDF and our method in resolution 512, 256 and 128. Our reconstructions (top row) are more accurate than those of UDF (bottom row) which have artifacts and uneven borders.
4.1 Dataset, Evaluation Metrics, and Baseline
To create training and test sets, we used the software of [46] to generate sewing patterns and the corresponding 3D garment meshes in their rest state, that is draped over a T-Posed body. Our training set comprises 400 shirts, 300 skirts, and 200 pairs of trousers. For testing, we use 20 shirts, 20 skirts, and 20 pairs of trousers. As discussed in Section 3.2, we trained the draping models using SMPL body poses  $\Theta$  randomly sampled from the AMASS [52] dataset and body shapes  $\mathbf{B}$  uniformly sampled from  $[-2,2]^{10}$ . We use the Chamfer Distance (CHD) and Normal Consistency (NC) to quantify garment reconstruction accuracy, along with the percentage of the garment mesh area that undergoes interpenetrations (Intersection), as in [30].
We compare our approach against recent and state-of-the-art methods DIG [29] and DrapeNet [30], which, like ours, can drape various garments over bodies of different shapes in arbitrary poses. Like our ISPs, DrapeNet is self-supervised using a physics-based loss and can prevent unwanted intersections between top (shirts) and bottom (trousers) garments. By contrast, DIG is a fully supervised method and cannot handle garment intersections.
4.2 Garment Reconstruction
Train	CHD (×10-4, ↓)	NC (%, ↑)	Time (ms, ↓)
UDF - 128	0.641	98.86	601
UDF - 256	0.338	99.20	2379
UDF - 512	0.262	98.77	13258
Ours - 128	0.454	99.20	25
Ours - 256	0.290	99.37	77
Ours - 512	0.250	99.41	261
Test	CHD (×10-4, ↓)	NC (%, ↑)
UDF - 128	0.803	97.71
UDF - 256	0.493	98.44
UDF - 512	0.424	98.09
Ours - 128	0.579	98.70
Ours - 256	0.392	98.83
Ours - 512	0.349	98.89
Table 1: Comparison of our method to UDF on shirts under the resolutions of 128, 256 and 512.
We first consider 3D garments in their rest pose and compare the accuracy of our ISPs against that of the UDF-based representation [30]. In Fig. 4, we provide qualitative results in a specific case and for resolutions of Marching Cubes [53] ranging from 512 to 128. Our result is visually superior and more faithful to the ground-truth garment, with UDF producing more artifacts and uneven borders, especially at resolution 512. The quantitative results reported in Tab. 1 for the training and test sets confirm this. For the test set garments, we reconstruct them by optimizing the latent code to minimize the Chamfer distance between the predicted and ground truth meshes, using the gradients of Eq. (6). Our approach consistently outperforms UDF at all resolutions while being faster, mostly because we evaluate our network on a 2D implicit field while UDF does it on a 3D one. For example, at resolution 256, our reconstruction time is  $77\mathrm{ms}$  on an Nvidia V100 GPU, while UDF requires 2379 ms. Interestingly, increasing the resolution from 256 to 512 improves the reconstruction accuracy
Figure 5: Realistic garment draping with our method, for different combinations of garments.
of our method, whereas that of UDF's drops. This is because precisely learning the 0 iso-surface of a 3D UDF is challenging, resulting in potentially inaccurate normals near the surface [54, 47]. We present similar results for trousers and skirts in the supplementary material.
4.3 Garment Draping
(a)
Intersection (%, ↓)
DrapeNet	0.536
Ours	0.276
(c)
Figure 6: Draping evaluation. (a) Human evaluation results. None refers to no preference. (b) Percentage of intersecting areas. (c) For each method, left is the draping results for a shirt and a pair of trousers, and right with only the pants. (d) The draping results of our method, DIG and DrapeNet.
Figs. 1 and 5 showcase our method's ability to realistically drape multiple garments with diverse geometry and topology over the body. Our approach can handle multi-layered garments, which is not achievable with DrapeNet. Additionally, unlike the method of [38] that is limited to multi-layered garments on the T-posed body, our method can be applied to bodies in arbitrary poses.
As pointed out in [13, 30], there are no objective metrics for evaluating the realism of a draping. Therefore, we conducted a human evaluation. As in [30], we designed a website displaying side-by-side draping results generated by our method and DrapeNet for the same shirts and trousers, on the same bodies. Participants were asked to select the option that seemed visually better to them, with the third option being "I cannot decide". 64 participants took part in the study, providing a total of 884 responses. As shown in Fig. 6(a), the majority of participants preferred our method (62.69% vs. 25.00%), demonstrating the higher fidelity of our results. The lower intersection ratio reported in Fig. 6(b) further demonstrates the efficacy of our draping model. In Figs. 6(c) and (d), we compare qualitatively our method against DrapeNet and DIG.
4.4 Recovering Multi-Layered Garments from Images
Thanks to their differentiability, our ISPs can be used to recover multi-layered garments from image data, such as 2D garment segmentation masks. Given an image of a clothed person, we can obtain the estimation of SMPL body parameters  $(\mathbf{B},\Theta)$  and the segmentation mask  $\mathbf{S}$  using the algorithms of [56, 57]. To each detected garment, we associate a latent code  $\mathbf{z}$  and reconstruct garment meshes
SMPLcit
ClothWild
Figure 7: Garment recovery from images. We compare the meshes recovered by our method and the state of the art methods SMPLlicit [28], ClothWild [55], DrapeNet [30] (unavailable for skirts).
DrapeNet
SMPLicit
ClothWild
Figure 8: Shape editing. Garment attributes can be edited by modifying the sewing pattern.
Short Sleeves
Short Body
by minimizing
$$
\mathbf {z} _ {1: N} ^ {*} = \underset {\mathbf {z} _ {1: N}} {\operatorname {a r g m i n}} L _ {\mathrm {I o U}} \left(R \left(\mathcal {G} (\mathbf {B}, \boldsymbol {\Theta}, \mathbf {z} _ {1: N}) \oplus \mathcal {M} (\mathbf {B}, \boldsymbol {\Theta})\right), \mathbf {S}\right), \tag {11}
$$
$$
\mathcal {G} (\mathbf {B}, \boldsymbol {\Theta}, \mathbf {z} _ {1: N}) = \mathcal {D} (\mathbf {B}, \boldsymbol {\Theta}, \mathbf {z} _ {1}, \mathbf {T} _ {G} (\mathbf {z} _ {1})) \oplus \dots \oplus \mathcal {D} (\mathbf {B}, \boldsymbol {\Theta}, \mathbf {z} _ {N}, \mathbf {T} _ {G} (\mathbf {z} _ {N})),
$$
where  $L_{\mathrm{IoU}}$  is the IoU loss [58] over the rendered and the given mask,  $R(\cdot)$  is a differentiable renderer [59],  $N$  is the number of detected garments, and  $\oplus$  represents the operation of mesh concatenation.  $\mathcal{M}$  is the SMPL body mesh, while  $\mathcal{G}(\mathbf{B},\Theta ,\mathbf{z}_{1:N})$  is the concatenation of garment meshes reconstructed from the implicit sewing pattern as  $\mathbf{T}_G(\mathbf{z}_i)$  and then draped by our draping model  $\mathcal{D} = \mathcal{D}_m\circ \mathcal{D}_s$ . In practice, the minimization is performed from the outermost garment to the innermost, one by one. Further details can be found in the Supplementary Material.
Fig. 7 depicts the results of this minimization. Our method outperforms the state-of-the-art methods SMPLicit [28], ClothWild [55] and DrapeNet [30], given the same garment masks. The garments we recover exhibit higher fidelity and have no collisions between them or with the underlying body.
4.5 Garment Editing
As the panel shape of the sewing pattern determines the shape of the garment, we can easily manipulate the garment mesh by editing the panel. Fig. 8 depicts this editing process. We begin by moving the sleeve edges of the panel inwards to shorten the sleeves of the mesh, then move the bottom edges up to shorten the length of the jacket, and finally remove the edges for the opening to close it. This is achieved by minimizing
$$
L (\mathbf {z}) = d \left(E (\mathbf {z}), \tilde {E}\right), \text {w h e r e} E (\mathbf {z}) = \left\{\mathbf {x} \mid s (\mathbf {x}, \mathbf {z}) = 0, \mathbf {x} \in \Omega \right\}, \tag {12}
$$
w.r.t.  $\mathbf{z}$ .  $d(\cdot)$  computes the chamfer distance,  $\tilde{E}$  represents the edges of the modified panel, and  $E(\mathbf{z})$  represents the 0 iso-level extracted from  $\mathcal{I}_{\Theta}$ , that is, the edges of the reconstructed panel. Our sewing pattern representation makes it easy to specify new edges by drawing and erasing lines in
the 2D panel images, whereas the fully implicit garment representation of [30] requires an auxiliary classifier to identify directions in the latent space for each garment modification. As shown in the supplementary material, the texture of the garment can also be edited by drawing on the UV panels.
We have introduced a novel representation for garments to be draped on human bodies. The garments are made of flat 2D panels whose boundary is defined by a 2D SDF. To each panel is associated a 3D surface parameterized by the 2D panel coordinates. Hence, different articles of clothing are represented in a standardized way. This allows the draping of multi-layer clothing on bodies and the recovery of such clothing from single images. Our current implementation assumes quasi-static garments and only deforms the outer garment to solve collisions in multi-layer draping. In future work, we will introduce garment dynamics and focus on more accurate physical interactions between the outer and inner garments.
Acknowledgement. This project was supported in part by the Swiss National Science Foundation.
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A.1 Texture Editing
A.2 Garment Reconstruction
A.3 Garment Draping
A.4 Multi-Layer Draping
B Technical Details
B.1 Sewing Patterns for Trousers and Skirts
B.2 Mesh Triangulation
B.3 Proof of the Differentiability of ISP
B.4 Garment Draping
B.5 Recovering Multi-Layered Garments from Images
B.6 Loss Terms, Network Architectures and Training
C Extension to Sewing Patterns with More Panels
D Failure Cases
A.1 Texture Editing
Figure 9: Texture editing. (a) A smiling face drawn on the front panel. (b) A flower pattern painted on both the front and the back panels. (c) A pocket drawn for the left shirt can be transferred to different garments.
As illustrated in Fig. 9, with our ISP, the texture of the garment can be easily edited by drawing on the UV panels. The figures drawn on the panel of one garment can be directly transferred to others as shown by Fig. 9(c), since panels are defined on the same UV space.
A.2 Garment Reconstruction
A.2.1 Evaluation Results
In Tabs. 2 and 3 we report the reconstruction results for skirts and trousers on the training and the test set. Similar to the results on shirts shown in the main paper, our method achieves better reconstruction quality than UDF [30] with lower CHD and higher NC at all resolutions, and needs less time to
Train	CHD (×10-4, ↓)	NC (%, ↑)	Time (ms, ↓)
UDF - 128	0.714	98.53	690
UDF - 256	0.408	98.93	2784
UDF - 512	0.331	98.43	17362
Ours - 128	0.538	98.80	25
Ours - 256	0.321	99.08	75
Ours - 512	0.267	99.14	262
Test	CHD (×10-4, ↓)	NC (%, ↑)
UDF - 128	0.734	97.79
UDF - 256	0.403	98.64
UDF - 512	0.324	98.27
Ours - 128	0.583	98.62
Ours - 256	0.362	98.85
Ours - 512	0.304	98.89
Table 2: Comparison of our method to UDF on skirts under the resolutions of 128, 256 and 512.
Train	CHD (×10-4, ↓)	NC (%, ↑)	Time (ms, ↓)
UDF - 128	0.758	98.22	661
UDF - 256	0.430	98.56	2650
UDF - 512	0.342	98.33	17141
Ours - 128	0.545	98.28	25
Ours - 256	0.363	98.59	82
Ours - 512	0.317	98.62	269
Test	CHD (×10-4, ↓)	NC (%, ↑)
UDF - 128	0.752	97.41
UDF - 256	0.425	98.09
UDF - 512	0.350	97.63
Ours - 128	0.529	98.03
Ours - 256	0.346	98.31
Ours - 512	0.300	98.32
Table 3: Comparison of our method to UDF on trousers under the resolutions of 128, 256 and 512.
reconstruct a single mesh. Figs. 10 to 12 show the qualitative results reconstructed by our method for shirts, skirts and trousers respectively.
A.2.2 Latent Space Interpolation
In Figs. 13 to 15, we display the results of interpolation in the latent space of shirts, skirts and trousers respectively. We observe a smooth transformation in both the reconstructed sewing patterns and the garment meshes, despite the different topology and geometry of the given garments.
A.2.3 Comparison with AtlasNet
In Fig. 16, we compare our method with AtlasNet [48] which learns to deform a square patch. AtlasNet struggles to learn a mapping function capable of accurately deforming the square patch to produce a surface that matches the ground truth, especially in the collar region. In contrast, our method leverages the pattern parameterization network  $\mathcal{I}_{\Theta}$  to simplify the training of our mapping function  $\mathcal{A}_{\Phi}$ . Specifically, our approach only requires learning the mapping for points within the panels, resulting in a reconstruction that is more faithful to the ground truth.
A.2.4 Ablation Study
To investigate the impact of the loss terms of Eq. (4) in the main paper on reconstruction quality, we performed an ablation study. We report the results of reconstructing 300 skirts using models trained with and without  $\mathcal{L}_{\text {normal }}$  in Tab. 4. We observe that training with  $\mathcal{L}_{\text {normal }}$  reduces the CHD and increases the NC, thus improving the reconstruction accuracy. In contrast, without  $\mathcal{L}_{\text {normal }}$ , the
Figure 10: Reconstruction samples of shirts.
Figure 11: Reconstruction samples of skirts.
Figure 12: Reconstruction samples of trousers.
Figure 13: Interpolation. We interpolate the latent code from a sleeveless shirt to a long-sleeve jacket. (a) and (b) show the reconstructed front and back panels, where the colors on them denote the edge label fields. (c) shows the reconstructed mesh.
CHD (×10-4, ↓)	NC (%, ↑)
w/o Lnormal	0.324	98.69
w/ Lnormal	0.321	99.08
Table 4: Comparison of the results reconstructed by the models trained w/o and w/  ${\mathcal{L}}_{\text{normal }}$  .
Figure 14: Interpolation. We interpolate the latent code from a short tight skirt to a long loose skirt. (a) and (b) show the reconstructed front and back panels, where the colors on them denote the edge label fields. (c) shows the reconstructed mesh.
Figure 15: Interpolation. We interpolate the latent code from a pair of short trousers to a pair of long trousers. (a) and (b) show the reconstructed front and back panels, where the colors on them denote the edge label fields. (c) shows the reconstructed mesh.
AtlasNet
w/  $\mathcal{L}_{norm}$
w/o  $\mathcal{L}_{\text {norm }}$
Figure 16: Comparison with AtlasNet. The meshes in black boxes are the source patches where the mapping function is applied: a square patch for AtlasNet, a garment panel for our method.
Figure 17: Ablation on  $\mathcal{L}_{\text {normal }}$ . Train-Figure 18: Ablation on  $\mathcal{L}_{\text {consist }}$ . The skirts reconstructed using without it yields flipped triangle by the models trained (a) with  $\mathcal{L}_{\text {consist }}$  and (b) without faces (shown in dark grey).  $\mathcal{L}_{\text {consist }}$ . The latter has a gap between its front and back panels.
model fails to learn the correct parameterization for the garment, resulting in a mesh with inverted faces as illustrated in Fig. 17. Fig. 18 shows a comparison of the results obtained by training models without and with  $\mathcal{L}_{\text{consist}}$  to help stitch the front and back panels. We can notice that without  $\mathcal{L}_{\text{consist}}$ , a spatial gap exists between the front (in gray) and back (in cyan) surfaces.
A.2.5 Visualization of the Chamfer Distance
A visualization of the spatial error distribution can be found in Fig. 19. In this figure, we compare the error distribution between our reconstructions and those produced by UDFs. Our reconstructions exhibit lower error across the entire surface compared to UDFs.
A.3 Garment Draping