CircNet: Meshing 3D Point Clouds with Circumcenter Detection
Authors: Huan Lei
Ruitao Leng
Liang Zheng
Hongdong Li
Venue: ICLR 2023 poster (2023)
Keywords: Meshing
3D Point Cloud
Point Cloud Triangulation
Surface Reconstruction
Geometry Processing

Abstract: Reconstructing 3D point clouds into triangle meshes is a key problem in computational geometry and surface reconstruction. Point cloud triangulation solves this problem by providing edge information to the input points. Since no vertex interpolation is involved, it is beneficial to preserve sharp details on the surface. Taking advantage of learning-based techniques in triangulation, existing methods enumerate the complete combinations of candidate triangles, which is both complex and inefficient. In this paper, we leverage the duality between a triangle and its circumcenter, and introduce a deep neural network that detects the circumcenters to achieve point cloud triangulation. Specifically, we introduce multiple anchor priors to divide the neighborhood space of each point. The neural network then learns to predict the presences and locations of circumcenters under the guidance of those anchors. We extract the triangles dual to the detected circumcenters to form a primitive mesh, from which an edge-manifold mesh is produced via simple post-processing. Unlike existing learning-based triangulation methods, the proposed method bypasses an exhaustive enumeration of triangle combinations and local surface parameterization. We validate the efficiency, generalization, and robustness of our method on prominent datasets of both watertight and open surfaces. The code and trained models are provided at \url{https://github.com/Ruitao-L/CircNet}.

Published as a conference paper at ICLR 2023
CIRCNET: MESHING 3D POINT CLOUDS WITH CIRCUMCENTER DETECTION
Huan Lei, Ruitao Leng, Liang Zheng, Hongdong Li School Computing, The Australian National University
ABSTRACT
Reconstructing 3D point clouds into triangle meshes is a key problem in putational geometry and surface reconstruction. Point cloud triangulation solves this problem by providing edge information to the input points. Since no ver- tex interpolation is involved, it is beneficial to preserve sharp details on the sur- face. Taking advantage of carming-based techniques methods enumerate the complete combinations of candidate triangles, which is both complex and inefficient. In this paper, we leverage the duality between a triangle and its circumcenter, and introduce a deep neural network that detects the circumcenters to achieve point cloud triangulation. Specifically, we intro- duce multiple anchor priors to divide the neighborhood space of each point. The neural network then learns to predict the presences and locations of circumeen- ters under the guidance of those anchors. We extract the triangles dual to the detected circumcenters to form a primitive mesh, from which an edge-manifole mesh is produced via simple post-processing. Unlike existing learning-basse tri- angulation methods, the proposed method bypasses an exhaustive enumeration of triangle combinations and local surface parameterization. We validate the ef- ficiency. generalization, and robustness of our method on prominent datasets of both watertight and open surfaces. The code and trained models are provided https: / / thub. com//uiito-LLan Laaa--L/CC rcNet.
triangulation, existing
Ru
INTRODUCTION
Point cloud triangulation (Cazals & Giesen 2004) aims at reconstructing triangle meshes of object surfaces by adding edge information to their point cloud representations. The input point clouds usually produced by either scanning sensors (e.g.. LiDAR) surface sampling methods. Com- pared to implicit surface reconstruction (e.g., Kazhdan et al. 2006), explicit triangulation has the advantages of preserving the original input points and fine-grained details of the surface. Moreover, it does not require oriented normals which are difficult to obtain in practice. Recent advances in geometric deep learning have seen widespread applications neural functions for surface represen- Park et al. 2019; Sitzmann et al. 2020b a Erler et al. 2020 Gropp et al. 2020 Atzmon tations Park
Lipman 2020a b) Ben-Shabat al. 2022 Ma 2021 2022). In comparison, only a few meth- ods have been proposed to directly learn triangulation of point clouds by using neural networks. This is probably attributed to the combinatorial nature of the triangulation task, hindering the up- take of learning-based methods. The existing works have enumerate combinations of candidate triangles around each input point, and use neural networks to predict their existence the triangle mesh (Sharp & Ovsjanikov 2020 Liu et al. 2020). Figure [[)) illustrates the local complexity of those combinatorial methods using a point with four neighboring points. Typically, for a point with K neighbors, the combinatorial methods propose (K) or O(K2) candidate triangles.
Different from these methods, propose exploit the duality relationship between triangle and its circumcenter to implement point cloud triangulation. That is, each vertex of a triangle is equally distant its circumcenter. We this characteristic find triangle triplets from their cir- cumcenters. Figure. [b)) shows the duality based on the same example of Fig. [[a. Our method recovers the vertex triplets of triangle (p, qı, qa) based on its circumcenter and the equidistant characteristic, i.e. ||p cll = ||q cll q| cll. To obtain circumeenters for point cloud trian- gulation, we introduce a neural network that is able detect the cireumcenters of all triangles in a mesh. To the best of our knowledge, this is the first single-shot detection architecture for point cloud triangulation. We are inspired by the one-stage methods in object detection (e.g., Liu et al. 2016).

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Published as a conference paper at ICLR 2023
Unlike previous combinatorial methods, the proposed method removes the requirement for detect
known triangle vertex neighboring points
X: triangle cireumeenter
radius of cireumeircle
candidate triangles. Specifically, circumeenters in the neighborhood space of each point, under the guidance of group of anchor priors. The neural network predicts whether a circumcenter exists in the recon- structed mesh, and where it is. We extract triangles induced by the detected circumcen- ters to obtain a primitive mesh. The final surface mesh is produced by enforcing edge- manifoldness and filling small holes on the primitive mesh.
43
P
41
Candidate triangles at pi {(p, 9: (.).) q:: qi),
(p. qi qr), (P, qu Qs);
r= pp-cl
o||
(p, 92 4c). qs; 94))
duality. (c)
ماك {(p. q1 9:))
(a) Combinatorial methods
The proposed method
To validate the proposed method, train the detection neural network on the ABC dataset (Koch et al. 2019). The trained model is eval- uated on the ABC and other datasets, includ- ing FAUST (Bogo et al. 2014), MGN (Bhat- nagar et al. 2019), and Matterport3D) (Chang al. 2017). ). The method not only recon- structs meshes in high quality, but also outper- forms the previous learning-basee based approaches largely in efficiency. It generalizes well to un- seen, noisy and non-uniform point clouds. Our main contributions are summarized below:
Figure An example of point p with four neighboring points q1 92, 93-94- 94- (a) The com- binatorial methods propose all of the six triangles incident p as candidate triangles. They are (p, qi, (2), (p, qi, q3), (p, qi, q4), (p. q2, qa). 43 91). The neural network has to classify the targeted triangle (p. qı, (x).)) out of the six candidates. (b) The proposed method clim- inates the candidate proposals by detecting a cir- cumcenter e and exploiting its duality with the tri- angle (p, qı, qa) to identify the targeted triangle.
(p, q2, 91), (p,43
We introduce the first neural architecture that triangulates point clouds by detecting circumcenters. The duality between triangle and its circumcenter is exploited afterwards extract the vertex triplets of each triangle in the mesh.
The proposed neural network is able reconstruct primitive meshes in milliseconds, due to its single-shot detection pipeline and its removal of candidate proposals. Normals are not required.
The proposed method casts no restriction on the surface topology, e.g., being watertight. Instead, it allows the surfaces to be open and have genus ("hole') larger than one.
The method generalizes well to unseen point clouds including those of large-scale scenes, It is robust to non-uniform and noisy data. These indicate its promise for real-world applications.
RELATED WORK
Point cloud triangulation and implicit surface functions are two important research directions surface reconstruction. Their major difference is that the former preserves input points, while the latter does not. Alpha shapes (Bddelbrrunner & Mücke 1994) and the ball pivoting algorithm (Bernardini et al.) 1999) are representatives among the traditional methods in point cloud triangulation. The Poisson surface reconstruction (Kazhdan et al. 2006 Kazhdan & Hoppe 2013) 3) is a classical approach in im- plicit surface functions, but it depends on oriented normals of the input points for good performance. Marching Cubes (Lorensen & Cline 1987) and Dual Contouring (Ju et al. 2002) are restricted to ex- tract the triangle meshes of isosurfaces from their signed distance fields. We refer interested readers to surveys Berger et al. 2017 Cheng et al. 2013)) Newman & Yi for more in depth discussions of the traditional surface reconstruction methods.
2.1 IMPLICIT NEURAL FUNCTIONS
Implicit neural functions are techniques in geometric deep learning. They exploit the approximation power of neural networks to represent shapes and scenes as level-sets of continuous functions (Atz-)
mon et al. p. Existing literature trains networks to learn either occupancy functions (Mescheder
et al. 2019 Peng et al. 2020) distance functions (Park et al. 2019 Sitzmann al. |020bb Atzmon & Lipman 2020a). Since the introduction of DeepSDF (Park et al. 2019). major advances in this research field include simplifying requirements the ground-truth (e.g., signs of distances) (Atz-
mon & Lipman 2020a b). exploring the figh-frequency features (Sitzmann et al, 2020b) Tancik et al. 2020), and improving loss functions for better surface representation (Gropp al. 2020 Ben-Shabat
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Published as a conference paper at ICLR 2023
et al. 2022). Implicit functions generate volumetric occupancy or distance fields of isosurfaces, and are followed by Marching Cubes for mesh extraction. Methods in this research direction usually require oriented normals of points, and tend to oversmooth sharp details on the surface. In addition, their neural networks have to be trained with careful initialisation, and are slow at inference stage due to the dense point queries.
There are also methods extending the traditional Marching Cubes, Poisson surface reconstruction, and Dual Contouring using neural networks (Liao al. 2018 Chen & Zhang 2021; Peng et al. 2021 Chen et al. 2022). Altogether, they demand interpolations of triangle vertices to reconstruct the mesh and are unlikely to preserve the fine- grained details carried by the imput points.
2.2 LEARNING-BASED POINT CLOUD TRIANGULATION
Compared to their popularity in implicit surface functions, neural networks are much less stud- ied in point cloud triangulation. Existing methods typically reconstruct the triangle mesh by pre- establishing the complete combinations of candidate triangles or parameterizing the local surface patches into the 2D space. SSharp & Ovsjanikov (2020) propose a two-component architecture, Poin It utilizes proposal network to recommend candidate triangles, and determines their existence in the triangle mesh with a classification network. By comparing the geodesic and Eu- clidean distances, [iu et al. (2020) introduce a metric IER indicate the triangle presence in the reconstructed mesh. They train a neural network to predict the IER values of O(K?N N) candidate triangles. Those candidates are established offline via K -eaarestt neighbor (KNN) search (Preparata & Shamos 2012). Here N represents the total number of points in the point cloud. As classi- cal method in computation geometry, Delaunay triangulation (Mark et al. 2008) guarantees point clouds to be triangulated into manifold meshes in the 2D scenario. To exploit this method, [Rako-] tosaona et al. (2021b) extract KNN patches from the 3D point cloud, and parameterize them into 2D space using neural networks. However, dividing point cloud triangulation into baanidg-based parameterization and computational triangulation makes their method computationally expensive. Later, Rakotosaona et al. (2021a) also study to differentiate the Delaunay triangulation by introduc- ing weighting strategies. Yet, this method is limited to triangular remeshing of manifold surfaces, and not applicable to triangulation of 3D point clouds.
Due to the local computational nature, beasing-basedd triangulation methods generalize well to un- seen point clouds of arbitrary shapes and scenes. On the other hand, the implicit neural functions are restricted to shape/surface representations in an instance or category level. It is non-trivial to apply them to cross-category data, e.g. mugs elephants, cars to indoor rooms. We note that even the local implicit functions often generalize poorly (Tretschk et al. 2020: Chabra et al. 2020).
2.3 LEARNING TRIANGULATION VIA CIRCUMCENTER DETECTION
Departing significantly from the learning-based triangulation approaches described above, we ex- ploit the duality between triangle and its circumeenter, and reformulate the combinatorial trian- gulation as a detection problem of triangle circumcenters. This would facilitate the geomtric deep learning techniques to be applied. Superior cessitates a two-stage design, our method enables the usage of a one-stage detection pipeline which largely contributes to its efficiency. It has time complexity of only O(tN) where indicates the number of anchors. This is significantly less than the O(K²N) of IER (Liu et al. 2020). Similar to existing learning- based methods, we triangulate point clouds based on local KNN patches.
PointTriNet (Sharp & Ovsjanikov 2020) which
3 METHOD
Given a point cloud representation of surface (Pn E R we focus on triangulat- ing the point cloud into mesh that reconstructs the underlying surface. Unlike implicit surface functions which generate new points for mesh reconstruction (Kazhdan et al. 2006), point cloud triangulation preserves the input points by only adding edge information to the existing points. Let T { 1 Pns) mi, n22, n3 E {1, .,.,,..., N., n2 # n2 # n3} be an optimal triangulation of P. Typically, it reconstructs the surface as edge-manifold mesh. This indicates that each edge in the triangulation such as (Pn,,Pa, ) is adjacent to two triangle faces at most. In particular, edges adjacent to one face are the boundary edges.
Overview. Based on the local geometrics in $3.1 we detect circumcenters to predict the Lst-order adjacent triangles of each point. In 4.2 we introduce the default anchor priors which help to
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Published as a conference paper at ICLR 2023
Duality triangle
Point Cloud
P = (pw) km
KNN Patch at pi
network Circumeenters
neural
Predicted
identification
Triangles
Predicted
Primitive Mesh
Surface Mesh
patch
:
post
extraction
union
process
neural
Predicted
triangle identification
Predicted
KNN Patch Pw
network Circumcenters
Triangles
Figure 2: The triangulation process of our method for point cloud P. We extract KNN patches obtain the local geometrics of each point Pv. The neural network detects circumcenters and identifies the adjacent triangles of each p, based on their patch inputs. The union of all identified triangles forms the primitive mesh, which is post-processed into an edge-manifold surface mesh.
guide the detection of circumcenters. Details of the detection architecture are presented in $33 We train the neural network with multi-task Ioss function discussed $3.4 During inference (335))
triangulates the input point cloud efficiently into primitive mesh. We post-process the primitive mesh to be an mangfodd surface mesh. Figure summarizes our triangulation process.
3.1 LOCAL GEOMETRICS
KNN patch. The local geometrics of point contain rich information for predicting its adjacent triangles. We exploit them as the inputs to our detection network. Specifically, we extract the local geometrics of each point based on their neighborhoods. Let K((p) {q * p)k be (KNN)
KNN patch composed of the K-nearest neighbor (KNN) points of E P. and do (p) > 0 be the distance from p to its nearest neighbor in (p)).. To make the neural network robust to density variations in the data, normalize the KNN patch (C(p) using a scalar 7(p) do(p)- Here nou a hyperparameter controlling the spatial resolution of each KNN patch. The normalized patch is K We design graph convolution in $3.3 to learn
represented as K(p)- = {qx q. m7()- (qi- - p)} global representations of each patch from the input geometrics K(p) for circumcenter detection.
Duality. Taking T as the optimal triangulation of P. we denote the adjacent triangles of point p as Tp) = (P) p E T:()), and the circumcenters of those triangles as C(p) = (X, Our network learns detect the cireumcenters and then extract the adjacent triangles. Let C(p) (pm{ 7(p) (p)lp E (p)))) be their respective predictions. To extract the triangle triplets T. (p) based on (p), we follow the characteristic that the three vertices of triangle are equidistant its circumcenter. In practice, the equidistant characteristic has to be applied with approximations due to the imperfections of the predicted (p). We compute the distance from p and each of its neighbor point E K(()) to a detected circumcenter X,, (p) as
dm (p) = -|p (p)ll,,, dm (qu) = || (n))la
The triangle vertices are determined by the difference between distances dmn (qp)) and dm (p). Let
(gk p) (dm(4s) - dm (p)),
(2)
Am (p) (5m(q))) (t.p))/. E K(()).
(3)
We recover the triangle triplets by selecting the two points qu; qu which induce the two smallest 5m (+. p) in (p). Finally, the triangle associated X,, (p) is identified as T. (p) (p, qu qu).
3.2 ANCHOR PRIORS
We multiple anchor points to partition the neighborhood space of each point into different cells. The predefined anchor points and cells guide the neural network in its detection of circumcenters.
We specify the anchor points in the spherical coordinate system (p, 0, Φ)) as it has fixed ranges along the azimuth (0) and inclination (o) directions, i.e. E (-T, r]. & E I- - Regarding the radius (p) direction,
the distributions of circumcenters in the training data, denoted as (0, R). With known ranges, we split the p. 0, 6 each uniformly using fixed steps Ap, A0, A respectively. This results in the number of splits for p, 0, 6 to be to = 1
determine its range according
R
We assume that K is large enough cover the 1-ring neighborhood of p in the triangle mesh.
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to 2x A0 to = =[ and total number of t tp x to to anchor points. We represent them as
A [aj (af, L2 22) トーz where on al 2 each are explicitly defined as
61 = Ae
2 + (ji - 1) p, J1 E (1, [b))
A + +(2 1)40, j2 E (1,-....0 .00) 2 2
0 = 2
Ae
+ (is 1) ja {1.... tt
origin
For each anchor point a, a
1 (a 22 27)) associate it with anchor cell defined by the partitioned space 1 = 1 x 1% x 1g The anchor cells play an important role in the matching of circumcenters and anchor points ($ (.4). We specify the intervals
a.
I
17, 12 1 as
1 jn
2 a,, + }
19 [0%
40
+ )
(5)
2
Figure 3: An example of the anchor priors in 2D. A 6 is used. The an- chor points are plotted in red cross, and the anchor cell is colorized as green.
1 [o%
Ae
2 31 + Ae].
See Fig.3 an example of the anchor points and cells in 2D (i.e. no el- evation direction). With the usage of anchor points and cells, we reduce the combinatorial triangulation of complexity O(K2N) to a dual prob- lem of complexity (IN)). Empirically, 1 < K22 Alternative methods for defining the anchor points can be in the Cartesian coordinate system or using the data clustering techniques (Bishop & Nasrabadi 2006). Yet, they either lead to larger and hence higher complexity, or make the anchor definition and network training complicated.
3.3 NETWORK DESIGN
Based on the normalized KNN patch ((p)) of point p. design neural network that is able to predict the circumcenters for adjacent triangle identification. The input to our network is a star graph which has point p its internal node and the neighborhoods {qx} } its leaf nodes. We present the graph convolution below to encode local geometries of p into a global feature representation. The depthwise separable convolution (Chollet 2017) is explored here. Let 3 be the depth multiplier, h²=²(qs) ) be the input features of point q at layer 1, C.n. be the dimension of h h and Cout be the expected dimension of output features. We compute the output features h (p) p as
K A
h'(p)) = ΣΣ
W (Wahh-"(qx)) @ h hq))()))) + b. k=
(6)
Here W 11, W b are learnable parameters in the graph convolution. The sizes of Wa. W Oin x Cm. Cout x C' respectively, and the length of b is Cout- We use the graph convolution only once to calculate global feature representations of each patch. The positional encoding in (Mildenhall et al. 2020 is also employed to transform the (z,, y, 2) coordinates into high-frequency input signals. Figure shows the configurations of our neural detection architecture. The ultimate output of our network is tensor of size 1 x x 4, where s indicates the number of circumcenters predict in each anchor cell, and contains confidence (z) about the existence of circumcenter in cell and its predicted coordinates in 3D. Because the usage of one-stage pipeline, the proposed network can detect circumcenters and adjacent triangles efficiently.
3.4 TRAINING
We train the neural network based on multi-task loss functions, similar to those exploited in object detection (Lu al. (016)) The binary cross-entropy used for classifying the anchor cells, and the smooth LI loss (Grshick 2015) is applied for localizing the circumcenters.
Matching strategy. To train the network accordingly, we have to match the ground-truth circum- centers to the anchor points. Thus, we transform the ground-truth circumcenters C(p) (p)) into a spherical coordinate system centered p. denoted as S(p) ((p., 0;, dx)) where (px. 6, Φ:) are the spherical coordinates of (p) p. For each X,(P), we match it to the anchor point
a. aL ...)) if (pi, 00,00,40 ( E Te. In this way, it is possible that anchor point is matched
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detected cicumcenters and triangles
patch features {q.}
predictions i
4
Pa
Reature h(p))
graph comy
(1024)
officts confidences
4B
Globu
milp
Figure 4: The neural network for circumeenter detection. It learns global feature representation for each patch using multi-layer perceptrons and the proposed graph convolution. The global feature h(p) is used to make predictions of the circumcenters. We show in the right a toy triangulation of the input patch p. The detected circumcenters in red cross and the triangle edges are in blue.
to multiple circumcenters. That is why we allow multiple circumcenters (s) to be detected in a sin- gle anchor cell. The proposed network detects each ground-trun circumcenter X,(p) C(p) by predicting its parameterized offsets g, (p)
(g. 12.99... 9.)) defined as
gf P: a
0: a Ae 9
g
Ap
AΦ
The predicted offsets are (ohh In P..) We recover its associated circumcenter prediction X. (p) C(p) with proper coordinate transformation. Furthermore, by analyzing the distributions of circum- centers in the training set, we find that two predictions per anchor cell (i.e. = 2) reaches good balance between performance and efficiency.
Binary cross-entropy loss. For each anchor cell, whether it contains any ground-truti circumcen- ters not is a binary classification task. We predict a confidence for each of them to indicate the existence of circumcenters. It can be seen from $3.2 that we define the anchor points compactly in the neighborhood space of a point. In reality, the circumcenters of adjacent triangles for each individual point distribute closely around the surface manifold. Such facts result in the majority of anchor cells to be unoccupied. They comprise the negative samples Weeg in our classification, while the occupied cells comprise the positive samples Noos- Assume [Nposl Np. |Wnegl = Nn. and p is the probability correlated to the confidence 2, we compute the binary cross-entropy as
1 N₂ No
log(p.) 1 Nn.
L1
L log(1 pt), where p: 1+ exp(-
1
Nn
We employ hard negative mining for better training (Liu et al. 2016).
Smooth L. loss. As mentioned above, we predict 8 = 2 circumcenters inside each cell. Let be the ground-truth offset coordinates of all circumcenters in the ith cell, and (g., 8:2) be the predicted offsets in the same cell produced by the network. Their computations are consistent with Eq. (7p. a positive cell contains only one circumcenter (i.e. T = 1), we consider as having two identical circumcenters inside. If it contains 7 2 2 circumcenters, we match the two predictions to the ground-truth circumcenters that contribute to the minimum loss. The localization enror is defined as average of the smooth L1 loss between all pairs of matched g. i.e.
G. (gii.... "..........: ggr
min Simoothy1(gaa. ga) + smooth 8i2)) C2 N (o.))EP(r.22)
(9)
P(r,2) represents the permutation of all selections from 7 elements, egg. P(2, ((1,2), (2, 1)]. For the special case of = is calculated by summing the scalar losses from each dimension of gi-
define P(1,2) {(1,1) The smooth (go gi)
Eventually, the multi-task loss function our neural network is formulated as +12, where A is a hyperparameter for balancing the different loss terms.
3.5 INFERENCE
We train the network on local patches, but performing the inference on the complete point cloud. After predicting the adjacent triangles of each point, take their union to form the primitive trian-

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Published as a conference paper at ICLR 2023
gulation (mesh). Since the primitive mesh is produced regardless of topological constraint, apply post-processing to make it Sige-manifold and fill the small holes. For convenience, we provide C implementations with Python interface for the post-processing
4 EXPERIMENT
ABC dataset. The ABC dataset (Koch et al. 2019) is a collection of one million CAD models for deep geometry research. provides clean synthetic meshes with high-quality triangulations. We use the first five chunks in this dataset to create the training and test sets. Each raw mesh is normalized into a unit sphere and decimated with a voxel grid of 0.01. This results in total of 9, 026 meshes, and we apply a train/test split of 25% 75% to validate effectiveness of the proposed model. The model trained on the ABC training set. We assess it on the ABC test set as well as other unseen datasets. The implementation details are discussed in the supplementary.
Evaluation criteria. We evaluate the overall surface quality of each reconstructed mesh using Chamfer distances (CD1, CD2), F-Score (F1), normal consistancy (NC), and normal reconstruction error (NR) in degrees. We also evaluate their preservation of sharp details on the surface using Edge Chamfer Distance (ECD1) and Edge F-score (EF1), similar to (Chen et al. 2022). See the supple- mentary for computational details about those surface quality metrics. To compare the triangulation efficiency of learning- basedd methods, we report their inference time on the same machine. The number of points in the point cloud is provided for reference.
4.1 PERFORMANCE
ABC test. Table compares the performance of the proposed method, abbreviated as 'CircNet',
with those of the traditional triangulation methods, iee, a-shapes (Edelsbrunner & Mücke 1 1994 and
ball-pivot (Bernardini al. 1999). the implicit surface method PSR (Kazhdan & Hoppe 2013 and
the lcarning-based triangulation methods (i.e. PointTriNet (Sharp & Ovsjanikov 22020). (2000),
IER (Liu
al. 2020), DSE (Rakotosaona et al. 2021b). We use the pre-trained weights of other learning- based methods to report their results. It is observed that training those methods from scratch on our ABC training set leads slightly worse performance. We report the performance of a-shapes 5%. We note that ball-pivot requires normals to be estimated first. The
using = 3% and performance of PSR reported by using normals n estimated from the point cloud, and normals ng computed from the ground-truth mesh. In the efficiency report, we also provide the network inference time of CireNet in brackets [.]. It can be seen that the proposed CircNet is much faster than the other learning methods. Besides, its reconstructed meshes are in high quality.
Generalization. We validate generalization of the proposed CircNet using unseen datasets. Those include FAUST (Bogo et al.[ [0014), dataset of watertight meshes of human bodies; MGN (Bhat- nagar et al. 2019). a dataset of open meshes of clothes; and several rooms of Matterport3D (Chang al. 2017), dataset of large-scale scenes reconstructed from RGB-D sequences. In all cireum- stances, the learning-basse based methods are evaluated without any fine-tuning. We report the results on FAUST and MGN in Table 2 and Table respectively. It can be noticed that CircNet outperforms the other approaches most of time, especially in the reconstruction of the open surfaces from MGN. We observe that IER prefers uniform point clouds as inputs. Due to the non-uniformity of point clouds in FAUST and MGN, its performance drops significantly. As reference, we provide its re- sults on the uniformly resampled point clouds generated by Poisson-disk sampling (Bridson 2007).
Table 1: Surface quality of different triangulation methods on the ABC test set. For each metric, we report the average results across all meshes. The total triangulation time of each learning- method is reported on the largest point cloud whose size is provided for reference. We also report the network inference time of CircNet brackets [.].
Surface Quality
Efficiency
Method
overall
sharp
total runtime/scconds
CDI(x 10
CD2((10'M))
F1f
NC
NR.
ECDI(X 10-))
HFT1
#points
a-shapes-36 3%
0.448
2,670
0.836
0.943
7.203
2.628
0.616
6.555
a-shapes-5%t
0.601
6.972
0.802
0.929
8.625
3.767
0.572
6.544
ball-pivot (+m)
0.297
0.684
0.939
0.981
2.244
0.782
0.873
0.347
PSR (+n)
0,403
6,700
0.894
0.971
6,493
32,402
0.095
12.571
PSR (+n,t)
0.400
6,081
0.901
0.972
6.020
26.160
0.108
19669
12.529
DSE
0.285
0,548
0.949
0.985
1.793
0.538
0.929
59.605
IER
0.289
0.580
0.945
0.983
1.949
0.890
0.914
37.683
PointTriNet
0.288
0.790
0.948
0.984
1.931
0.688
0,926
38.063
CircNet (Prop.)
0.284
0.544
0.950
0.985
1.758
0.708
0.924
3.316 [0.996]

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Published as a conference paper at ICLR 2023
Table 2: Method comparison the watertight meshes of FAUST dataset. The 100 point clouds in
this dataset each have 6890 points. We report the average runtime of each method per sample.
Surface Quality
Efficiency
Method
overall
sharp
#points
total
CDI(X109)
CD2(x 172(x107)) 10")
FIf
NC1
NR.
ECDI(x10")
EFI
runtime/seconds
a-shapes-3%
0,551
3.689
0.757
0.894
18.197
7.222
0.087
0.684
a-shapes-5%%
1.225
19.779
0,531
0.807
27.286
7.879
0.056
0.681
ball-pivot (+n)
0.323
1.002
0.923
0.970
6.037
2.887
0.184
0.138
PSR (+n)
1.119
39.229
0.564
0.863
21.721
4.161
0.438
10.674
PSR (+nge)
0.427
4.108
0.915
0.969
10.269
1.069
0.810
10.643
6890
DSE
0.218
0.307
0.995
0.984
3,910
0.883
0.801
23.792
IER
4.649
339.565
0.160
0.786
31.195
2.081
0.376
13,949
IER (Poisson)
0.257
0,406
0.989
0.973
8.692
2.170
0.456
10.628
PointTriNet
0.219
0.308
0.995
0.983
4.393
1.233
0.807
13.344
CireNet (Prop.)
0.221
0.316
0.993 0.980 4.557
0.939
0.820
3.471 [0.382]
Table 3: Method comparison on the open surfaces of MGN dataset.
Surface Quality
Efficiency
Method
overall
sharp ECDI(x 10
max #points
total
CDI(x 10%)
CD"((100)
FIf
NC1
NR.
EFIf
runtime/seconds
a-shapes-3%
0,517
2.687
0.757
01927
14.797
11.976
0.046
1.399
a-shapes-5%
0,899
10.322
0.578
0.883
20.233
14.227
0.023
1.390
ball-pivot (+n)
0.462
4.917
0.844
0.974
5.803
11.847
0.083
0.279
PSR (+n)
1.319
18.542
0.356
0.892
18.329
12.286
0.071
10.389
PSR (+ng))
1.077
10.481
0.402
0.948
12.224
7.912
0.137
10.623
10116
DSE
0,270
0.530
0.968
0.983
3.970
4,508
0.440
32.433
IER
0.827
23.464
0.796
0.972
6.220
4.932
0).477
12.143
IER (Poisson)
0.310
0.635
0.948
0.980
7.073
6.777
0.317
13.279
Poin/TriNet
0,272
0.562
0.967
0.981
4.398
5,936
0.399
19.906
CireNet (Prop.)
0.269
0,512
0.968
0.981
4.230
3,231
0.486
4.536 [0.535]
Table 4: Our results on Matterport3ID, as well as the uniform, non-uniform and noisy data.
Surface Quality
Efficinccy
Data
overall
sharp
#points
CD1(x10P)
CD2(x10')
Fl
NCT
NR.
ECDI(x10')
EF11
runtime/seconds
Matterport3D
0.151
0.144
0.999
0.933
10,870
0.249
0.974
10F
~9.7 minutes
Robustness
poisson
0.278
0.533
0.949
0.976
4.033
1.281
0.660
10
3.190 [0.562]
(ABC)
= 0.1
0.328
0.720
0.908
0.965
10.053
1.500
0,630
10*
3,368 [0.499)
0.2
0.419
1.245
0.793
0.931 16.735
4.396
0.467
10*
5,921 [0.549]
0.3
0.523
2.076
0.689
0.880 23.287
6.790
0.294
104
9,776 [0.627]
non-uniform
0.395
1.852
0.858
0.942 8.693
3.490
0.457
5085
(mcan)
1.958 [0.525]
For Matterport3D, we report the quantitative results of CircNet over 25 scenes in Table The input point clouds are generated by uniformly sampling 5 x 10 points from the raw meshes. We compare the reconstructed meshes of CircNet with others on a large building in Fig. 5
Robustness. To test the robustness of CircNet, we generate point clouds that are uniform, noisy and non-uniform using 100 meshes of the ABC test set. Specifically, apply the Poisson disk sampling to generate uniform point clouds with 10t points each. We also add different levels of Gaussian noise (i.e., o 0.1, 0.2, 0.3) to the data obtain noisy point clouds. To get non-uniform point clouds, we vary the densities of the uniform data along an axis, similar to DSE (Rakotosaonal al. 2021b). The quantitative results of CircNet for each category are provided Table We report the quantitative comparisons in the supplementary. Figure (euurer]sshon shows the reconstructed meshes of CircNet for point clouds of varying densities or with noise using an interesting shape from the ThingilOK dataset (Zhou & Jacobson 2016). The point cloud data are generated in similar ways.
Limitations. We analyze detection accuracy of different triangles according to their maximum inte- rior angles. Figure F such results for the ABC and FAUST datasets. Without loss of generality, we randomly sample 500 meshes in ABC to plot the results. We compute the detection accuracy as the ratio between the number of detected triangles and the ground-truth number. When the maximum interior angle becomes large, the radii of the triangle circumeircles can be in an intractable ( (->+oo) range. This makes the circumcenter detection difficult using fixed anchor priors. As expected, the detection accuracy decreases with the increase of the maximum angle. So far, handling edge- manifoldness takes non-trivial amount of time in all learning- because the classification or detection networks are unaware of any surface topology.
triangulation methods. This is
8

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Published as a conference paper at ICLR 2023
Metries: CDJ.CDEANCIR
DSE: 0.0880005110994418..22
(c) PrineTriNet
0.089/0.052/00 944/8.384
31.9 minutes
23.0
Materport
(d) 0.8880004990.9444
CircNet (Proposed)
000660..4470.9507..66
16.4 minutes
9.1 minutes
(a) point cloud (10" points)
(o) Poisson
(c) 0.3
(d) Non-unifom
(b) 0.1
Figure 5: Visualization of the reconstructed meshes. Quantitative results of CD1/CI2//NC/NR and the reconstruction time are reported for different methods over a scene of Matterport3D. The pro- posed CircNet takes the shortest time but reconstructs the scene in best quality. The bottom two rows demonstrate the robustness of CircNet for the fact that it still reconstructs the underlying shape well when the point cloud becomes highly noisy or the non-uniformity becomes severe.
x10
x100
GT
0.9
GT
0.9
Frequency x
on
Pred
Accuracy
Frequency
Pred
Accuracy
0.6
2
0.3
0.3
90
12C
120
0
60
90
Maximum Interiar Angle
Maximum Interior Angle
Maximum
Interior Angle
Maximum Interior Angle
(a) ABC
(b) FAUST
Figure 6: Detection frequency and accuracy with respect to the maximum interior angles (in degree) of ground-truth triangles. We provide results on two datasets, ABC and FAUST. For each dataset, the left plot shows the frequencies of both ground-truth and correctly predicted triangles, while the right plot shows the prediction accuracy. It can be noticed that triangles ABC are distributed more closely equilateral triangles, compared those in FAUST.
5 CONCLUSION
By exploiting the duality between a triangle and its circumeenter, we have introduced neural detec- tion architecture for point cloud triangulation. The proposed network employs a single-shot pipeline, and takes local geometrics as inputs to detect the cireumcenters of adjacent triangles of each point. We predefine multiple anchor points to guide the detection process. Based the detected circum- centers, we reconstruct the 3D point cloud into primitive triangle mesh. can simply post- processed into surface mesh. Compared to the previous learning-based triangulation methods, the proposed method has lower complexity, single-shot architecture, and does not depend on any tradi- tional method to triangulate the points. We demonstrate that the method, though trained on CAD models, is able to reconstruct unseen point clouds including the large-scale scene data satisfactorily. It is also robust noisy and non-uniform data.

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Published as a conference paper at ICLR 2023
6 ACKNOWLEDGEMENT
This research is funded part by the ARC Discovery Grant DP220100800 to HL. We thank the anonymous reviewers for their comments on improving the quality of this work.
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12


Reviews:
[{"review_id": "v_NnK55mCv-", "reviewer": "Reviewer_7M62", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The paper proposes a method for point cloud triangulation by creating local per-point triangulations and then post-processing these local triangulations into a global point cloud triangulation. The first step is performed using a graph neural network and it is the main contribution of the paper. Specifically, the paper proposes to predict the presence and the location of the circumcenters of the triangles around each point using a graph neural network. The paper further proposes to discretize the space around each point into predefined anchor cell and predict the circumcenters inside these anchor cells.   ", "summary_of_the_review": "* The attached code does not include the code for training the model, or for post-processing the network output (local per-point triangulations) into a global triangulation.\n\n* Not all parameter choices are explained - e.g. how is M chosen (Sec. 3.1).\n\n* In section 3.1 and Figure 4: what constraints the network to produce valid local triangulations? E.g. that the triangles in this 1-ring neighborhood of a point are non-overlapping. Provide some quantitative experiments.\n\n* I suggest to move Eq. (7) and the preceding sentence starting with \"The proposed network detects each circumcenter\" to section 3.2, to explain how anchors are used to predict circumcenters. Also, use “hat” above \"g\"s in Eq. (7) to specify that these are offsets from predicted circumcenters, not from the ground truth ones.\n\n* At the end of Section 3.5, the paper states \"Since the primitive mesh is produced regardless of topological constraint, we apply post-processing to make it edge-manifold and fill the small holes. For convenience, we provide C implementations with Python interface for the post-processing.\" This post-processing seems like a very important part of the proposed method. Since nothing constraints neighboring points to have consistent triangulations after the inference, the postprocessing step is essential to fix the inconsistencies and to produce consistent and useable point cloud triangulation. For such an important step, the two line explanation which does not contain any detail about the method is not sufficient. Also, as stated above, the code linked to the submission does not include the postprocessing code.\n\n* Evaluation criteria: Elaborate on why CD1, CD2, F1 are the right metrics here. E.g. what exactly does Chamfer distance measure here and how it is related to the quality of the triangulation. Add an evaluation metric measuring the quality of the constructed meshes in terms of how well they approximate 2D surfaces.\n\n* Figure 5:\n    * (a) Add visualization of a small parts of the mesh showing the quality of the triangulation. Render the resulting mesh to show the triangulation quality visually.\n    * (d) The triangulation seems to contain holes for non-uniformly sampled point cloud, contradicting the statement in the caption that the method is robust to variations in the point cloud density.\n    * The caption is very lengthy and can be improved by moving come explanations to the main text.\n\n", "strength_and_weaknesses": "Strengths\n* The paper is clearly written and easy to follow.\n* The paper proposes a novel method to predict local per-point triangulation of a point cloud with a graph neural network.\n\nWeaknesses\n* The proposed deep learning method only predicts local per-point triangulation (1-ring neighborhood). Even this steps does not provide any guarantees of the validity or quality of the local triangulation - e.g. can the triangles overlaps? Some experiments and metrics need to be added to illustrate and validate this step.\n* The main weakness of the proposed method is the fact that it does not discuss in any detail how these per-point triangulations are post-processed into a valid (e.g. non-overlapping triangles) and useable (e.g. for rendering) triangulation of the whole point cloud. Since nothing in the network design constraints neighboring points to have consistent triangulations after the inference, the postprocessing step seems to be essential to fix the inconsistencies. The paper also does not provide any metrics and almost no visualizations to illustrate the validity and useability of the reconstructed meshes. In addition, it is mentioned in the paper that a C implementation of the postprocessing is provided, however it does not appear in the attached code submission. ", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "1: The contributions are neither significant nor novel."}, "extra_text": {}}, {"review_id": "SoYBQ-r0QMV", "reviewer": "Reviewer_VP72", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The paper introduces a novel method to generate triangular meshes for the the input 3D point cloud. The authors introduce multiple anchors  to divide the neighborhood space of each input 3D point. A deep neural network is then used to predict the presence and the locations of cirumcenters in the point local neighborhood space. Then the dual of the circumcenter is used to extract triangular mesh.\nContributions:-\n1. This paper shows that their method is more efficient and accurate than the state of the art learning based techniques on point cloud triangulation.\n2. The proposed method generalizes on real scenes with noisy data and doesn't hold restrictions on mesh topology as in contrast to some other learning based techniques. \n", "summary_of_the_review": "The paper introduces a novel method to generate triangular meshes for the the input 3D point cloud. The authors use a deep neural network  to predict the presence and the locations of circumcenters in the point local neighborhood space. Then the dual of the circumcenter is used to extract triangular mesh. The paper provides some evidence that their method is more efficient and accurate than the state of the art mesh triangulation techniques. The impact of the paper can be improved by improving the quality of visualization of the results by highlighting, the regions of improvements. Discussing the results with other class of methods such as implicit surface reconstruction ones will bring out true benefits and impact of such method.", "strength_and_weaknesses": "Strengths:-\n1. A novel method to generate  triangular meshes for the the input 3D point cloud. First learning based technique to generate point cloud by estimating the cirumcenters in point local neighborhood space.\n2. Method seems to generalize on real scenes with noisy data. \n3. Method is much faster than other state of the art learning based techniques.\n4. Theoretical foundations of the paper seem to be correct.\n\nWeakness:-\n1. The paper lacks to provide enough visual evidences of real benefits of the paper over standard point cloud triangulation techniques. In my opinion, the authors should make it very clear how is accuracy improving in comparison to other techniques. While, some metrics like chamfer dist. (and edge distance) speak for the accuracy, I believe visual aspect of highlighting the regions where accuracy or completeness is improved increases the actual impact and brings more clarity for the reader.  Authors can highlight regions where standard techniques struggle, for example, thin structures, bad triangulation (non-manifold errors). \n2. Although, it is fair to say implicit surface representation works are fundamentally different than mesh triangulation but I guess comparing results with such methods might highlight the strengths/weakness of both classes of methods. This enables complete and higher level study to understand true value of choosing learning based mesh triangulation over something like Poisson surface reconstruction.\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "KQS4XwU5uf", "reviewer": "Reviewer_Sk4W", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper tackles the problem of point cloud triangulation. The authors introduce a deep neural network to detect circumcenters from point patches, and then they extract triangles dual to the detected circumcenters to form a primiteive mesh. The proposed method can reconstruct meshes within a couple of seconds, and poses no restriction on the surface topology. Evaluation in terms of quality, efficiency, and robustness has been carried out on 4 prominent datasets.", "summary_of_the_review": "The idea of detecting circumcenters from point cloud patches and extracting traingles dual to the circumcenters is technically sound and novel. Sufficient evalations have been carried out to demonstrate the effectiveness, efficiency, and the robsutness of the proposed method. Experimental results show that the proposed single-stage pipeline outperforms existing two-stage pipelines in terms of reconstruction quality and efficiency. I would support accepting this paper.", "strength_and_weaknesses": "Strength\n+ The formulation of the problem as circumcenter detection sounds novel in deep learning based point cloud triangulation.\n+ The formulation of the problem as circumcenter detection is technically sound.\n+ The proposed method does not require exhaustive enumeration of traingle combinations or local surface parameterization, which are computationally expensive procedures.\n+ The proposed method does not require any surface normal information, which are typically not available for a point cloud.\n+ The proposed method is a single-stage pipeline and has high efficiency compared to exsiting two-stage pipelines.\n+ The proposed method has achieved SOTA results in term of quality in the ABC dataset and MGN dataset, and highly competitive results in the FAUST dataset.\n+ The proposed method has achieved SOTA results in term of efficieny among deep learning based methods.\n+ The proposed method is robust to noisy and non-unifrom data.\n+ The proposed method works for both water-tight and open meshes.\n\nWeaknesses\n- The anchor based detection approach is not novel but borrowed from existing object detection networks. Novelty is limited in this technical aspect.\n- There is no evaluation on the effect of K (in KNN patch composition) and s (in detecting multiple circumcenters in a single anchor cell).", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "0-KXEL-KB0", "reviewer": "Reviewer_78GV", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The authors propose a method for creating a mesh from point clouds taking advantage of learning-based techniques.\n\nThe main contribution to the paper is the use of the duality relationship between the mesh triangle and the respective circumcenter, in which each triangle vertex is equally distant from the circumcenter. This is done using a deep neural network.\n", "summary_of_the_review": "The paper has some interesting contributions and, although the proposed meshing is still slower than the traditional baselines, results show that it is significantly faster than previous learning-based methods.", "strength_and_weaknesses": "Strength:\n1) The paper is well-written and easy to follow.\n2) The method is technically sound.\n3) Although the method does not beat the state-of-the-art in runtime neither surface quality, authors show a significant speedup compared with learning-based baselines for good surface quality.\n\nWeaknesses:\n1) The method is still slow compared to the traditional baselines.\n\nIssues/questions:\n1) It would be good to define an \"optimal triangle\";\n2) The authors mention that the final mesh is obtained by filling small holes in the primitive mesh. It is unclear to me why is this needed, and how are they being filled.\n3) The authors use Anchor priors using spherical coordinates. The motivation for the use of spherical coordinates is not clear to me.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}]

Author rebuttal:

Decision: Accept: poster