SpelsNet: Surface Primitive Elements Segmentation by B-Rep Graph Structure Supervision
Authors: Kseniya Cherenkova
Elona Dupont
Anis Kacem
Gleb A Gusev
Djamila Aouada
Venue: NeurIPS 2024 poster (2024)
Keywords: Surface Primitives Segmentation;Scan2Brep;B-Rep Topology Supervision;
Primary area: machine_vision

Abstract: Within the realm of Computer-Aided Design (CAD), Boundary-Representation (B-Rep) is the standard option for modeling shapes. We present SpelsNet, a neural architecture for the segmentation of 3D point clouds into surface primitive elements under topological supervision of its B-Rep graph structure. We also propose a point-to-BRep adjacency representation that allows for adapting conventional Linear Algebraic Representation of B-Rep graph structure to the point cloud domain. Thanks to this representation, SpelsNet learns from both spatial and topological domains to enable accurate and topologically consistent surface primitive element segmentation. In particular, SpelsNet is composed of two main components; (1) a supervised 3D spatial segmentation head that outputs B-Rep element types and memberships; (2) a graph-based head that leverages the proposed topological supervision. To enable the learning of SpelsNet with the proposed point-to-BRep adjacency supervision, we extend two existing CAD datasets with the required annotations, and conduct a thorough experimental validation on them. The obtained results showcase the efficacy of SpelsNet and its topological supervision compared to a set of baselines and state-of-the-art approaches.

SpelsNet: Surface Primitive Elements Segmentation by B-Rep Graph Structure Supervision
Kseniya Cherenkova SnT, University of Luxembourg, Artec3D kseniya. chnnyya.cherenkoa@@un.... lu
Elona Dupont
SnT, University of Luxembourg elona. cona.dupont@un lu
Anis Kacem
Gleb Gusev
Djamila Aouada SnT, University of Luxembourg dj ami la. auoada@uni .uu
SnT, University of Luxembourg anis kacem@uni........ lu
Artec3D gl glebBartec3d.com com
Abstract
Boundary Representation (B-Rep) is the standard approach for modeling shapes in Computer-Aide Aided Design(CAD). We present SpelsNet, a neural architecture for segmenting 3D point clouds into surface primitive elements under topologi- cal supervision of its B-Rep graph structure. We also propose a point-to-BRee adjacency representation that allows for adapting conventional Linear Algebraic Representation of B-Rep graph structure to the point cloud domain. Thanks to this representation, SpelsNet learns from both spatial and topological domains enable accurate and topologically consistent surface primitive element segmentation. In particular, SpelsNet is composed of two main components; (1) a supervised 3D spatial segmentation head that outputs B-Rep element types and memberships; (2) graph-based head that leverages the proposed topological supervision. To train SpelsNet with the proposed point-to- Bo-p adjacency supervision, extend two existing CAD datasets with the required annotations, and conduct a thor- ough experimental validation them. The obtained results showcase the efficacy SpelsNet and its topological supervision compared to a set of baselines and state-of-the of-the-art approaches.
Introduction
Creating a structured and editable Computer- Aided Design (CAD) representation Mortenson [2006), Shah and Mäntylä [1995] from an unstructured 3D scan (e.g. point cloud) is a core challenge, often referred to reverse engineering. This field has a long history of extensive research due to its numerous commercial applications Abella et al. 1994). Varady et al. 1997], Bénière et al.) (203))
Liu et al. 2023 Modern CAD workflows commonly
Boundary Representation the primary
format to model complex shapes Lambourne et al. [2021] Guo et al. [202).. The wide adoption of B-Rep in most CAD software and recent advances in neural point cloud representations challenges the
reverse engineering research towards the problem of learnable B-Rep inference from point clouds Liu
al. 2023). Guo al. 2022] Yan al. [2021] Huang et al. 2021
Boundary Representation (B-Rep) is a collection of connected surface elements with their geometric definitions in form of parametric surfaces, curves and points (haah and Mäntylä 1195). The topology of these elements is also described by the connection of face, edge and vertex components. Thus, face is bounded surface, edge is bounded curve, and vertex is realisation of 3D point DDCarlo et al. [2014). B- B-Rep is a compact representation and it retains more structural information about an object than point cloud. Most popular approaches to reverse engineer B- B-Reps from point clouds follow a segmenntation paradigm, i.e. the point cloud is firstly segmented into surface patches,
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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and then parameterized by fitting a specific surface type Sharma et al. [2020), Li et al. (2019), Yan al. [02T]. Huang et al. [02T]. However, existing segmentation basedd approaches mostly deal with either surface patches or boundary curves, ignoring the full B B-Rep structure. This often leads to inaccurate and disjoint reconstruction of elements (Sharma et al. [2020]. To address this, ComplexGen Guo et al. [2022] modeled the B-Rep as a chain complex Hatcher [2002) and formulated the prediction of validness and primitive types as classification tasks to recover corners, curves, and patches together with their mutual topological features. Assembled in probabilistic graph constraints, this topological information further used in a time consuming post-processing topological and geometrical optimization recover plausible geometry.
In this work, we propose to exploit the topological information from B-Rep as a direct neural supervision within a Graph Neural Network (GNN) paradigm. To incorporate this supervision together with geometric data into a single learnable pipeline, we consider the Linear Algebraic Representation (LAR) of B-Rep chain complex DiCarlo et al. (2014). LAR is defined on B-Reps and fully encodes their chain complex in sparse and compact matrices offering desirable learning properties. To enable direct supervision on point clouds using LAR, we adapt it to the point cloud domain and propose novel point-to-BRey adjacency representation. Furthermore, we design a novel end-to-end trainable network architecture, named SpelsNet, for the inference of B-Rep elements from point clouds. SpelsNet is composed of a spatial and a topological component leveraging both the classical segmentation and the proposed point-to- to-B adjacency supervision signals, respectively. The contributions of this work can be summarized to:
A novel LAR-based representation of B-Rep chain complex adapted to point clouds, called point-to-BRep adjacency, that allows for direct neural supervision of B-Rep topological information on point clouds. To the best of our knowledge, we are the first to propose a direct B-Rep chain complex supervision on point clouds;
SpelsNet, an end-to-end trainable architecture for B-Rep element segmentation from point clouds. SpelsNett unifies 3D spatial and graph neural networks in single design and exploits the proposed ---baaed point-to-BRey adjacency supervision in addition to the classical B-Rep element segmentation supervision;
Extended versions of two existing CAD datasets ABCParts Li et al. [019 and
CC3D Cherenkova et al. (020). The new versions, called ABC-VEF and CC3D-VER include the proposed
point-to-BRep adjacency representation clouds and will be made publicly available to enable further research;
the point
A thorough experimental validation showcasing the superiority of the proposed method over multiple baselines and state-of-the-art approaches.
The rest of the paper is organized as follows: Section 2 discusses the related works. In Section 3 we provide background on Rep chain complex and present the proposed point-to-Bae -Rep adja- cency representation. Section 4 offfers detailed description of the proposed SpelsNet network. The experiments are reported and discussed in Section Finally, Section 6 concludes the paper and provides perspectives for future works.
2
Related Works
Existing research Scan-to-Brep often focuses on specific aspects of the problem, such enhancing segmentation, improving surface fitting, or refining topology. We categorize these approaches accordingly in the following discussion.
Starting with Efficient Ransac Schnabel et al. 2007], which progressively estimates primitive parameters within point cloud in sample consensus paradigm, continuing with data-driven learning methods Li et al. 2019). [Sharma et al. 2020)) that train point-based neural networks to assign patch primitive types and parameters to each input point, it became common to solve Scan-to-Ban Brep problem in two-phase manner, namely, decomposition (segmentation) and fitting. PrimitiveNet Huang et al. [2021] proposes to treat primitive types as semantic classes and use adversarial learning to guide feature enrichment for better surface property representation. HPNet Yan et al.] [202T) runs a mean-shift clustering over the hybrid representations that are combined by learnt weights.
Compared to SPFN Li et al. [2099, ParSeNet Sharma et al. [2020] constructs an additional SplineNet component to extend the set of supported surface primitives with bspline surfaces. BPNet Fu et al.

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2023] discards the primitive types and approximates all surface patches with bspline surfaces. QuadricsNet Wu al. [2023] defines fitting process in form of quadrics. Several approaches focus solely on edge reconstruction to generate wireframes. For instance, NerVE Zhu et al. [2023] utilizes a neural volumetric edge representation for piecewise linear curves extraction, while DEF Matveev et al.. [022] regresses continuous distance field to the closest edge supplemented by spline-based curve extraction. SepicNet(Chie Cherenkova et al. (2023) builds an end-to-end trainable network, where the curve fitting is formulated in a crimitiveddifieenttin
manner. Mentioned above et al. (2023), Wu et al. 2023 Zhu et al. 2023] can be considered as alternative representations, though interesting, but fall off the traditional B Rep structure.
major challenge in previous work has been the discontinuity of predicted surface elements, often requiring extra post processoo..nn While ParSeNet Sharma et al. (2020) offers an optional refinement module, Li et al. 2023] tackle this issue directly by simultaneously detecting surfaces and edges using a two-branch network. AutoGPart[Liiu et al. (2022) presents generalizable approach for 3D) part segmentation with geometric priors, potentially improving continuity.
We propose to leverage B-Rep inherent graph structure, with nodes representing elements like vertices, edges, and faces, directly within a Graph Neural Network by developing a unified representation for both spatial and graph domains. This allows us to directly incorporate B-Rep topological relationships and node features, such as element type and potentially even edge classifications (e.g.. sharp vs. smooth).
Various graph-based learning techniques, particularly Graph Convolutional Networks (GCNs) and Message Passing Neural Networks (MPNNs), have been applied to diverse data types such as part assemblies, social networks, etc /hhou et al. 2020 Notably, GCNs have been successfully employed in tasks like automatic mating prediction in CAD assemblies (Jenees (Jones et al. [2021] while MPNNs have been adapted for specific B-Rep tasks, such as face segmentation in BrepNet LarpneetLLmmburnn Lambourne et al. [2021)
While Spectral Convolutional Networks offer potential e.g., [Smirnov and Solomon [002] their computational cost can be prohibitive for large graphs. ComplexGen Guo al. [0222] predicts validity and primitive types while recovering topological features, but relies on time-consuming post-processing.
Our approach employs a unified segmentation framework with trainable LAR characteristic matrices to directly learn the B-Rep structure.
Point-to-BRep Adjacency Formulation
Given an input 3D point cloud, our method aims to identify and extract individual elements of the corresponding CAD model's addition, the method determines the primitive type these elements and their topological connectivity information. We present the essential background on B- B-Reps. including theis key elements and their connectivity relationships, then detail our approach for adapting them to point cloud data.
(B-Rep), i.e. vertices, edges, and faces. In
3.1 Background on Boundary- (B-Rep) Chain Complex
B-Rep LAR
Point Cloud LAR
11
M
f
M,
M
M
Figure 1: Left panel: The B-Rep elements and their topological connectivity in the form of LAR brep with edge-vertex characteristic matrix M, and face-vertex characteristic matrix M2. Right panel: The proposed point-to-Bal adjacency representation LAR and its characteristic matrices M and M. for points on edges (in red) and faces (in blue).
3

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A B-Rep B is composed of three elements, namely faces, edges and vertices. V = { } is as the set of all vertices where N, is the number of vertices. Similarly, E = {er} is the set of N₂ edges. and F = (fi} } the set of N faces. Each edge is defined by curve of specific type (e.g. line, arc, etc). Each face fi is also defined by a surface (e.g. planar, spherical, etc) and its corresponding parametric description. Crucially, a B-Rep B not only stores information about these individual elements but also encapsulates the connectivity information between vertices, edges, and faces. This connectivity information is essential for defining the overall topology of the model. As shown in an example in the left panel of Figure T a pyramid's B-Rep data structure stores information about its vertices, edges, and faces. The topologcal relationships between these elements represented in Vertex-Edge- Eaixe--dge-eeeee Face graph, defining the pyramid's 's overall topology.
Formally, the B- B-Rep can be described as chain complex C = EV, II) of order d = 3. where boundary operator 5 connects the elements of different orders, and IT a set of possible attributes (refer to Hatcher| [0022] for more details). For instance, 52ʃi E F gives the edges which define the boundary of a face J, and d1e; E V the end vertices of the edge e;- other words, each element
62, E 5i V.
set V, F,, F induces a corresponding vector space V, E, F and its boundary transition F
Further, we use of the Linear Algebraic Representation (LAR) described in DiCarlo et al. [2014), convenient and efficient representation that supports topological constructions that typically arise in cellular decomposition of B-Rep space. Formally, LAR encodes a chain complex C' of order d by a set of binary characteristic matrices M,, with I u < d, encoding the incidence of B B-Rep elements. These matrices provide a convenient and sparse-compact form for defining topological relations of B-Rep elements. For a B-Rep chain complex (i.e. of order 3) there exist two characteristic matrices,
M, = A (E, V) E {0, 1] N.NN, and M2 = AFF, V) E {0, 1 N Here, A V) assigns 1 to M [ if an edge E E is bounded by vertex by E V and O, otherwise. Similarly, (FF, V) operates on faces and vertices to construct M2. An example of a characteristic matrix M1 can be found in the left panel of Figure [ As mentioned in [Diarloo et al. [0044), M1 and M2 can fully characterize the B BeRep chain complex and can be used to obtain the following incidence and adjacency matrices,
AfF McM - A -
Here, Ay represents the adjacency of faces in a B-Rep, that is the faces that are bounded by a common edge. Similarly, Ace provides the edges that are bounded by a common vertex and Agr provides the vertices that bound a common edge. Note that as explained in [DiCarlo et al.) (2014), the characteristic matrices are typically sparse for actual B-Rep chain complexes, so they can be stored and operated in memory-efficient Compressed Sparse Row (CSR) format. The product and transposition of such CSR matrices, needed to compute the boundary, adjacency and incidence operators between such linear spaces, are intrinsically efficient, since the sparse matrix-vector (SpMV) multiplication is linear in the size of the output.
3.2 Proposed Point-to-BRa BRep Adjacency Representation
The LAR representation is the core concept for our proposed topological supervision. As LAR are defined on BeRep, we formulate mechanism to transfer LAR elements from B- B-Rep to point cloud domain such that the learning of the B-Rep characteristics from a point cloud can be facilitated. We use the terminology LAR brep and LARPad to distinguish between the LAR of B-Rep and its point cloud reformulation.
The right panel of Figure I depicts an example of the topological transfer to a point cloud. Let P= (p: E Idd |i = N..Npp be a point cloud composed of N, points, where d, denotes the dimension of point features. We define the characteristic matrix Mº A (E, P) E 1) N. N,N,, in LARded as binary matrix with rows representing the edges of the B- B-Rep and columns the points of P. Here, (E, P) assigns the value of M k] to if given point p: This function also sets the value Mf I] to if the edge et E
E P belongs to an edge ek E E. E is adjacent to eg. Otherwise, the
{0, 1) 1 NrXN in LAR is also a binary matrix. The rows correspond to the faces of the B-Rep and the columns to the points of the point cloud. Here also, (F, P) operates in the same way as A, (E, P) but on faces instead of edges. Note that the characteristic matrices LAR encode the per-point B- B-Rep edge and face memberships along with their connectivity that are essential elements of the B- B-Rep structure. As in
value is set O. Similarly, the characteristic matrix M. (F,P))

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Spalitee
Spelsher
Output
cloue encoderr
Typa
Edge Ispe
Face Type
and
T
T.
Input
N, ny
Typee
P
Edge and Face Hembhrechpp
F
N, x d,
1288oon
Segmantcttin
Spkrn
Cirole
Morroershig
N₂ x xd
rhace
Cior
Edge
N2 x
t GSL
M
P CCN
Choroceenste stl
Manne
Segmanichaon
W
Segmentation
W
n Topolog cal Supere nion Cadss
Spabllet
Figure 2: SpelsNet architecture overview. The SparseCNN encoder outputs the point-wise spatial embeddings Fe. Primitive types and membership segmentation learning is done in spatial domain in the SpelsNet" module together with topological supervision by B-Rep-level elements and structure prediction in Graph Neural Network in the SpelsNer"
LAR drep the adjacency of edges can be computed as Ace MMM?" and the adjacency of faces as A, M
Given point cloud P, the goal of SpelsNet to predict the corresponding B-Rep structure including the connectivity and adjacency between the primitives (i.e. edges and faces) and their types. In addition to per-point face and edge memberships, SpelsNet leverages the proposed formulation of LAR to guide the adjacency learning via topological supervision. The proposed SpelsNet is described in the next section.
4 Proposed Network
We design SpelsNet, a network architecture to segment an input point cloud P into B-Rep ele- ments. The overall structure of SpelsNet depicted Figure SpelsNet operates on point clouds with a SparseCNN encoder CChy et al. (2019) and it is composed of two main components: (1) SpelsNet" operates the spatial domain and consists of type classification head and membership head; (2) SpelsNer"e leverages the point-toBBRep adjacency supervision to learn the B-Rep topology. In the following, the individual components of SpelsNet are described.
4.1 Point Cloud Encoding
The point cloud encoder 4 is composed of sparse 3D convolutions Choy et al. [2019] in geometric space. practice, we use a SparseCNN encoder module with a ResUnet backbone, implemented as in Choy al. (2019). The input point cloud P is discretized on voxel grid with chosen resolution p, the input features of dimension d, are the 3D coordinates each point and optionally its point normal. As result, the point cloud is encoded into per-point features F. of dimension de 92.
4.2 Spatial Domain Classification and Segmentation, SpelsNet
Type Classification:
The first component of the SpelsNet classifies each point as belonging to an edge or a face well the type of the primitive Tp. This is achieved by decoding the point embedding F, with an MLP &, and using the soft logits to classify each point into one of ny = 11 types. The nr types unknown types. As a result, it possible to deduce whether a point is an edge or a face point from the predicted type T,. Point-wise primitive element types are learnt with multi-clat cross-entropy loss,
composed of 4 curve types, surface types and class for all possible
No
Lpels
CE,T,EE,,,I.)) T, N
5

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where Tp, Tp stands for ground-truth and predicted primitive types.
Memhership Segmentation:
In order segment points as belonging the same curve or surface patch a metric learning approach is followed. As depicted in Figure the point-wise embeddings F. encoded using MLP $, into features F, R.N, xd, with d' 128. The learning of F, is conducted using triplet loss Eseg. For a triplet of doint-e f f f E F of positive, negative and anchor input, respectively, the triplet loss is given by
Sag max(1
f. 2|2 |[
- f 12 m,
The default margin value m set to 0.05 and for each sample the number of points is restricted to 8000 for efficiency reasons. At inference time, the clustering step is done using HDBScan McInnes et al. (2017) to segment the points into edge membership W. and face membership W that approximate the ground truth memberships W. and W,, respectively.
4.3 B-Rep Topological Supervision, SpelsNet*e/
The topological supervision includes two main modules, a Graph Structure Learning (GSL) layer and Graph Convolutional Network (GCN). The GSL aims to learn the point-to-BRep adjacency LARPed whereas the GCN learns the B-Rep element types.
Graph Structure Learning (GSL): Inspired by the idea of dynamically learning to construct graph from a point cloud Wang et al. 2019], we develop a method to connect the spatial 3D shape features, Fe, with the learning of graph structure that reflects the B-Rep topology. In particular, the goal of the GSL layer is to learn the characteristic matrices of LAR i.e. Mf and Mž. In order to facilitate the learning, the matrices Mf and M2 are concatenated in a row-wise manner to form a single matrix
M {0, 1] x Np, Given the matrix of per per-point point cloud embeddings F. Np de where Np is the number of points in the point cloud and de is the dimension of each point embedding, the GSL layer PGSL predicts the following weighted characteristic matrix,
M = @GLL LeakyReLUUTTanbMMLPPRR
In the initial experiments, the ReLU activation, was utilized to directly enforce sparsity on the output. Due to stability issues discovered during training, this was changed in further experiments to LeakyReLU, for which outputs are further clamped to 0 as minimum value. The use of Tanh is advocated by the finding that empirically LARPad with both positive and negative weights gives better results than other options. We employ direct supervision induced by LAR with an /1-loss defined by
Liar
|M - MP
Graph Convolutional Network (GCN): Once the characteristic matrix M. has been obtained from the GSL layer, it is possible to leverage these topological features to build an adjacency graph in order predict the B-Rep elements such as the edge types (e.g. lines, spline) and face types (e.g. plane, cylinder). As mentioned in Section 3.2] the edge and face adjacency matrices, Ace and Afs- can be obtained from M. and ME. respectively. These adjacency matrices are combined into one matrix given by = M,M,. p of dimension dim(A) = (N₂ + N2) x (N₂ + Ny). A two-layer GCN PCON is introduced to exploit the graph structure inferred by GSL and defined by (Mp, A). The main idea is to further supervise this graph with an additional head via B- B-Rep element types. The initial node features of the graph are obtained by a row-wise mean pooling Pool(.) of MP. The graph embedding Z are learnt according
Z &GON (Mp. A) AReLU(APOol
(6)
where θ and ! are learnable parameters. The embedded Z is finally passed to a toft layer with a number of nodes equal to that of primitive types Finally, primitive type classification
cross entropy loss Lyele is introduced on the output of Sof tmax similarly to Cpels in Eq. (2)
Total Loss: The overall network SpelsNet is trained in an end-to-end manner and the loss is given by,
Liotal ar Epcls + a2Loeg + azLyels + as Liar with a1 24 set to 1 and 02=a3 2.

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5 Experiments
5.1 Experimental Setup
ABCParts-VEP Dataset: SpelsNet is trained and evaluated on the ABCParts dataset Li et al. 2019 using the same train (22k), test (3.5k) and validation (3.5k) splits. We prepare the updated version of this dataset, the ABCParts- VEF dataset, by extending it with B-Rep structural information in the form of characteristic matrices Mc and Mg. Refer to the supplementary materials for further details.
To evaluate the ability of SpelsNet to generalize to real-world data, a cross cross-dataset experiment on the proposed CC3D- -EF dataset is conducted. The CC3D CC3D/Cherenkons Cherenkoval al. [2020) dataset contains 3D scans along with corresponding B-Rep. Similar to ABCParts- VEF dataset, we extend the CC3D dataset with the R-Rep topological information. This proposed version of the dataset is referred to as CC3D-VEF Testing the model using 3D scans offers an opportunity not only to evaluate how the model generalizes to out-of- -ff-offfitttttttion data, but also to evaluate how the presence of realistic artifacts such as missing parts, smooth edges, and noise affects the performance. Details of the proposed ABC-VEF and CC3D-VEF datasets are provided in supplementary materials.
CC3D- VEF Real Scan Dataset:
Training and Inference: The input point cloud is normalized to unit sphere. randomly rotated and discretized on a voxel grid with resolution P 0.01. SpelsNet is trained with Adam W solver with a cosine annealing learning rate schedule starting at 10 3 and weight decay 10 for 250 epochs to convergence. The training takes approximately 10 days on node with 4 Nvidia A100(40Gb) GPUs. In order to facilitate the learning, we set the number of edges Na 128 and faces to Ny 128.
The average inference time per model is 0.5 s per model.
5.2 Classification and Segmentation Evaluation
In this section, we evaluate the results of SpelsNet on the per-point classification and segmentation tasks against state-of-thh-ar methods. In this context, only the face type output T, p and face segment output W, from the SpelsNer* module are considered.
The results are compared to state-of-the-an methods, namely, ParSeNet Sharma et al. 2020). HPNet Yan et al. [021] on patches and PrimitiveNet Huang et al. [202T] on surface patches and boundary. For the first two methods we use the checkpoints and datasets, provided by the authors. PrimitiveNet does not provide full training and testing data, thus it was retrained on ABCParts -CEF.
Baselines:
We also assess ComplexGen Guo et al. [002 by obtaining per-point segmentation and type labels from its predictions, transferring them to the original point cloud in a nearest neighbor manner. This enables the alignment of the datasets and metrics, that were not reported in ComplexGen paper due to the implementation differences.
Test-time Augmentation: When evaluating Scan-to-Brey Brep in the context of reverse engineering, it is crucial consider that 3D scans or 3D reconstructions from methods like Multi-View Stereo (Setz et al. (2066) or Nerfs Mildenhall et al. (2021) often lack the alignment to standard axes found in CAD designs. Therefore, addition to the usual assessment using aligned point clouds (w/o aug), evaluating performance under random input rotations (w/ aug) is a key indicator of how well the method generalizes to real-world, unaligned data. Typical 3D scanning artifacts(e,p noise, missing parts and details smoothing) are well represented in CC3D dataset Cherenkova et al. [2020).
Metrics: We evaluate the per-point classification and segmentation using the same metrics as in Huang et al. [202T], Yan et al. [0211. Sharma et al. [2020). These include mean type IoU denoted as tToU and mean segmentation IoU denoted as sloU. More details are in the supplementary.
[ the quantitative evaluation results on the ABCParts VEF and CC3D- VEF test sets. Clearly, the results demonstrate that all methods have learnt the dataset bias to a different extent. Such, in the presence of unconventional alignment of input point cloud the performance of ParSeNet (Sharma al. [2020) and HPNet Yan al. [202T] drops significantly. Contrary, PrimitiveNet Huang et al. [2021] and SpelsNet demonstrate more stable results under augmentation by rotation. Our method performs superior in terms of segmentation metrics, and more evidently, in primitive types prediction. Visual results in Figure depict the curves, patches segments along with their type for GT data, and the predictions of SpelsNet, PrimitiveNet and ComplexGen methods.
Results:
7

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W
T
T
T
Input
GT
PrimitieNeet
ComplexCen
Spelahiet lours)
Figure 3: Visual results of comparisons ABCParts-VEF for PrimitiveNet and our SpelsNet. From-left-to-rightt input point cloud, face types (Ty) and segmentation (W,) y), edge types (T.) and segmentation (W.).
5.3 Topology Evaluation
In this section, evaluate the topology predictions of SpelsNet and provide comparison with
ComplexGen Guo et al. [022] method.
SpelsNet is the first end-to-end trainable network that predicts the topological connectivity of B-Rep given an input point-cloud at per-point level. ComplexGen Guo et al. [2022] predicts
Baselines:
B-Rep topological elements as well but rather B-Rep-level. Namely, ComplexGen generates parametric curves and surfaces that correspond to B-Rep elements, along with their topological relationships (vertices, edges, face connectivity) represented by adjacency matrices. Then, topology prediction compared against ground truth for matched elements, and further topological optimiza- tion ensures valid B- Rep structure. SpelsNet decomposes the input point cloud based per-point labels obtained from nearest B- Rep elements as the ground truth. It uses B-Rep element connectivity for segmentation supervision at point-level, constructing point-to- B-Rep adjacency. The core idea of SpelsNet is to exploit GCNs to capture relationships between B-Rep elements based on the adjacency reformulation directly within point cloud data.
Metrics: The evaluation of the topological predictions done using metrics described in Complex- Gen Guo al. [2022] paper. Specifically,
compute the type accuracy for both edges and faces using the predictions Te and T of the GCN. To evaluate the prediction of the topology, we consider the face-edge connectivity in LARtrep using the characteristic matrix M' E (0, N The
ABCParts VEF
CC3D-VEF
Face w/o aug
Face w/aug
Face whaug
Method
sloU
IloUt
sloU1
tloU f
sloU
tloUt
ParSeNe(Sharma et al. 2020
78.19
81.86
34.49
45.99
13.42
18.16
HPNet Yan et al. 2021
40.71
83.25
21.72
14.93
11.34
10.17
PrimitiveNet Huang el al
2021
60.85
69.72
55.75
55.39
15.22
11.25
ComplexGen Guo al. 2022
33.08
45.92
32.17
45.40
14.47
19.66
SpelsNet (ours)
65.72
82.35
65.60
81.93
21.23
45.15
Table Evaluation results on face type and segmentation for the ABCParts- -VE and CC3D-VEF datasets. The metrics are averaged over 5 runs with different random seeds.

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Type Acct
Method
Edge
Face
tfe +
ComplexGen
76.3
74.2
0.201
SpelsNet (ours)
77.22
90.01
0.06
Figure 4: Qualitative results for face and edge
Table 2: Evaluation of topology results on ABCParts- VEF dataset.
segmentation for ComplexGen and our method.
value of M' A] is 1 if the face fi is bounded by the edge ck. and 0 otherwise. This characteristic matrix can be easily computed from the predictions SpelsNet as M' = MYMP Note that unlike ComplexGen, do not need to compute the matching pairs within each group of primitive elements as it is inherently defined by our representation. We define the error fe of the predicted topological
structure M' with respect to the ground truth matrix M' as
fec
1
Σ JEN;.JEN.
MM (((
NONo
Metrics presented Table are are fully aligned for both our SpelsNet and ComplexGen approaches.
The results are reported in Table 2 SpelsNet achieves superior performance in its topology reconstruction as well as type prediction. visual comparison of predictions for both methods is illustrated in Figure | The examples with segmentation results on faces and edges here are obtained from unaugmented results publicly shared by the authors ComplexGen. The discontinuity artifacts in the B- B-Rep reflect the higher topological error compared to method.
Results:
5.4 Ablation Study
In order to demonstrate the advantage of the joint learning of the SpelsNet*P and SpelsNet
module, we conduct the following experiment. Three different SpelsNet models are trained: I) Sp: SpelsNet without the SpelsNet* module and only point coordinates input features (dp = 3), 2) SpelsNethp: SpelsNet," with added point normals to the input features (dp = 6) and 3) SpelsNergptreff all the components of SpelsNet with point coordinates and normals as input features. Moreover, the test data is augmented with random rotation (w/aug). The results are shown in Table 3 Adding the point normal slightly increases the segmentation results for both edges and types. These segmentation results are further increased by the joint supervision of the two modules of the network, spatial and topological.
pm
Voxel resolution sensitivity: The input point cloud, P, is discretized into voxel grid with quantization size p. which determines the size of each voxel in the unit grid. A default value of p 0.01 was chosen, balancing model training time and geometric detail resolution on the ABCParts dataset. To investigate resolution sensitivity, the model was evaluated on test data quantized at levels 2p and 5.p, with all other settings held unchanged. The results, summarized in Table 4 and Figure 5 indicate the model's sensitivity to the input resolution. Furthermore, we show that the robustness could be enhanced by using dynamic resolution with respect to adequate selection voxel density z (the average number of points per occupied voxel), during testing. For our backbone, an optimal voxel resolution corresponds to a voxel density &o 4 - points per voxel. This improves testing metrics compared to fixed resolution, without retraining the model. Future work could explore dynamic resolution selection strategies to further enhance the model's 's adaptability to varying input data during training.

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Edge
Face
Method
sloUt
tloUt
sloUt
tloU
SpelsNet,
45.47
73.08
58,53
82.24
SpelsNet,r. "p SpolsNetph
46.69
72.86
59.69
81.26
0.02
50.01
72.34
65.60
81.93
Table 3:
Ablation studies of SpelsNet
0.005
ABCParts- VEF dataset.
Edge
Face
P
sloUt
tloUt
sloUt
tloU
0.01
0.02
35.60
46.56
56.59
59.04
0.005
43.76
61.80
61.86
61.96
0.01
50.01
72.34
65.60
81.93
1-3
47.14
59.55
58.91
66.13
51.54
73.22
65.45
83.74
0.005
7-10
45.16
49,41
59.16
72.07
Table 4: SpelsNet<Ptuef ablation studies re- sults on the ABCParts dataset with respect to voxel quantization size p and voxel den- sity v!.
T
T,
w
W.
Figure 5: SpelsNet results on real scanned data with respect to various voxel quantization size p=0.01 (default), 0.02, 0.005.
5.5 Discussions and Limitations
The degradation of performance under rotation can evaluated as a negative outcome. We argue, that uncanonical alignment, specific to real scanned data, offers way effectively enlarge the training data and to generalize to unseen data. The CC3D dataset was chosen to demonstrate the model's s generalization and robustness to realistic data it holds large-scale collection of 3D CAD models and their corresponding 3D scans, exhibiting realistic artifacts like missing parts, surface noise, and smoothed details. The sparse spatial representation allows to support the input data of dynamic resolutions. While the spatial and topological components of SpelsNet ultimately produce equivalent B-Rep predictions, the topological module was initially introduced for supervising B-Rep elements segmentation. Various other attributes available from B-Rep can be helpful for topological supervision, including sharpness of edges, connectivity degrees, surface area, convexity/concavity of faces etc. In our experiments, the spatial module's 's predictions outperform the topological module. This could be attributed to insufficient capacity of the GCN network. One of the major limiting factors of our method in terms of learning highly varied graph-structure is the choice of characteristic matrix of fixed size, implying that this size should be adjusted according to the data distribution for each new dataset. As future directions, we acknowledge several experiments that could be part of further SpelsNet performance improvement: (I) Training on CC3D data and validating on other datasets to estimate the effect of different data augmentations and artifacts; (2) The thorough investigation of spatial backbone choice; (3) The GNN powered by Transformers Kim et al. 2022 is promising direction to enhance the topological supervision part.
Conclusions
We present novel learning approach to B-Rep elements segmentation and type prediction from point cloud data. Our design incorporates features of traditional 3D spatial learning with direct topology supervision through Graph Neural Network. This is achieved by extending the point cloud data with corresponding B-Rep structure, using an efficient reformulation based on Linear Algebraic Representations. This unified representation allows us to combine spatial convolutional and graph convolutional networks in a single end-to-end trainable architecture. This leads to more accurate and structurally consistent reconstruction of CAD models from point cloud data and realistic 3D scans.
10

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Acknowledgement
The present project supported by Artec3D, and the National Research Fund, Luxembourg under the BRID0E55002//11164499999EEEEE- /tt.:////.............///////.a.
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Reviews:
[{"review_id": "Wpe6b9Aqr8", "reviewer": "Reviewer_LGxC", "summary": "This paper presents a novel model called SpelsNet for surface elements segmentation task based on boundary representation, which uses two heads for predicting B-Rep element types and extracting topological information, respectively. Experiments are evaluated on two extended datasets and the results illustrate the efficacy of the proposed method.", "questions": "Can the proposed method be applied on pure point cloud (without edge connectivity) as input?", "limitations": "Detailed discussion about the ablation study is insufficient. The insights behind the proposed modules of SpelsNet should also be discussed here.", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1.\tThis work proposes an approach to exploit the topological feature within B-Rep graph structure.\n2.\tA LAR-based point-to-BRep adjacency supervision is integrated for B-Rep element segmentation supervision.", "weaknesses": "1.\tThe concrete voxel grid resolution for the input seems unclear. How does the performance vary with respect to different resolution settings? A related sensitivity analysis is desired. \n2.\tThe resolution of Figure 2 is a bit low. It’s difficult to see the subscript of notations clearly even already zoomed in.\n3.\tThe topological information supervision based on B-Rep chain complex sounds not a unique way. Methods related to topological optimization should also provide a workaround for this task. Further comparisons and analysis with this approach should be appended.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "1. The input point cloud $\\mathbf{P}$ is discretized on a voxel grid with a fixed voxel quantization size $\\rho$. The default value is set to $\\rho=0.01$ corresponding to the voxel grid size of $100^3$. This value is chosen considering the trade-off between the model's training time and its ability to resolve the geometric details on ABCParts dataset. In order to further investigate the sensitivity of the model to the voxel resolution, we evaluate the SpelsNet$^{sp+vef}$ model on test data quantized with a voxel quantization size $2\\rho$ and $\\frac{1}{2}\\rho$. All other settings remain unchanged. The resulting metrics are summarized in the top section of Table 2 of the attached document. The model is sensitive to the input voxel resolution. In fact, it can be observed that a $\\rho$ value of $0.02$ leads to degradation of the results. This resolution is likely too low to capture the fine grained details. The higher resolution ($\\rho=0.005$) induces arbitrarily more noise in the predictions. This could be caused by the difference in voxel quantization size between training and testing. In Figure 2 of the attached document the results on real scanned data (no ground truth is known) are presented. Given various voxel quantization size, the proposed method tends to either obliviate intricate details (the thread part of the top model) or to generate noisier segments.\n    The robustness of SpelsNet is further investigated with a dynamic voxel resolution selection. Let $\\psi$ be the voxel density, that is the the average number of points belonging to the occupied voxel after quantization. The performance of SpelsNet for different values of $\\psi$ at test time can be found in the lower part of Table 2. We find that a voxel density $\\psi$ of $4-6$ points per voxel improves the metrics without having to retrain the model compared to a fixed voxel quantization size. These results will be included in the final version of the paper.\n\n2. The resolution of Figure 2 will be improved.  \n\n3. Topological optimization can explicitly reward or penalize specific topological characteristics. However, topological optimization based methods tend to be computationally intensive, especially for feature-rich models. As an example, one can perform a topology optimization step with explicit constraints inherited from B-Rep graph structure validness (see equations 1-3 in ComplexGen). The topology information generated by ComplexGen in the form of B-Rep chain complex elements is used to guide a topology optimization process. As reported in ComplexGen, this process is computationally intensive, especially for the models with a large number of elements. On average it takes 8-10 minutes for one model to be solved. As a result, topology optimization based methods may have limited practical applications with realistic and complex datasets such as the CC3D-VEF dataset. We opted for an end-to-end neural-based approach to supervise the topology. The computational impact is significantly lower at inference time which makes it more applicable for realistic scenarios.\n\n4. The proposed method operates on a point cloud without any additional input other than point coordinates (and optional point normals) during inference. The connectivity information is only used during training.", "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": "", "extra_scores": {}}, {"review_id": "TQArYp8lCg", "reviewer": "Reviewer_js6S", "summary": "This paper focused on reverse engineering where cad brep is reconstructed from point cloud. Authors extended the definition of face-edge-vertex incidence matrix to point-face, point-edge adjacency. A new SpelsNet module is added on top of existing pipeline to also predict point assignment w.r.t the primitives. They showed that the predicted topology can be passed to another gcn to better predict the brep components.", "questions": "Can authors explain the major difference between SpelsNet and ComplexGen? Both network predicts the topology and show that this is better for the final reconstruction. \n\nHow are the comparisons between SplesNet and ComplexGen conducted? Is ComplexGen evaluated using the pretrained public model without any finetuning?", "limitations": "Yes, the authors adequately addressed the limitations.", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "Paper is well-written and easy to follow. The extension from brep adjacency graph to point assignment is straight forward. It is interesting to see that the predicted topology from per-point prediction can help downstream brep component classification. Results are good versus baseline without the topology prediction module.", "weaknesses": "The idea of using predicted topology to help with brep reconstruction has already been proposed by previous method ComplexGen. SpelsNet seems similar in terms of predicting the adjacency matrix. It also has similar results on edges but much better for faces. This is very interesting as the much larger surfaces are usually easier to reconstruct than curves.  The results reported here seem to contradict this. I wonder what would happen is ComplexGen is trained with the same data? Would the difference be much smaller?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Firstly, we would like to clarify the difference between SpelsNet and ComplexGen. Both SpelsNet and ComplexGen demonstrate the importance of topology for B-Rep reconstruction, but they differ in their approach. \n\nComplexGen generates the B-Rep level geometric primitives as parametric curves and surfaces  along with the topological relations of B-Rep elements, such as vertices $V$, edges $E$ and faces $F$ connectivity. The curve and surface parameters are estimated by fitting the primitive of respective type into the detected points. Single feature vector corresponds to each predicted element within the $V$, $E$, $F$ sets. The connectivity is represented via the adjacency matrices of respective elements, and explicitly constructed as their pairwise dot product. Topology prediction is compared with the ground-truth adjacency topology for the matched elements only. Furthermore, the topological optimization solves for the topological objective and geometric fitness to ensure the structural validity of the final B-Rep chain complex with respect to the explicit topological constraints (see Eq. (1)-(3) in ComplexGen paper). This valid structure is further used in an iterative geometry refinement process where the parameters of the primitives are improved with respect to input point cloud geometry. \n\nSpelsNet follows a different approach. The input point cloud is decomposed into B-Rep elements based on per-point labels assignment. SpelsNet uses B-Rep element's connectivity in the form of two characteristic matrices $\\mathbf{M}_1^p$ and $\\mathbf{M}_2^p$ for edge and face segmentation supervision respectively. As there is no direct way to relate point cloud connectivity with B-Rep topology, we develop a straightforward method to construct point-to-BRep adjacency, described in Section 3.2 of the main paper. This formulation provides a convenient input for learning the graph structure intrinsic to B-Rep, and enables the Graph Convolution Network (GCN) supervision. The core idea of our approach is to use GCNs as they are well-suited for capturing the inherent relationships between faces, edges, and vertices in B-Rep models. Unlike 3D CNNs, which are designed for regular grids, GCNs can operate on irregular graph structures, such as B-Rep and can be trained to directly predict B-Rep-level labels from raw input data in an end to end manner. This approach simplifies the overall pipeline.\n\nA second point we would like to clarify concerns the comparison between SpelsNet and ComplexGen. Both SpelsNet and ComplexGen are trained and tested on the same splits of the ABCParts data obtained from the same B-Rep and point cloud counterparts. The ground truth data is prepared differently with specifics of each method. The visual example of both predictions is given in Figure 4 of the main paper. SpelsNet predicts per-point type and segment labels along with point-to-BRep adjacency matrices, whereas ComplexGen predicts parametrized curves and surface patches with their respective types, and B-Rep level adjacency matrices. For SpelsNet the type of the predicted segment is defined by a majority voting of the points assigned to it.\n   \nFor ComplexGen, the ground truth and predictions of B-Rep elements are approximated with a fixed number of points (30 for any curve, and 10x10 for a patch) irrespective of the actual size of the element. While one would expect large surfaces to be easier to reconstruct than edges, the aforementioned design choice in ComplexGen leads to a comparable performance in type accuracy for edges and faces (Table 2 of the main paper). On the other hand, as SpelsNet predicts per-point labels on the input point cloud it achieves a higher face type accuracy than edge type accuracy as expected.\n\nThe metrics in Table 2 of the main paper for ComplexGen are evaluated with their publicly shared code using the pretrained model and preprocessed dataset shared by the authors. The metrics for SpelsNet are computed from the outputs of our topological supervision module SpelsNet$^{vef}$.\n\nIn Table 1 of the attached document, we also report the performance of ComplexGen with respect to $sIoU$ and $tIoU$ metrics common to other state-of-the-art approaches. The predictions of ComplexGen in this case were transferred into the original input point cloud using a nearest neighbor assignment strategy. The differences between ComplexGen and SpelsNet as well as the clarification on the comparison method will be added to the final version of the paper.", "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": "", "extra_scores": {}}, {"review_id": "uqbFyMkh6L", "reviewer": "Reviewer_PwTs", "summary": "This paper proposes a method to segment and classify surface primitive elements (B-rep) from point cloud data. Previous approaches independently deal with the surface patches or boundary curves and ignores the full B-rep structure. This leads to inaccurate and disjoint primitive approximation of the surface. Unlike these approaches, this paper proposes a method to consider topological information of the 3D model through direct supervision during the B-rep learning process. For this, the paper adapts the Linear Algebraic representation of B-rep chain complex into a point-to-B-rep adjacency representation. A thorough experimental validation on ABCparts and CC3D datasets is shown showcasing the improvements over the current methods. Additionally, this method yields compelling results in scenarios where 3D models are not aligned with standard axes, a common occurrence in CAD models, thus proving its efficacy for real-world scans.", "questions": "1. **Training time:** Although not a big problem, was curious about the training time of the model. Despite training on only 22k models, it takes 10 days on 4 Nvidia A100 40 Gb gpus. What is the reason behind this long training time? \n\n\nPlease follow the weakness for more points.", "limitations": "The paper discusses the limitations adequately.", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. **Clarity:** The paper is well written with each component of the method explained clearly. In addition to this, B-rep representation is adequately explained along with the proposed point-to-B-rep representation in Section 3.2.\n2. **Quantitative Analysis:** The approach has been validated against variety of contemporary approaches. Results are comparable with previous methods like ParSeNet [1] and HPNet[2] when the 3D model is aligned with its axes. However, when the data is augmented with transformation SpelsNet achieves SOTA performance which is fair. \n\n\n[1] Sharma, Gopal, et al. \"Parsenet: A parametric surface fitting network for 3d point clouds.\" ECCV, 2020. \\\n[2] Yan, Siming, et al. \"Hpnet: Deep primitive segmentation using hybrid representations.\" ICCV, 2021.", "weaknesses": "1. **Lack of clarity on ground truth:** The information on how exactly the ground truth is obtained to train the model is not clearly explained. For e.g. it would be good if the paper had some explanation on how the point-to-Brep ground truth is obtained for supervision in Eq. 5 for $L_{lar}$ loss.\n2. **Quantitative Evaluation:** Although quantitative results for face type and segmentation are provided for the previous methods. Quantitative comparison with ComplexGen (the most recent one) is missing in Table 1. \n3. **Intuition behind the generalization and robustness:** The model shows strong generalization ability as results are shown when the model is trained on ABC dataset and tested on CC3D and real scans (Table 1 in main paper and Fig 3 in supplementary). In addition to this the model shows robustness especially in cases where the 3D model is not aligned with the axes. However, it is not very clear from the paper how this generalization and robustness is achieved. A brief information on this will be very helpful.\n4. **Qualitative Evaluation:** Qualitative results in Fig. 3 is shown only PrimitiveNet and SpelsNet. Additional results of other methods will be helpful.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Ground Truth Preparation**: Details on data preparation were included in Section 3.1 of the supplementary material due to space constraints. The labeling information of a B-Rep structure is transferred into its mesh representation using a per triangle nearest neighbor assignment under the tolerance threshold $\\tau = 0.008$. The B-Rep level topology in the form of $LAR^{brep}$ is extracted directly from B-Rep $V$, $E$, $F$ elements relation. The point-to-BRep adjacencies are calculated as described in Section 3.2 of the main paper, where $LAR^{pcd}$ is represented by its two characteristic matrices $\\mathbf{M}_1^p$ and $\\mathbf{M}_2^p$. The matrices $\\mathbf{M}_1^p$ and $\\mathbf{M}_2^p$ are row-wise concatenated into a single matrix for the supervision in Eq.5.\n\n**Quantitative and Qualitative evaluation**: For a fair comparison with ComplexGen, we need to note first that the implementation differences between ComplexGen and SpelsNet do not allow to account the same $sIoU$ and $tIoU$ metrics as for the methods reported in Table 1 of the main paper. More clarification on the main differences in the predictions of SpelsNet and ComplexGen can be found in the reply to the comments of Reviewer js6S. To compute the same metrics on the same data, we have to obtain the per-point segmentation and type labels from the predictions of ComplexGen. Similarly to data preparation, we compute this by transferring predictions from the approximated curves and patches in a nearest neighbor manner into the original input point cloud. The quantitative results are supplemented in Table 1 of this rebuttal. The visual results are also amended to include the ComplexGen predictions obtained (Figure 1 of this rebuttal text). Those metrics were not presented in the original ComplexGen work for the reasons mentioned above. Thus, we initially opted to compare with this work on the metrics (Table 2 of the main paper) that are strictly aligned with our approach. We will clarify this point in the final version of the paper.\n\n**Generalization and Robustness**: The robustness towards input data orientation is achieved by training with random rotation augmentations. Additionally, noise injection allow for better generalization to more realistic CC3D-VEF data. We also point out that even better results could be obtained when training on the CC3D-VEF dataset (Section 5.5 of the main paper). \n\n**Training time**: The convergence of the model during training when rotation and noise augmentations are added is significantly slower than without augmentations. Another reason for a significantly large training time is the high resolution nature of the input data compared to the methods that learn to segment point cloud with $2k$-$8k$ points. On average, the input point cloud size is $50k$-$~100k$ points. The last factor in the slow convergence is the dynamic nature of the batch size that is dealt in sparse convolution framework. It typically does not allow to utilize computation resources optimally, as we have to guarantee for an amount of memory available at peak usage. For comparison, ComplexGen takes 3 days on 8 Nvidia V100 GPUs to converge in 500 epochs.", "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": "", "extra_scores": {}}, {"review_id": "7ewiCsrHkE", "reviewer": "Reviewer_9eMm", "summary": "This paper proposes SpelsNet, a novel point-to-BRep adjacency representation learning method that integrates conventional Linear Algebraic Representation of B-Rep graph structures into the point cloud domain. SpelsNet consists of two main components: a supervised 3D spatial segmentation head that classifies B-Rep element types and memberships, and a graph-based head that utilizes the proposed topological supervision. To facilitate SpelsNet's learning, the paper extends two existing CAD datasets with necessary annotations and conducts extensive experiments. The results demonstrate SpelsNet's effectiveness and superiority in achieving accurate and topologically consistent segmentation results compared with existing baselines and state-of-the-art methods.", "questions": "The paper aims to predict primitives including surfaces and edges. It’s not clear why the edges need to be predicted? In practical applications, the engineers may only need to design and combine surfaces. And a second reason is once surfaces are determined, the edges are also fixed.", "limitations": "More realistic scenarios like occlusion, noisy and shape variations should also be considerd.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. This paper uses the boundary information by a Linear Algebraic Representation and combines it into a neural network framework, which is novel and has clear explanations.\n\n2. To learn more discrmitive and informative features, this paper leverages GNN to learn from the edge and face matrix. This sparse matrix is exactly an graph, so it can be greatly handled by GNN.\n\n3. Compared with existing baselines, this proposed SpelsNet achieves impressive improvements in most cases.", "weaknesses": "1. The paper only cosiders CAD models, which have nearly no noises, occlusions and distortions. Although very good performance has been achieved, but there is a lack of validation on more realitsitc data.  \n\n2. Some parts are confusing and need to be clarified:\n\n2.1. In Eq.(4), the input is point feature, but the prediction of the connectivity matrix should consider multiple points, there is not connectivity on one point. \n\n2.2. In Eq.(4), the paper uses leaky relu for sparsity, but leaky relu cannot output sparse results. They should use relu here.\n\n2.3. The segmentation loss for predicting primitive types has been used more than once in this framework, like in pcls loss and gcls loss, and seg loss also has similar effects. So it’s not clear which predictions should be taken in inference.\n\n2.4 In Section 5.2, all results come from the SpelsNet sp part, why not use vef part? \n\n3. In line 260, the paper mentions that it costs 10 days on 4 A100 GPUs for training. Since the SparseCNN is not a big model, why does it cost so significant time and computation?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "1. The CC3D-VEF dataset is a large-scale collection of 3D CAD models and their corresponding 3D scans. Many realistic artifacts, such as missing data, surface noise, smoothing of sharp details are intrinsic to it (see Figure 3 in supplementary material). The CC3D-VEF dataset was considered with exactly this incentive - to demonstrate the robustness to more realistic data. The cross-dataset experimental results on the CC3D-VEF dataset can be found in Table 1 of the main paper, in which it can be observed that SpelsNet is more robust to such realistic artifacts on the input test data than other SOTA models. The training with this data is left for future work. Additionally, more experiments with varying voxel resolution, another essential aspect of real data analysis, are presented in Table 2 of the rebuttal text (see answer to Reviewer LGxC for more details).\n\n2.1. $\\textbf{F}_e$ is a matrix with per-point embeddings of a point cloud. The dimension of $\\textbf{F}_e$ is $N_p \\times d_e$ where $N_p$ is the number of points in the point cloud and $d_e$ is the dimension of each point embedding. This will be clarified in the final version of the paper.\n\n2.2. The remark is totally correct. In the initial experiments, the ReLU activation, was utilized to enforce sparsity on the output. Due to stability issues discovered during training, this was changed in further experiments to LeakyReLU, for which outputs are further clamped to $0$ as minimum value. The statement of sparseness in Eq.4 in its current form does not hold and will be clarified in the final version of the paper.\n\n2.3. The topological module SpelsNet$^{vef}$ is introduced to supervise the B-Rep elements segmentation of SpelsNet$^{sp}$ and provide relevant signal to the point cloud features $\\textbf{F}_e$. As shown in Table 3 of the main paper, the additional supervision by SpelsNet$^{vef}$ leads to an improvement of the results, in particular for the edge and face point segmentation task of the spatial module SpelsNet$^{sp}$. While we chose the supervision of SpelsNet$^{vef}$ to output similar results to SpelsNet$^{sp}$, it is technically possible to conduct it alternative ways. For instance, one can opt to supervise for adjacency alone, or a different criteria considering other attributes available from B-Rep, such as sharpness of edge features, the degrees of connectivity, surface area, convexity/concavity of elements or other attributes. This clarification will be included in the final version of the paper.\n\n2.4. In our experiments, we found that the predictions of spatial module SpelsNet$^{sp}$ are more favorable in term of performance. One explanation is that the capacity of the GCN module is not enough to perform on par with its spatial counterpart. We plan to investigate this further in future work.\n\n3. There are several factors that impact the overall training time. The model's robustness to variations in input data orientation is achieved by incorporating random rotation augmentations during training. Additionally, noise injection techniques are used to enhance generalization to more realistic CC3D-VEF data. These augmentations make the convergence slower.  Another contributing factor to the extended training time is the high-resolution nature of the input data, which contrasts with methods designed for segmenting point clouds with significantly fewer points ($2k$-$8k$). In this case, we are working with an average of approximately $50k$-$100k$ points per point cloud. Finally, the dynamic batch size inherent to sparse convolution frameworks presents a challenge in optimizing computational resources, as sufficient memory must be allocated to accommodate peak usage. \n\n\nIn CAD applications, B-Rep models can be constructed as the combination of surfaces, where the edges are calculated as a result of their intersections. The final geometry is commonly described via a Boundary Representation. The overall B-Rep structure is comprised of connected elements, i.e., vertices $V$, edges $E$ and faces $F$. The Scan-to-BRep problem can be approached from various directions. One line of work is to recover the surface patches alone. It is followed by state-of-the-art methods such as ParSeNet. An alternative line of work could be described as the detection of edge elements solely. Then the surface patches are defined accordingly as the surfaces that are bounded by the closed loops within the set of edges (e.g. PrimitiveNet). Either way, reconstructing the B-Rep from a point cloud has to address the issue of disjoint surfaces and edges that is a limitation of the aforementioned works. One of the main objective of SpelsNet is to compensate for disjoint artifacts on the reconstructed elements by supervising their connectivity. We argue, that incorporating both edges and faces ensures for more accurate reconstruction of B-Rep structure.", "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": "", "extra_scores": {}}]

Author rebuttal:
First of all, we express our gratitude to the reviewers for their valuable feedback. We retain that our model SpelsNet is "novel"(LGxC, 9eMm). "The results illustrate the efficacy of the proposed method"(LGxC), and "are good versus baseline without the topology prediction module"(js6S). "The approach has been validated against variety of contemporary approaches"(PwTs) and "compared with existing baselines, ... SpelsNet achieves impressive improvements"(9eMm). The "paper is well-written and easy to follow""(js6S) "with each component of the method explained clearly"(PwTs). 

Further, we clarify the specific points in their comments and provide, where possible, the supporting experiments.

**Difference between SpelsNet and ComplexGen**: Overall, SpelsNet proposes a novel approach to exploit the topological information from Boundary Representation (B-Rep) models as a direct neural supervision within a Graph Convolutional Network (GCN) framework for segmenting B-Rep elements (edges and faces) on a point cloud. The approach offers an adaptation of the Linear Algebraic Representation (LAR) of B-Rep chain complex to point clouds via point-to-BRep adjacency formulation, that enables direct supervision of B-Rep topology on point clouds. 

Both SpelsNet and ComplexGen leverage topology for B-Rep reconstruction, but with distinct methodologies. ComplexGen generates parametric curves and surfaces that correspond to B-Rep elements, along with their topological relationships represented by adjacency matrices. Topology prediction is compared against ground truth for matched elements, and further topological optimization ensures a valid B-Rep structure. SpelsNet decomposes the input point cloud based on per-point labels obtained from nearest B-Rep elements as the ground truth. It uses B-Rep element connectivity for segmentation supervision at point-level, constructing point-to-B-Rep adjacency. The core idea is to further exploit GCNs to capture relationships between B-Rep elements based on this B-Rep adjacency reformulation directly within a point cloud data. The topological module, SpelsNet$^{vef}$ provides additional supervision that improves the results.

**Additional ComplexGen evaluation**: The differences between ComplexGen and SpelsNet, which prevent a direct comparison using the same $sIoU$ and $tIoU$ metrics, are important. For a fair assessment, we obtained per-point segmentation and type labels from ComplexGen predictions, transferring them to the original point cloud using a nearest neighbor approach. This allows us to compute the same metrics on the same data, with results presented in Table 1 of this rebuttal. We updated the visuals to incorporate these ComplexGen predictions. Notably, the metrics were not presented in the original ComplexGen work due to the aforementioned implementation differences. Thus, our initial comparison focuses on metrics (Table 2 of main paper) that are aligned with our approach.

**Voxel resolution sensitivity**: The input point cloud, $\mathbf{P}$, is discretized into a voxel grid with a quantization size $\rho$. A default value of $\rho=0.01$ was chosen, balancing model training time and geometric detail resolution on the ABCParts dataset. To investigate resolution sensitivity, the model was evaluated on test data quantized at levels $2\rho$ and $\frac{1}{2}\rho$, with all other settings held unchanged. The results, summarized in Table 2 of the rebuttal, indicate the model's sensitivity to the input resolution. Furthermore, we show that the robustness could be enhanced by using a dynamic resolution with respect to adequate selection of voxel density, $\psi$ (the average number of points per occupied voxel), during testing. For the ResNet34 backbone, an optimal voxel resolution corresponds to a voxel density $\psi$ of $4-6$ points per voxel. This improves testing metrics compared to a fixed resolution, without retraining the model. Future work could explore dynamic resolution selection strategies to further enhance the model's adaptability to varying input data during training as well.

**Generalization and robustness**: The CC3D-VEF dataset offers a large-scale collection of 3D CAD models and their corresponding 3D scans, exhibiting realistic artifacts like missing data, surface noise, and smoothed details (Figure 3 in supplementary material). This dataset was specifically chosen to demonstrate the model's robustness on more realistic data. The model's robustness to input data orientation is achieved through training with random rotation augmentations. Furthermore, noise injection improves generalization to more realistic CC3D-VEF data. While training on CC3D-VEF is planned for future work, additional experiments varying voxel quantization size $\rho$ – another crucial aspect of real data analysis – are presented in Table 2 of this rebuttal.

**Training time**: While training with these augmentations improves robustness, it significantly slows down the convergence process compared to training without them. The high resolution of the input data (~100k point clouds on average) further contributes to the extended training time, especially compared to methods designed for 2k-8k point clouds. Additionally, the dynamic batch size inherent in the sparse convolution framework prevents optimal utilization of computational resources due to memory constraints.

**Topological supervision**: While the spatial and topological components of SpelsNet ultimately produce equivalent B-Rep predictions, the topological module was initially introduced for supervising B-Rep element segmentation. Various other attributes available from B-Rep can be helpful for topological supervision, including sharpness of edges, connectivity degrees, surface area, convexity/concavity of faces etc. In our experiments, the spatial module's predictions outperform the topological module. This could be attributed to insufficient capacity of the GCN network, which we plan to investigate in future work.

Meta-review: The paper received positive reviews, with one *borderline accept* and three *weak accept* ratings. The reviewers maintained their positive perspectives after the rebuttal and did not raise any further concerns. Additionally, no ethical issues were identified by the reviewers.

Therefore, the area chair recommends accepting this paper. The authors are encouraged to incorporate the clarifications provided in the rebuttal into the final version to address points such as comparisons with ComplexGen, generalization, voxel resolution sensitivity, and training time.
Decision: Accept (poster)