Original: GenSDF: Two-Stage Learning of Generalizable Signed Distance Functions
Revised: GenSDF: Two-Stage Learning of Generalizable Signed Distance Functions

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

Original: AffiliationAddress email
Revised: AffiliationAddress email

Original: Abstract
Revised: Abstract

Original: We investigate the generalization capabilities of neural signed distance functions(SDFs) for learning 3D object representations for unseen and unlabeled pointclouds.
Revised: We investigate the generalization capabilities of neural signed distance functions(SDFs) for learning 3D object representations for unseen and unlabeled pointclouds.

Original: Existing methods can fit SDFs to a handful of object classes and boast finedetail or fast inference speeds, but do not generalize well to unseen shapes.
Revised: Existing methods can fit SDFs to a handful of object classes and boast finedetail or fast inference speeds, but do not generalize well to unseen shapes.

Original: Weintroduce a two-stage semi-supervised meta-learning approach that transfers shapepriors from labeled to unlabeled data to reconstruct unseen object categories.
Revised: Weintroduce a two-stage semi-supervised meta-learning approach that transfers shapepriors from labeled to unlabeled data to reconstruct unseen object categories.

Original: Thefirst stage uses an episodic training scheme to simulate training on unlabeled dataand meta-learns initial shape priors.
Revised: Thefirst stage uses an episodic training scheme to simulate training on unlabeled dataand meta-learns initial shape priors.

Original: The second stage then introduces unlabeleddata with disjoint classes in a semi-supervised scheme to diversify these priorsand achieve generalization.
Revised: The second stage then introduces unlabeleddata with disjoint classes in a semi-supervised scheme to diversify these priorsand achieve generalization.

Original: We assess our method on both synthetic data andreal collected point clouds.
Revised: We assess our method on both synthetic data andreal collected point clouds.

Original: Experimental results and analysis validate that ourapproach outperforms existing neural SDF methods and is capable of robust zeroshot inference on 100+ unseen classes.
Revised: Experimental results and analysis validate that ourapproach outperforms existing neural SDF methods and is capable of robust zeroshot inference on 100+ unseen classes.

Original:  Introduction
Revised:  Introduction

Original: Learned 3D representations can form the core of shape recovery [1], robotic manipulation [2],scene understanding [3] and content generation [4] tasks.
Revised: Learned 3D representations can form the core of shape recovery [1], robotic manipulation [2],scene understanding [3] and content generation [4] tasks.

Original: While simple to interpret, high-qualityexplicit 3D representations can come with a slew of hidden costs.
Revised: While simple to interpret, high-qualityexplicit 3D representations can come with a slew of hidden costs.

Original: Conventional voxel grids withoutacceleration suffer from cubical memory requirements [5, 6, 7], dense point clouds contain largeamounts of redundant information make querying local structures computationally expensive [8, 9],and direct optimization of mesh representations is often infeasible [10].
Revised: Conventional voxel grids withoutacceleration suffer from cubical memory requirements [5, 6, 7], dense point clouds contain largeamounts of redundant information make querying local structures computationally expensive [8, 9],and direct optimization of mesh representations is often infeasible [10].

Original: As an alternative, works suchas [11, 12, 13] propose implicit learned representations; networks trained to functionally approximatesome underlying 3D geometry.
Revised: As an alternative, works suchas [11, 12, 13] propose implicit learned representations; networks trained to functionally approximatesome underlying 3D geometry.

Original: These methods can offer lower memory requirements and fastertraining and inference speeds [14] than conventional explicit representation methods [5, 8].
Revised: These methods can offer lower memory requirements and fastertraining and inference speeds [14] than conventional explicit representation methods [5, 8].

Original: Neural signed distance functions (SDFs) [11] are a subset of this work which implicitly modelthe distance from a queried location to the nearest point on a shape’s surface – negative inside theshape, positive outside, zero at the surface.
Revised: Neural signed distance functions (SDFs) [11] are a subset of this work which implicitly modelthe distance from a queried location to the nearest point on a shape’s surface – negative inside theshape, positive outside, zero at the surface.

Original: Existing methods are capable of approximating diversesynthetic geometry, including multiple objects [11, 15, 16] and varying levels of detail for singleobjects [17, 18].
Revised: Existing methods are capable of approximating diversesynthetic geometry, including multiple objects [11, 15, 16] and varying levels of detail for singleobjects [17, 18].

Original: However, most successful methods are fully supervised–they require access toground truth signed distance values to fit to an object.
Revised: However, most successful methods are fully supervised–they require access toground truth signed distance values to fit to an object.

Original: As ordinary point clouds lack these values, afully-supervised approach cannot learn from such unlabeled data.
Revised: As ordinary point clouds lack these values, afully-supervised approach cannot learn from such unlabeled data.

Original: To replace the need for any annotated data, fully unsupervised approaches [19, 20, 21] operate directlyon point clouds.
Revised: To replace the need for any annotated data, fully unsupervised approaches [19, 20, 21] operate directlyon point clouds.

Original: These methods leverage pseudo-labels and proxies for ground truth signed distancevalues, for example the unsigned distance to the nearest point in the point cloud.
Revised: These methods leverage pseudo-labels and proxies for ground truth signed distancevalues, for example the unsigned distance to the nearest point in the point cloud.

Original: Unfortunately, existing unsupervised methods can only reconstruct a handful of shapes, and break down when weintroduce just three or four additional additional object categories.
Revised: Unfortunately, existing unsupervised methods can only reconstruct a handful of shapes, and break down when weintroduce just three or four additional additional object categories.

Original: As a result, these approachescan also not take advantage of large unlabeled point cloud datasets [22, 23, 24] and their real-worldapplications are limited.
Revised: As a result, these approachescan also not take advantage of large unlabeled point cloud datasets [22, 23, 24] and their real-worldapplications are limited.

Original: Our proposed method lifts this limitation, and learns from large-scaleunlabeled data, successfully reconstructing an order of magnitude more categories in inference thanseen during training.
Revised: Our proposed method lifts this limitation, and learns from large-scaleunlabeled data, successfully reconstructing an order of magnitude more categories in inference thanseen during training.

Original: To achieve this we propose a semi-supervised learning approach.
Revised: To achieve this we propose a semi-supervised learning approach.

Original: Existing semi-supervised methodsuse labeled and unlabeled data of the same class to improve intra-class performance for tasks suchas 3D reconstruction from images [25, 26, 27] and scene reconstruction from point clouds [3, 28].
Revised: Existing semi-supervised methodsuse labeled and unlabeled data of the same class to improve intra-class performance for tasks suchas 3D reconstruction from images [25, 26, 27] and scene reconstruction from point clouds [3, 28].

Original: Although they perform well on seen data, these methods are trained on labeled and unlabeled data ofthe same class, and so do not by themselves generalize well to unseen classes.
Revised: Although they perform well on seen data, these methods are trained on labeled and unlabeled data ofthe same class, and so do not by themselves generalize well to unseen classes.

Original: We propose a novelsemi-supervised meta-learning learning approach that learns geometric relations between labeled andunlabeled data of non-overlapping categories.
Revised: We propose a novelsemi-supervised meta-learning learning approach that learns geometric relations between labeled andunlabeled data of non-overlapping categories.

Original: One which learns an SDF that generalizes to a diverseset of unseen, out-of-distribution geometries.
Revised: One which learns an SDF that generalizes to a diverseset of unseen, out-of-distribution geometries.

Original: We train in two stages.
Revised: We train in two stages.

Original: In the first meta-learning stage, we learn shape priors from the labeled set.
Revised: In the first meta-learning stage, we learn shape priors from the labeled set.

Original: Different from existing supervised methods, we introduce an episodic training scheme where wesplit data into subsets with disjoint classes to learn a generalized shape representation.
Revised: Different from existing supervised methods, we introduce an episodic training scheme where wesplit data into subsets with disjoint classes to learn a generalized shape representation.

Original: One part ofthis split is treated as a labeled supervised set of data, with ground truth signed distance penalties,while the other is used to emulate unlabeled data samples, with only self-supervised losses.
Revised: One part ofthis split is treated as a labeled supervised set of data, with ground truth signed distance penalties,while the other is used to emulate unlabeled data samples, with only self-supervised losses.

Original: Wevalidate that this first stage provides a generic shape prior which favors expressiveness at the cost ofreconstruction quality.
Revised: Wevalidate that this first stage provides a generic shape prior which favors expressiveness at the cost ofreconstruction quality.

Original: In the second, semi-supervised stage, we introduce a new fully disjoint set ofunlabeled data to the training scheme.
Revised: In the second, semi-supervised stage, we introduce a new fully disjoint set ofunlabeled data to the training scheme.

Original: Successful training hinges on our novel self-supervised signprediction loss, which diverges from the unsigned convention of previous works [19, 20, 21].
Revised: Successful training hinges on our novel self-supervised signprediction loss, which diverges from the unsigned convention of previous works [19, 20, 21].

Original: Thissecond stage allows the model to ingest large amounts of unlabeled data to diversify the shape modellearned in the first stage, which significantly increases the quality of the signed distance predictionsover a wide set of unseen shape classes.
Revised: Thissecond stage allows the model to ingest large amounts of unlabeled data to diversify the shape modellearned in the first stage, which significantly increases the quality of the signed distance predictionsover a wide set of unseen shape classes.

Original: We evaluate our method on Acronym [29], a synthetic dataset, and YCB [23], a collection of realworld point clouds.
Revised: We evaluate our method on Acronym [29], a synthetic dataset, and YCB [23], a collection of realworld point clouds.

Original: We validate the generalization capabilities of our approach, and find that itoutperforms state-of-the-art learned SDF methods and is capable of robust zero-shot inference [30]on 100+ unseen classes and scanned point clouds.
Revised: We validate the generalization capabilities of our approach, and find that itoutperforms state-of-the-art learned SDF methods and is capable of robust zero-shot inference [30]on 100+ unseen classes and scanned point clouds.

Original: We will release code and trained models.
Revised: We will release code and trained models.

Original:  Related Work
Revised:  Related Work

Original: Learning Implicit Surface Representations.
Revised: Learning Implicit Surface Representations.

Original: Implicit neural representations form the backboneof many modern 3D reconstruction and view synthesis works [11, 12, 13, 31, 32].
Revised: Implicit neural representations form the backboneof many modern 3D reconstruction and view synthesis works [11, 12, 13, 31, 32].

Original: They useneural networks as universal approximators [33] to directly learn a mapping between spatial orspatio-temporal [34] coordinates and scene attributes, which offers a fully-differentiable and spaceefficient [28] way to represent 3D geometry.
Revised: They useneural networks as universal approximators [33] to directly learn a mapping between spatial orspatio-temporal [34] coordinates and scene attributes, which offers a fully-differentiable and spaceefficient [28] way to represent 3D geometry.

Original: Park et al.
Revised: Park et al.

Original: [11] first experimented with mappingcoordinates to signed distance values – a neural signed distance function (SDF) – whereby an objectis implicitly represented by the distances between 3D coordinate queries their closest surface point.
Revised: [11] first experimented with mappingcoordinates to signed distance values – a neural signed distance function (SDF) – whereby an objectis implicitly represented by the distances between 3D coordinate queries their closest surface point.

Original: With labeled data – when all 3D query points are annotated with ground truth signed distance values –predictions of signed distance values can be supervised directly [11, 15].
Revised: With labeled data – when all 3D query points are annotated with ground truth signed distance values –predictions of signed distance values can be supervised directly [11, 15].

Original: Existing methods [11, 15]require test-time fine-tuning even for a single class, prohibiting real-time inference or predictionon unlabeled data, or overfit to single objects [17, 18].
Revised: Existing methods [11, 15]require test-time fine-tuning even for a single class, prohibiting real-time inference or predictionon unlabeled data, or overfit to single objects [17, 18].

Original: Occupancy-based methods [16, 35, 36] canlearn a rudimentary shape prior, but still struggle to reconstruct fine features in unseen shapes.
Revised: Occupancy-based methods [16, 35, 36] canlearn a rudimentary shape prior, but still struggle to reconstruct fine features in unseen shapes.

Original: Theproposed semi-supervised method learns a robust shape prior, and substantially outperforms fullysupervised methods when tested on a set of over one hundred unseen categories.
Revised: Theproposed semi-supervised method learns a robust shape prior, and substantially outperforms fullysupervised methods when tested on a set of over one hundred unseen categories.

Original: With only unlabeled data – un-annotated point clouds – approaches try to generate proxies for signeddistance values for supervision.
Revised: With only unlabeled data – un-annotated point clouds – approaches try to generate proxies for signeddistance values for supervision.

Original: Ma et al.
Revised: Ma et al.

Original: [19] look at the unsigned distance to the nearest point in thepoint cloud as a proxy, and Atzmon and Lipman [20] propose a class of loss functions and geometricinitializations such that these unsigned distances converge to signed values.
Revised: [19] look at the unsigned distance to the nearest point in thepoint cloud as a proxy, and Atzmon and Lipman [20] propose a class of loss functions and geometricinitializations such that these unsigned distances converge to signed values.

Original: We propose a signed nearest neighbor loss and demonstrate that our approach, unlike existing unsupervised methods, isable to reconstruct thin object structures and converge on a dataset with large object variance.
Revised: We propose a signed nearest neighbor loss and demonstrate that our approach, unlike existing unsupervised methods, isable to reconstruct thin object structures and converge on a dataset with large object variance.

Original: Semi-supervised Surface Representations.
Revised: Semi-supervised Surface Representations.

Original: Traditional semi-supervised methods rely on learningfrom datasets where each category contains labeled and unlabeled samples.
Revised: Traditional semi-supervised methods rely on learningfrom datasets where each category contains labeled and unlabeled samples.

Original: During inference theyrely on pseudo-labels [37, 38], or employ ensemble techniques to enforce consistency [39].
Revised: During inference theyrely on pseudo-labels [37, 38], or employ ensemble techniques to enforce consistency [39].

Original: Thesemethods cannot be directly applied to target data from unseen categories.
Revised: Thesemethods cannot be directly applied to target data from unseen categories.

Original: For 3D representation tasks, existing methods [25, 26, 27] use semi-supervision to reconstructgeometries from images or point clouds [3, 28].
Revised: For 3D representation tasks, existing methods [25, 26, 27] use semi-supervision to reconstructgeometries from images or point clouds [3, 28].

Original: Elich et al.
Revised: Elich et al.

Original: [25] pretrain their model with labeleddata to learn 3D representations, to recover known shapes from RGBD data.
Revised: [25] pretrain their model with labeleddata to learn 3D representations, to recover known shapes from RGBD data.

Original: Li et al.
Revised: Li et al.

Original: [3] use labeleddata as dense boundary values for semi-supervised SDF learning, and fit road scenes from pointclouds.
Revised: [3] use labeleddata as dense boundary values for semi-supervised SDF learning, and fit road scenes from pointclouds.

Original: While these approaches improve predictions on seen data, they cannot generalize well tounseen classes, even with test-time optimization [3].
Revised: While these approaches improve predictions on seen data, they cannot generalize well tounseen classes, even with test-time optimization [3].

Original: Recently, person re-identification and domainadaptation methods perform semi-supervision on non-overlapping labeled and unlabeled classes andhave shown to generalize better [40, 41, 42].
Revised: Recently, person re-identification and domainadaptation methods perform semi-supervision on non-overlapping labeled and unlabeled classes andhave shown to generalize better [40, 41, 42].

Original: This has not been attempted for learning SDFs, andour method introduces a meta-learning approach to learn shape priors, where we emulate training onunlabeled data with pseudo-labels.
Revised: This has not been attempted for learning SDFs, andour method introduces a meta-learning approach to learn shape priors, where we emulate training onunlabeled data with pseudo-labels.

Original: Generalization.
Revised: Generalization.

Original: The ability to learn generalizable 3D representations is necessary for real-worldapplications, as real objects exhibit significantly more diversity than any dataset.
Revised: The ability to learn generalizable 3D representations is necessary for real-worldapplications, as real objects exhibit significantly more diversity than any dataset.

Original: In learning implicitfunctions, one approach [43, 44] is to break down shape features to find common properties, but thisalso requires prior knowledge about target shapes which might not be available.
Revised: In learning implicitfunctions, one approach [43, 44] is to break down shape features to find common properties, but thisalso requires prior knowledge about target shapes which might not be available.

Original: We propose a meta-learning approach that does not make assumptions or require prior informationabout target data.
Revised: We propose a meta-learning approach that does not make assumptions or require prior informationabout target data.

Original: Meta-learning has been extensively studied in few-shot learning [45, 46], domaingeneralization [47], and image retrieval [39], 3D reconstruction from 2D or 2.5D images [48, 49, 50],and point cloud classification and segmentation tasks [51, 52, 53].
Revised: Meta-learning has been extensively studied in few-shot learning [45, 46], domaingeneralization [47], and image retrieval [39], 3D reconstruction from 2D or 2.5D images [48, 49, 50],and point cloud classification and segmentation tasks [51, 52, 53].

Original: However, meta-learning has notbeen extensively investigated in the context of SDFs.
Revised: However, meta-learning has notbeen extensively investigated in the context of SDFs.

Original: The most relevant method is MetaSDF [15],albeit it is fully supervised and exhibits large time and memory complexity due to inner loop gradientdescent steps.
Revised: The most relevant method is MetaSDF [15],albeit it is fully supervised and exhibits large time and memory complexity due to inner loop gradientdescent steps.

Original: Furthermore, MetaSDF overfits to single objects and requires ground truth signeddistance values during test time.
Revised: Furthermore, MetaSDF overfits to single objects and requires ground truth signeddistance values during test time.

Original: The proposed episodic training approach avoids this costly innerloop, and learns a unified network that only requires a raw input point cloud for reconstruction.
Revised: The proposed episodic training approach avoids this costly innerloop, and learns a unified network that only requires a raw input point cloud for reconstruction.

Original:  Semi-supervised Meta-Learning of Implicit Functions
Revised:  Semi-supervised Meta-Learning of Implicit Functions

Original: We next formalize the problem we are solving in Sec. 3.1, then describe the proposed learning methodand training objectives in Sections 3.2 and 3.3.
Revised: We next formalize the problem we are solving in Sec. 3.1, then describe the proposed learning methodand training objectives in Sections 3.2 and 3.3.

Original: 3.1 Problem Formulation
Revised: 3.1 Problem Formulation

Original: Conditional Signed Distance Functions
Revised: Conditional Signed Distance Functions

Original: We are interested in learning a generalized representationfor shapes.
Revised: We are interested in learning a generalized representationfor shapes.

Original: We learn a signed distance function (SDF), which is a continuous function that representsthe surface of a shape approximated by the zero level-set of a neural network.
Revised: We learn a signed distance function (SDF), which is a continuous function that representsthe surface of a shape approximated by the zero level-set of a neural network.

Original: Given a raw inputpoint cloud P = { p i ∈ R 3 } Ni =1 with N points and a 3D query point x ∈ R 3 , we learn a conditional
Revised: Given a raw inputpoint cloud P = { p i ∈ R 3 } Ni =1 with N points and a 3D query point x ∈ R 3 , we learn a conditional

Original: SDF Φ : R 3 × { p i ∈ R 3 } Ni =1 → R such that the function Φ predicts the signed distance value for a3D coordinate conditioned on a sparse point cloud.
Revised: SDF Φ : R 3 × { p i ∈ R 3 } Ni =1 → R such that the function Φ predicts the signed distance value for a3D coordinate conditioned on a sparse point cloud.

Original: Then Φ is a unified function that can be directlyapplied to any target point cloud.
Revised: Then Φ is a unified function that can be directlyapplied to any target point cloud.

Original: [Equation]
Revised: [Equation]

Original: where s denotes the predicted signed distance value between x and the shape described by P .
Revised: where s denotes the predicted signed distance value between x and the shape described by P .

Original: The surface boundary of a shape described by P is its zero-level set S 

Revised: The surface boundary of a shape described by P is its zero-level set S

Original: (Φ( P )) , which can beexpressed as
Revised: (Φ( P )) , which can beexpressed as

Original: [Equation]
Revised: [Equation]

Original: Thus, given a trained Φ , we can visualize the surface of some P by drawing its zero-level set.
Revised: Thus, given a trained Φ , we can visualize the surface of some P by drawing its zero-level set.

Original: [Figure]
Revised: [Figure]

Original: Decoder
Revised: Decoder

Original: PredictedValues
Revised: PredictedValues

Original: Concat.
Revised: Concat.

Original: [Figure]
Revised: [Figure]

Original: Labeled
Revised: Labeled

Original: [Figure]
Revised: [Figure]

Original: Problem Setting We assume both labeled and unlabeled datasets are available, denoted X and
Revised: Problem Setting We assume both labeled and unlabeled datasets are available, denoted X and

Original: R , respectively.
Revised: R , respectively.

Original: X
Revised: X

Original: = { P X , SDF } , where P X is a set of point clouds and SDF( · ) denotes theground-truth SDF operator that is defined for all query points x ∈ R 3 .
Revised: = { P X , SDF } , where P X is a set of point clouds and SDF( · ) denotes theground-truth SDF operator that is defined for all query points x ∈ R 3 .

Original: R =
Revised: R =

Original: { P R } , where P R is aset of point clouds belonging to classes disjoint with those of P X .
Revised: { P R } , where P R is aset of point clouds belonging to classes disjoint with those of P X .

Original: Note that each point cloud is aset of 3D coordinates that describe on the surface boundary of an object, and contains no additionalinformation such as normals.
Revised: Note that each point cloud is aset of 3D coordinates that describe on the surface boundary of an object, and contains no additionalinformation such as normals.

Original: To learn a generalizable conditional SDF, we propose a two-stage semi-supervised meta-learningalgorithm.
Revised: To learn a generalizable conditional SDF, we propose a two-stage semi-supervised meta-learningalgorithm.

Original: In the first stage, we aim to learn shape priors using X .
Revised: In the first stage, we aim to learn shape priors using X .

Original: As illustrated in Figure 1, wepropose to train our model using an episodic scheme [47], where every f epochs we randomly split
Revised: As illustrated in Figure 1, wepropose to train our model using an episodic scheme [47], where every f epochs we randomly split

Original: X into two subsets with disjoint categories.
Revised: X into two subsets with disjoint categories.

Original: In the second stage, as shown in Figure 1, we continue totrain the pretrained weights from the first stage and train the model on X and R in a semi-supervisedfashion.
Revised: In the second stage, as shown in Figure 1, we continue totrain the pretrained weights from the first stage and train the model on X and R in a semi-supervisedfashion.

Original: We obtain a unified neural network Φ that learns from one dataset and can generalize torepresent SDFs of objects in unseen categories during test time; i.e., zero-shot inference [30].
Revised: We obtain a unified neural network Φ that learns from one dataset and can generalize torepresent SDFs of objects in unseen categories during test time; i.e., zero-shot inference [30].

Original: 3.2 Stage 1: Meta-Learning a Shape Prior
Revised: 3.2 Stage 1: Meta-Learning a Shape Prior

Original: Inside
Revised: Inside

Original: Outside
Revised: Outside

Original: Our eventual goal is to train on labeled and unlabeled data simultaneously, so we mimic this goalin a meta-learning approach as we learn shapepriors from X .
Revised: Our eventual goal is to train on labeled and unlabeled data simultaneously, so we mimic this goalin a meta-learning approach as we learn shapepriors from X .

Original: Every f epochs, we split X intotwo subsets X L and X U with disjoint categories.
Revised: Every f epochs, we split X intotwo subsets X L and X U with disjoint categories.

Original: We train X L with a supervised loss L sup , similar to typical supervised approaches on labeleddata.
Revised: We train X L with a supervised loss L sup , similar to typical supervised approaches on labeleddata.

Original: We take away ground-truth signed distancevalues from X U making it “pseudo-unlabeled”,and train it with our self-supervised loss L self .
Revised: We take away ground-truth signed distancevalues from X U making it “pseudo-unlabeled”,and train it with our self-supervised loss L self .

Original: Our training objective is to minimize
Revised: Our training objective is to minimize

Original: [Equation]
Revised: [Equation]

Original: where λ m controls the strength of the self supervised loss L self .
Revised: where λ m controls the strength of the self supervised loss L self .

Original: Compared to only training with asupervised loss, this meta-learning approach intends to accomplish two goals.
Revised: Compared to only training with asupervised loss, this meta-learning approach intends to accomplish two goals.

Original: First, the model learnsto backpropagate with our self-supervised loss, which we need for training unlabeled data in thesecond stage.
Revised: First, the model learnsto backpropagate with our self-supervised loss, which we need for training unlabeled data in thesecond stage.

Original: Second, episodic training on non-overlapping categories forces the model to developgeneralized representations as it cannot overfit to the data.
Revised: Second, episodic training on non-overlapping categories forces the model to developgeneralized representations as it cannot overfit to the data.

Original: We empirically show in our ablation studythat our method has stronger representation power for both seen and unseen classes.
Revised: We empirically show in our ablation studythat our method has stronger representation power for both seen and unseen classes.

Original: We provide anexample of a training step in Alg.
Revised: We provide anexample of a training step in Alg.

Original: 1 and a diagram in Fig.
Revised: 1 and a diagram in Fig.

Original: Next, we explain our loss functions inmore detail.
Revised: Next, we explain our loss functions inmore detail.

Original: X L , X U ← split (
Revised: X L , X U ← split (

Original: L sup = 1 | X L | (cid:80) ( x,
Revised: L sup = 1 | X L | (cid:80) ( x,

Original: SDF ) ∈
Revised: SDF ) ∈

Original: X L ∥
Revised: X L ∥

Original: [Equation]
Revised: [Equation]

Original: ( x ;
Revised: ( x ;

Original: [Equation]
Revised: [Equation]

Original: e ) , SDF ( x
Revised: e ) , SDF ( x

Original: [Equation]
Revised: [Equation]

Original: ▷ Eq.
Revised: ▷ Eq.

Original: L self =
Revised: L self =

Original: [Equation]
Revised: [Equation]

Original: X
Revised: X

Original: [Equation]
Revised: [Equation]

Original: (cid:80) ( x,t )
Revised: (cid:80) ( x,t )

Original: [Equation]
Revised: [Equation]

Original: X U ∥ (
Revised: X U ∥ (

Original: [Equation]
Revised: [Equation]

Original: x
Revised: x

Original: [Equation]
Revised: [Equation]

Original: t ∥ x − t ∥ · Φ( x ; θ e )) , t ∥▷ Eq.
Revised: t ∥ x − t ∥ · Φ( x ; θ e )) , t ∥▷ Eq.

Original: (7), simplified
Revised: (7), simplified

Original: L meta =
Revised: L meta =

Original: L sup + λ m L self ▷ Eq.
Revised: L sup + λ m L self ▷ Eq.

Original: (3) meta
Revised: (3) meta

Original: Supervised Loss Component
Revised: Supervised Loss Component

Original: In the supervised setting, we have the ground truth SDF operator;i.e.
Revised: In the supervised setting, we have the ground truth SDF operator;i.e.

Original: , we know the signed distance values for all query points x .
Revised: , we know the signed distance values for all query points x .

Original: Therefore, the loss function is simply
Revised: Therefore, the loss function is simply

Original: [Equation]
Revised: [Equation]

Original: [Equation]
Revised: [Equation]

Original: where ∥ · ∥ 1 is the L1 loss.
Revised: where ∥ · ∥ 1 is the L1 loss.

Original: Self-supervised Loss Component for Unlabeled Training Samples
Revised: Self-supervised Loss Component for Unlabeled Training Samples

Original: For each point x ∈ R 3 , weuse its closest point p ∈ P to approximate its projection to the surface, defined as
Revised: For each point x ∈ R 3 , weuse its closest point p ∈ P to approximate its projection to the surface, defined as

Original: [Equation]
Revised: [Equation]

Original: In the literature [54], it is common to use
Revised: In the literature [54], it is common to use

Original: [Equation]
Revised: [Equation]

Original: (6) to approximate the closest point t on the object surface to query point x given some trained SDFfunction Φ for tasks such as collision detection.
Revised: (6) to approximate the closest point t on the object surface to query point x given some trained SDFfunction Φ for tasks such as collision detection.

Original: We build on this insight: we want to predict ˆ t toapproximate t on the point cloud by using the predicted signed distance value.
Revised: We build on this insight: we want to predict ˆ t toapproximate t on the point cloud by using the predicted signed distance value.

Original: However, we find thatdirectly using Eq.
Revised: However, we find thatdirectly using Eq.

Original: (6) leads to highly inaccurate sign predictions.
Revised: (6) leads to highly inaccurate sign predictions.

Original: There are no explicit penalties forpredicting the wrong sign and when the query point is close to the surface, an ℓ 2 loss between ˆ t and tcan be very low even when the sign is predicted incorrectly.
Revised: There are no explicit penalties forpredicting the wrong sign and when the query point is close to the surface, an ℓ 2 loss between ˆ t and tcan be very low even when the sign is predicted incorrectly.

Original: For a surface boundary to be accuratelyestimated, there must be accurate sign changes between 3D coordinates.
Revised: For a surface boundary to be accuratelyestimated, there must be accurate sign changes between 3D coordinates.

Original: Thus, we substitute ∇ Φ( x ) with the direction vector between t and x .
Revised: Thus, we substitute ∇ Φ( x ) with the direction vector between t and x .

Original: Our formulation has an explicitpenalty for incorrect sign predictions: the vector would point in the direction opposite to the pointcloud, guaranteeing a larger error.
Revised: Our formulation has an explicitpenalty for incorrect sign predictions: the vector would point in the direction opposite to the pointcloud, guaranteeing a larger error.

Original: Furthermore, we can leverage sign predictions from labeled datato directly supervise the sign.
Revised: Furthermore, we can leverage sign predictions from labeled datato directly supervise the sign.

Original: This is not possible in the original formulation since ∇ Φ( x )Φ( x ) iscalculated as a unit that points in the direction of maximum distance change.
Revised: This is not possible in the original formulation since ∇ Φ( x )Φ( x ) iscalculated as a unit that points in the direction of maximum distance change.

Original: We denote our approachself-supervised because the predictions of the signs are used as labels.
Revised: We denote our approachself-supervised because the predictions of the signs are used as labels.

Original: Our training objective is tominimize the distance between ˆ t and t .
Revised: Our training objective is tominimize the distance between ˆ t and t .

Original: Furthermore, we add an additional ℓ 1 loss by leveraging thepoint clouds which have a distance value of 0 .
Revised: Furthermore, we add an additional ℓ 1 loss by leveraging thepoint clouds which have a distance value of 0 .

Original: We find that this helps with thinner structures.
Revised: We find that this helps with thinner structures.

Original: Ourfinal loss function is
Revised: Ourfinal loss function is

Original: [Equation]
Revised: [Equation]

Original: where λ p determines the weight of the point cloud predictions and
Revised: where λ p determines the weight of the point cloud predictions and

Original: [Equation]
Revised: [Equation]

Original: Previous work [19] has predicted t by directly calculating Eq.
Revised: Previous work [19] has predicted t by directly calculating Eq.

Original: (6) during training, but their resultingsign predictions are substantially less accurate than ours for the reasons we discuss.
Revised: (6) during training, but their resultingsign predictions are substantially less accurate than ours for the reasons we discuss.

Original: We validate thiswith the results shown in Tab. 1.
Revised: We validate thiswith the results shown in Tab. 1.

Original: We note that a point cloud P is sampled from a surface and does notrepresent the continuous boundary.
Revised: We note that a point cloud P is sampled from a surface and does notrepresent the continuous boundary.

Original: Thus, t is the nearest neighbor that exists in P but not necessarilythe true one that exists in the target object we want to reconstruct.
Revised: Thus, t is the nearest neighbor that exists in P but not necessarilythe true one that exists in the target object we want to reconstruct.

Original: Therefore, unlike using labeleddata, there are inaccuracies when using P as a proxy.
Revised: Therefore, unlike using labeleddata, there are inaccuracies when using P as a proxy.

Original: As a result previous unsupervised work [19]that use P as a proxy are not robust when training on multiple classes.
Revised: As a result previous unsupervised work [19]that use P as a proxy are not robust when training on multiple classes.

Original: Our semi-supervised methodlifts this constraint in the training so that these inaccuracies do not build up.
Revised: Our semi-supervised methodlifts this constraint in the training so that these inaccuracies do not build up.

Original: 3.3 Stage 2: Semi-supervision with Unlabeled Training Samples
Revised: 3.3 Stage 2: Semi-supervision with Unlabeled Training Samples

Original: In our second stage, visualized in Fig.
Revised: In our second stage, visualized in Fig.

Original: 1, we train our conditional SDF from the meta-learning stageon both labeled and unlabeled data in a semi-supervised fashion.
Revised: 1, we train our conditional SDF from the meta-learning stageon both labeled and unlabeled data in a semi-supervised fashion.

Original: As a result of the learned priorsfrom the previous stage, this stage of training remains robust even with large amounts of unlabeleddata.
Revised: As a result of the learned priorsfrom the previous stage, this stage of training remains robust even with large amounts of unlabeleddata.

Original: We show in our experiments (see Sec.
Revised: We show in our experiments (see Sec.

Original: 4.4 for an ablation study) that without meta-learningpriors, semi-supervision is not as robust.
Revised: 4.4 for an ablation study) that without meta-learningpriors, semi-supervision is not as robust.

Original: Furthermore, continuing to train with labeled data providesstrong supervision to ensure inaccuracies from unlabeled data do not build up.
Revised: Furthermore, continuing to train with labeled data providesstrong supervision to ensure inaccuracies from unlabeled data do not build up.

Original: Given labeled set Xand unlabeled set R , our training objective is to minimize
Revised: Given labeled set Xand unlabeled set R , our training objective is to minimize

Original: [Equation]
Revised: [Equation]

Original: (9) where λ s controls the strength of the self supervised loss L self .
Revised: (9) where λ s controls the strength of the self supervised loss L self .

Original:  Experiments
Revised:  Experiments

Original: In this section, we analyze and validate the proposed representation method for seen and unseenobject categories.
Revised: In this section, we analyze and validate the proposed representation method for seen and unseenobject categories.

Original: We begin with a discussion of implementation details and experimental setup.
Revised: We begin with a discussion of implementation details and experimental setup.

Original: Implementation For our experiments, we borrow the encoder architecture from [16] which isa modified PointNet [8] that uses plane projection to learn local geometric features, and parallel
Revised: Implementation For our experiments, we borrow the encoder architecture from [16] which isa modified PointNet [8] that uses plane projection to learn local geometric features, and parallel

Original: UNets [55] to aggregate spatial information.
Revised: UNets [55] to aggregate spatial information.

Original: For the decoder we use an 8-layer multi-layer perceptronwith 512-dimensional hidden layers, similar to the architecture from [11, 15, 19, 20].
Revised: For the decoder we use an 8-layer multi-layer perceptronwith 512-dimensional hidden layers, similar to the architecture from [11, 15, 19, 20].

Original: We emphasize,that our two-stage training pipeline is designed to be architecture-agnostic, and we provide resultsfor alternate encoders and decoders in the supplement.
Revised: We emphasize,that our two-stage training pipeline is designed to be architecture-agnostic, and we provide resultsfor alternate encoders and decoders in the supplement.

Original: For Eqs.
Revised: For Eqs.

Original: (3) and (9) we the set the losscoefficients to λ m =
Revised: (3) and (9) we the set the losscoefficients to λ m =

Original: λ s = 0 .
Revised: λ s = 0 .

Original: 1 , and λ p = 0 .
Revised: 1 , and λ p = 0 .

Original: 01 in Eq.
Revised: 01 in Eq.

Original: We provide a full architecture descriptionand additional training details in the supplemental document.
Revised: We provide a full architecture descriptionand additional training details in the supplemental document.

Original: Experimental Setup We source training and evaluation data from Acronym [29] and YCB [23].
Revised: Experimental Setup We source training and evaluation data from Acronym [29] and YCB [23].

Original: Acronym is a post-processed subset of the popular ShapeNet [56] dataset which contains 8,872 clean,synthetic 3D models in 262 shape categories.
Revised: Acronym is a post-processed subset of the popular ShapeNet [56] dataset which contains 8,872 clean,synthetic 3D models in 262 shape categories.

Original: In contrast to ShapeNet, all of Acronym’s meshes arewatertight , which ensures that they have well-defined SDFs.
Revised: In contrast to ShapeNet, all of Acronym’s meshes arewatertight , which ensures that they have well-defined SDFs.

Original: We use the 20 largest classes (2,995meshes) as a labeled dataset X for all fully-supervised methods, including our meta-learning firststage.
Revised: We use the 20 largest classes (2,995meshes) as a labeled dataset X for all fully-supervised methods, including our meta-learning firststage.

Original: The next 76 classes (3,408 meshes) form our unlabeled dataset R for semi-supervised training.
Revised: The next 76 classes (3,408 meshes) form our unlabeled dataset R for semi-supervised training.

Original: The remaining 166 classes (1,525 meshes) are withheld for testing.
Revised: The remaining 166 classes (1,525 meshes) are withheld for testing.

Original: Preprocessing details can befound in the supplemental document.
Revised: Preprocessing details can befound in the supplemental document.

Original: The YCB dataset [23] contains point clouds from 3D scans ofcommon real-world objects and does not contain ground truth meshes.
Revised: The YCB dataset [23] contains point clouds from 3D scans ofcommon real-world objects and does not contain ground truth meshes.

Original: We use these point clouds asadditional unlabeled test data to assess SDF predictions on out-of-distribution objects.
Revised: We use these point clouds asadditional unlabeled test data to assess SDF predictions on out-of-distribution objects.

Original: Evaluation Given a point cloud P that describes the surface of an object, the proposed methodreturns an implicit signed distance function Φ( P ) .
Revised: Evaluation Given a point cloud P that describes the surface of an object, the proposed methodreturns an implicit signed distance function Φ( P ) .

Original: We construct a cube with each dimension rangingfrom -1 to 1, then discretize it into a set of grids with resolution 256 3 .
Revised: We construct a cube with each dimension rangingfrom -1 to 1, then discretize it into a set of grids with resolution 256 3 .

Original: We run Marching Cubes [57]at each grid point to reconstruct a mesh surface for qualitative assessment.
Revised: We run Marching Cubes [57]at each grid point to reconstruct a mesh surface for qualitative assessment.

Original: For quantitative evaluationwe measure the Chamfer Distance [8] between 30,000 randomly sampled points on the surfaces ofthe reconstructed and ground truth meshes.
Revised: For quantitative evaluationwe measure the Chamfer Distance [8] between 30,000 randomly sampled points on the surfaces ofthe reconstructed and ground truth meshes.

Original: [Figure]
Revised: [Figure]

Original: Unseen Classes
Revised: Unseen Classes

Original: DeepSDF 18.26 / 10.
Revised: DeepSDF 18.26 / 10.

Original: MetaSDF 4.269 / 1.
Revised: MetaSDF 4.269 / 1.

Original: ConvOccNet 1.348 / 0.
Revised: ConvOccNet 1.348 / 0.

Original: Proposed 0.351 / 0.
Revised: Proposed 0.351 / 0.

Original: [Figure]
Revised: [Figure]

Original: Experiments We conduct experiments to investigate the generalizability and representationalpower of our method.
Revised: Experiments We conduct experiments to investigate the generalizability and representationalpower of our method.

Original: Specifically, we analyze the effects of reconstructing seen and unseen objects(Sec. 4.1), self-supervision on unlabeled data (Sec. 4.2), performance on real-world point cloud scans(Sec. 4.3), and ablation experiments (Sec. 4.4).
Revised: Specifically, we analyze the effects of reconstructing seen and unseen objects(Sec. 4.1), self-supervision on unlabeled data (Sec. 4.2), performance on real-world point cloud scans(Sec. 4.3), and ablation experiments (Sec. 4.4).

Original: 4.1 Reconstructing Seen and Unseen Shapes
Revised: 4.1 Reconstructing Seen and Unseen Shapes

Original: In this subsection, we compare our method to existing approaches: DeepSDF [11], MetaSDF [15],and Convolutional Occupancy Networks (ConvOccNet) [16] on both seen and unseen shapes.
Revised: In this subsection, we compare our method to existing approaches: DeepSDF [11], MetaSDF [15],and Convolutional Occupancy Networks (ConvOccNet) [16] on both seen and unseen shapes.

Original: 1 Forreconstructing seen data, we evaluate results on the 20 shared classes (see the experimental setupparagraph in Sec. 4).
Revised: 1 Forreconstructing seen data, we evaluate results on the 20 shared classes (see the experimental setupparagraph in Sec. 4).

Original: For testing on unseen classes, we use the remaining 166 categories that aredisjoint with any class used for training.
Revised: For testing on unseen classes, we use the remaining 166 categories that aredisjoint with any class used for training.

Original: To improve visual results, we apply refinement by fittingthe model on the point cloud for a few iterations.
Revised: To improve visual results, we apply refinement by fittingthe model on the point cloud for a few iterations.

Original: Specifically, we employ our self-supervised losswithout using any additional information beyond 5,000 raw input points.
Revised: Specifically, we employ our self-supervised losswithout using any additional information beyond 5,000 raw input points.

Original: In contrast, DeepSDF [11]and MetaSDF [15] use ground truth signed distance values for refinement.
Revised: In contrast, DeepSDF [11]and MetaSDF [15] use ground truth signed distance values for refinement.

Original: We include specificrefinement details in our supplement.
Revised: We include specificrefinement details in our supplement.

Original: Since ConvOccNet [16] does not perform refinement, we reportquantitative results of the proposed method without refinement for a fair comparison.
Revised: Since ConvOccNet [16] does not perform refinement, we reportquantitative results of the proposed method without refinement for a fair comparison.

Original: Seen Categories.
Revised: Seen Categories.

Original: Fig.
Revised: Fig.

Original: 4 shows reconstruction results on seen shapes.
Revised: 4 shows reconstruction results on seen shapes.

Original: We observe that existingmethods and our approach are capable of reconstructing seen data.
Revised: We observe that existingmethods and our approach are capable of reconstructing seen data.

Original: However, DeepSDF and MetaSDFfail to reconstruct thin structures such as the lamp poles due to the lack of a shape prior.
Revised: However, DeepSDF and MetaSDFfail to reconstruct thin structures such as the lamp poles due to the lack of a shape prior.

Original: Quantitatively,reported in the middle column of Fig.
Revised: Quantitatively,reported in the middle column of Fig.

Original: 3, even though we use the same encoder as ConvOccNet [16]to learn shape priors, we achieve a lower CD by an order of magnitude.
Revised: 3, even though we use the same encoder as ConvOccNet [16]to learn shape priors, we achieve a lower CD by an order of magnitude.

Original: Unseen Categories.
Revised: Unseen Categories.

Original: When tested on unseen categories, as shown in Fig.
Revised: When tested on unseen categories, as shown in Fig.

Original: 5, only our proposedmethod is able to reconstruct unseen categories, and accurately represents fine details such as narrowgaps in the Shelf example.
Revised: 5, only our proposedmethod is able to reconstruct unseen categories, and accurately represents fine details such as narrowgaps in the Shelf example.

Original: Quantitatively, as shown in the right column of the table in Fig.
Revised: Quantitatively, as shown in the right column of the table in Fig.

Original: 3, theproposed method achieves better performance.
Revised: 3, theproposed method achieves better performance.

Original: Notably, the gap between the CD of seen and unseenclasses is lower in our case.
Revised: Notably, the gap between the CD of seen and unseenclasses is lower in our case.

Original: While the CD of most methods double between seen and unseen classes,there is only a marginal increase for ours.
Revised: While the CD of most methods double between seen and unseen classes,there is only a marginal increase for ours.

Original: B i r d
Revised: B i r d

Original: T eapo t
Revised: T eapo t

Original: S
Revised: S

Original: he l f
Revised: he l f

Original: Point Cloud
Revised: Point Cloud

Original: DeepSDF
Revised: DeepSDF

Original: B unn y
Revised: B unn y

Original: [Figure]
Revised: [Figure]

Original: 4.2 Comparison to Unsupervised Methods on Unlabeled Data
Revised: 4.2 Comparison to Unsupervised Methods on Unlabeled Data

Original: We report pre-refinement numbers for our approach, scale
Revised: We report pre-refinement numbers for our approach, scale

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

Original: A self/unsupervised method is essential forour semi-supervised stage to train on unlabeled data and for test-time refinement on onlythe raw input point cloud.
Revised: A self/unsupervised method is essential forour semi-supervised stage to train on unlabeled data and for test-time refinement on onlythe raw input point cloud.

Original: In this subsection,we compare to existing unsupervised baselines:
Revised: In this subsection,we compare to existing unsupervised baselines:

Original: NeuralPull [19] and SAL [20].
Revised: NeuralPull [19] and SAL [20].

Original: For a faircomparison, we use only our self-supervisedloss in Eq.
Revised: For a faircomparison, we use only our self-supervisedloss in Eq.

Original: (7) to train directly on unlabeleddata and do not perform test-time refinement( self in Tab. 1).
Revised: (7) to train directly on unlabeleddata and do not perform test-time refinement( self in Tab. 1).

Original: Tab. 1 validates that when training a single
Revised: Tab. 1 validates that when training a single

Original: Queen Bed class, our explicit sign penalty allows our self-supervised method to reconstructsharper details from irregular surfaces.
Revised: Queen Bed class, our explicit sign penalty allows our self-supervised method to reconstructsharper details from irregular surfaces.

Original: On the other hand, existing methods [20, 19] produce lowlosses for close approximations to the absolute values of the signed distances, rather than accurate signpredictions, resulting in loss of details where there is abrupt change in the surface (see supplementfor visualizations).
Revised: On the other hand, existing methods [20, 19] produce lowlosses for close approximations to the absolute values of the signed distances, rather than accurate signpredictions, resulting in loss of details where there is abrupt change in the surface (see supplementfor visualizations).

Original: All non-supervised methods we test on, including ours, degrade when trainingdegrade quickly as the number of meshes increases.
Revised: All non-supervised methods we test on, including ours, degrade when trainingdegrade quickly as the number of meshes increases.

Original: The proposed method with semi-supervision scales well as we increase the number of classes.
Revised: The proposed method with semi-supervision scales well as we increase the number of classes.

Original: Thus,our method can tackle large-scale operations and take advantage of the availability of large amountsof unlabeled data.
Revised: Thus,our method can tackle large-scale operations and take advantage of the availability of large amountsof unlabeled data.

Original: We also show in our supplement that using our self-supervised variant from thissection leads to significantly more robust training.
Revised: We also show in our supplement that using our self-supervised variant from thissection leads to significantly more robust training.

Original: 4.3 Reconstruction of Real-World Raw Point Clouds
Revised: 4.3 Reconstruction of Real-World Raw Point Clouds

Original: Next, we test our model on the YCB [23] dataset, which contains scanned point clouds and 2D imagesbut no ground truth meshes.
Revised: Next, we test our model on the YCB [23] dataset, which contains scanned point clouds and 2D imagesbut no ground truth meshes.

Original: YCB is a different domain from Acronym [29] and we perform no
Revised: YCB is a different domain from Acronym [29] and we perform no

Original: [Figure]
Revised: [Figure]

Original: scaling or normalization of the input point cloud to thoroughly test performance of out-of-distributiondata.
Revised: scaling or normalization of the input point cloud to thoroughly test performance of out-of-distributiondata.

Original: We omit results from DeepSDF [11] and MetaSDF [15] since they use ground truth signeddistance values during test time.
Revised: We omit results from DeepSDF [11] and MetaSDF [15] since they use ground truth signeddistance values during test time.

Original: As shown in Fig.
Revised: As shown in Fig.

Original: 6, ConvOccNet [16] fails to reconstruct input datawith a different scale and loses detail such as the handle of the pitcher.
Revised: 6, ConvOccNet [16] fails to reconstruct input datawith a different scale and loses detail such as the handle of the pitcher.

Original: The proposed method, incontrast, is able to approximate the 3D shape with detail and results in plausible shape geometry,illustrating the ability of handling in-the-wild and out-of-distribution data.
Revised: The proposed method, incontrast, is able to approximate the 3D shape with detail and results in plausible shape geometry,illustrating the ability of handling in-the-wild and out-of-distribution data.

Original: In the future, adding more diverse unlabeled data to the training of the the to any
Revised: In the future, adding more diverse unlabeled data to the training of the the to any

Original: 4.4 Ablation Experiments
Revised: 4.4 Ablation Experiments

Original: [Table]
Revised: [Table]

Original: In this subsection, we analyze individual components of our two-stage learning.
Revised: In this subsection, we analyze individual components of our two-stage learning.

Original: We show quantitative results in Tab. 2.
Revised: We show quantitative results in Tab. 2.

Original: Only meta refers hereto the meta-learning first stage.
Revised: Only meta refers hereto the meta-learning first stage.

Original: This outperformsexisting fully supervised methods (see Fig.
Revised: This outperformsexisting fully supervised methods (see Fig.

Original: 3)for both seen and unseen data, while using thesame amount of data and no additional manualannotations.
Revised: 3)for both seen and unseen data, while using thesame amount of data and no additional manualannotations.

Original: The favorable results validate thegeneralization capabilities of our episodic training scheme.
Revised: The favorable results validate thegeneralization capabilities of our episodic training scheme.

Original: Our semi-supervision stage furtherimproves reconstruction quality by introducingmore shapes without requiring annotations.
Revised: Our semi-supervision stage furtherimproves reconstruction quality by introducingmore shapes without requiring annotations.

Original: No split refers to training on the labeled set without episodic training and resplitting.
Revised: No split refers to using our architecture to onlytrain on the labeled set without episodic training and resplitting of subsets.

Original: This setting issimilar to that of ConvOccNet [16]  withthe only difference being the choice of decoder. Our decoderproduces a lower CD because it does not produce artifacts in empty space.
Revised: This setting is nearlyidentical to those of ConvOccNet [16] but with a lower CD because our choice of decoder does notproduce artifacts in empty space.

Original: The CD for seen classes issimilar to that of our meta-learning stage, but falls behind when reconstructing unseen classes.
Revised: The CD for seen classes is similar to that of our meta-learning stage,but falls behind when reconstructing unseen classes.

Original: Onlysemi refers to only training the proposed semi-supervision stage from scratch without transferringthe learned representation from the meta-learning stage.
Revised: Only semi refers to only training the proposedsemi-supervision stage from scratch without transferring the learned representation from the metalearning stage.

Original: Even though this stage has access to bothlabeled and unlabeled data, it has a higher CD compared to our final two-stage approach.
Revised: Even though this stage has access to both labeled and unlabeled data, it has a higher CD compared to our final two-stage approach.

Original: This isbecause errors in the proxies of unlabeled data accumulate and result in training that is less robust.
Revised: This is because errors in the proxies of unlabeled dataaccumulate and result in training that is less robust.

Original: This indicates that our meta-learning stage indeed builds a strong foundational prior that ensures thesecond stage semi-supervised training is robust.
Revised: This indicates that our meta-learning stage indeedbuilds a strong foundational prior that ensures the second stage semi-supervised training is robust.

Original:  Conclusion
Revised:  Conclusion

Original: In this work, we devise a two-stage semi-supervised meta-learning approach that achieves stronggeneralization to unseen object categories.
Revised: In this work, we devise a two-stage semi-supervised meta-learning approach that achieves stronggeneralization to unseen object categories.

Original: This method is able to fit to any target point cloud withoutadditional annotations and outperforms existing SDF methods in both seen and unseen categories.
Revised: This method is able to fit to any target point cloud withoutadditional annotations and outperforms existing SDF methods in both seen and unseen categories.

Original: Our method is not without limitations, which we plan to address in the future.
Revised: Our method is not without limitations, which we plan to address in the future.

Original: Similar to existing SDFrepresentations [16], we do not achieve real-time inference due to large number of model parameters.
Revised: Similar to existing SDFrepresentations [16], we do not achieve real-time inference due to large number of model parameters.

Original: Learning from large-scale multi-object point clouds, with abundant datasets for automotive scenes[59, 60] is also an exciting future direction.
Revised: Learning from large-scale multi-object point clouds, with abundant datasets for automotive scenes[59, 60] is also an exciting future direction.

Original: The proposed approach may also serve as a representationfor inverse rendering methods that tackle vision tasks in an analysis-by-synthesis approach.
Revised: The proposed approach may also serve as a representationfor inverse rendering methods that tackle vision tasks in an analysis-by-synthesis approach.

Original: Checklist
Revised: Checklist

Original: For all authors...
Revised: For all authors...

Original: (a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope?
Revised: (a) Do the main claims made in the abstract and introduction accurately reflect the paper’scontributions and scope?

Original: [Yes]
Revised: [Yes]

Original: (b) Did you describe the limitations of your work?
Revised: (b) Did you describe the limitations of your work?

Original: [Yes] See Experiments (Sec. 4) andConclusion (Sec. 5).
Revised: [Yes] See Experiments (Sec. 4) andConclusion (Sec. 5).

Original: (c) Did you discuss any potential negative societal impacts of your work?
Revised: (c) Did you discuss any potential negative societal impacts of your work?

Original: [No] We do not believe that our work has potential negative societal impacts.
Revised: [No] We do notbelieve that our work has potential negative societal impacts.

Original: (d) Have you read the ethics review guidelines and ensured that your paper conforms to
Revised: (d) Have you read the ethics review guidelines and ensured that your paper conforms to

Original: them?
Revised: them?

Original: [Yes]
Revised: [Yes]

Original: If you are including theoretical results...
Revised: If you are including theoretical results...

Original: (a) Did you state the full set of assumptions of all theoretical results?
Revised: (a) Did you state the full set of assumptions of all theoretical results?

Original: [N/A](b)
Revised: [N/A](b)

Original: Did you include complete proofs of all theoretical results?
Revised: Did you include complete proofs of all theoretical results?

Original: [N/A]3.
Revised: [N/A]3.

Original: If you ran experiments...
Revised: If you ran experiments...

Original: (a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)?
Revised: (a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)?

Original: [Yes] We will release
Revised: [Yes] We will release

Original: code and pretrained models.
Revised: code and pretrained models.

Original: Full reproduction details are in supplement.
Revised: Full reproduction details are in supplement.

Original: (b) Did you specify all the training details (e
Revised: (b) Did you specify all the training details (e

Original: g., data splits, hyperparameters,
Revised: g., data splits, hyperparameters,

Original: how they
Revised: how they

Original: were chosen)?
Revised: were chosen)?

Original: [Yes] Implementations details can be found in supplement.(c)
Revised: [Yes] Implementations details can be found in supplement.(c)

Original: Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)?
Revised: Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)?

Original: [No]
Revised: [No]

Original: (d) Did you include the total amount of compute and the type of resources used (e g., typeof GPUs, internal cluster, or cloud provider)?
Revised: (d) Did you include the total amount of compute and the type of resources used (e.g., typeof GPUs, internal cluster, or cloud provider)?

Original: [Yes] Provided in supplement.
Revised: [Yes] Provided in supplement.

Original: If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...
Revised: If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...

Original: (a) If your work uses existing assets, did you cite the creators?
Revised: (a) If your work uses existing assets, did you cite the creators?

Original: [Yes]
Revised: [Yes]

Original: (b) Did you mention the license of the assets?
Revised: (b) Did you mention the license of the assets?

Original: [N/A]
Revised: [N/A]

Original: (c) Did you include any new assets either in the supplemental material or as a URL?
Revised: (c) Did you include any new assets either in the supplemental material or as a URL?

Original: [Yes] We will release code.
Revised: [Yes]We will release code.

Original: (d) Did you discuss whether and how consent was obtained from people whose data you’re
Revised: (d) Did you discuss whether and how consent was obtained from people whose data you’re

Original: using/curating?
Revised: using/curating?

Original: [No] We use datasets that are publicly available.
Revised: [No] We use datasets that are publicly available.

Original: References are
Revised: References are

Original: provided.
Revised: provided.

Original: (e) Did you discuss whether the data you are using/curating contains personally identifiable
Revised: (e) Did you discuss whether the data you are using/curating contains personally identifiable

Original: information or offensive content?
Revised: information or offensive content?

Original: [N/A]
Revised: [N/A]

Original: If you used crowdsourcing or conducted research with human subjects...
Revised: If you used crowdsourcing or conducted research with human subjects...

Original: (a) Did you include the full text of instructions given to participants and screenshots, if
Revised: (a) Did you include the full text of instructions given to participants and screenshots, if

Original: applicable?
Revised: applicable?

Original: [N/A]
Revised: [N/A]

Original: We did not use human subjects.
Revised: We did not use human subjects.

Original: (b) Did you describe any potential participant risks, with links to Institutional Review
Revised: (b) Did you describe any potential participant risks, with links to Institutional Review

Original: Board (IRB) approvals, if applicable?
Revised: Board (IRB) approvals, if applicable?

Original: [N/A]
Revised: [N/A]

Original: (c) Did you include the estimated hourly wage paid to participants and the total amount
Revised: (c) Did you include the estimated hourly wage paid to participants and the total amount

Original: spent on participant compensation?
Revised: spent on participant compensation?

Original: [N/A]
Revised: [N/A]

Original: A Appendix

Original: In this Appendix, we provide additional experimental results based on reviewer comments.

Original: In thenext revision we will integrate these additional results into our main text and supplementary material.

Original: A.1 Additional YCB Results

Original: We provide additional reconstructions for samples from the YCB [23] dataset in Fig.

Original: 7 after recentering and coordinate normalization.

Original: YCB point clouds are obtained by fusing real RGB-D images,which result in measurements with different canonicalization and distribution from our the simulateddata we use for training.

Original: ConvOccNet [16] produces irregular surfaces and holes in the reconstruction,while our method generalizes to these real-world measurements and produces smooth surfaces anddetailed structures such as Pitcher ’s handle and spout holes, and the inner curves of the Mustard

Original: Bottle .

Original: [Figure]

Original: A.2 Detailed Comparison of Our Self-Supervised Loss vs NeuralPull

Original: An unsupervised loss is essential for training with unlabeled data.

Original: In this subsection, we dive into adeeper comparison between our self-supervised loss and the approach described in NeuralPull [19].

Original: First, we report accuracies of sign predictions between NeuralPull and our self-supervised method.

Original: For this experiment, we train on five point clouds from the QueenBed class (same setup as Sec.

Original: 5of our supplementary), and run inference on 130,000 points near the surface of each point

Original: cloud(130,000 * 5 = 650,000 total).

Original: While both methods produced low ℓ 2 losses, in Tab. 4 our methodachieves higher accuracy in sign prediction.

Original: clouds of the QueenBed class.

Original: Of the five point clouds, there are a total of 650,000 points to predict, with 449,650 being positive and 200,350 being negative

Original: NeuralPull

Original: [Table]

Original: Our SSL

Original: [Table]

Original: [Figure]

Original: [Figure]

Original: We show visualizations in Fig.

Original: Due to the more accurate sign predictions, our reconstruction resultshave sharper edges and details, while NeuralPull reconstructions often appear overly smooth andcontain significantly more holes.

Original: Next, we train the meta-learning first stage of our GenSDF model but swap out our self-supervisedloss for NeuralPull’s loss.

Original: We train on six classes from our labeled dataset.

Original: As we can see in Fig.

Original: 9,with NeuralPull’s loss training converges at a local minima.

Original: We also provide quantitative results in

Original: Tab. 4.

Original: To visually understand the extremely high CD of NeuralPull, we visualize a reconstructionresult in Fig.

Original: Sign predictions for points inside the surface are mostly incorrect and a reasonablesurface boundary is not formed.

Original: We manually inspected dozens of samples and confirm that allreconstructions share this problem.

Original: Mean/median Chamfer Distance (CD) of 166 unseen classes, scale is 10 − 4 .

Original: [Equation]

Original: Chamfer Distance

Original: [Equation]

Original: NeuralPull’s inaccuracies build up as we increase the number of meshes, and its training objectiveconflicts with that of the supervised loss, which has accurate sign predictions.

Original: Thus, the model isunable to converge at the appropriate signed distance function.

Original: A.3 Understanding the Effectiveness of Our Meta-learning Training

Original: We provide two experiments to understand the effectiveness and limitations of our meta-learningapproach.

Original: points are mostly inaccurate and a reasonable surface boundary formed.

Original: All reconstructed samples we inspected share this problem regardless of the input point

Original: Training on diverse vs similar classes We train two models on our meta-learning first stage.

Original: Thefirst trains on the following six diverse shape classes, with a mix of small, large, planar, convex, andconcave surfaces: ’Bench’, ’QueenBed’, ’EndTable’, ’FloorLamp’, ’Monitor’, ’PottedPlant’ Thesecond trains on six classes that are semantically and geometrically similar, large planar shapes:‘EndTable’, ’AccentTable’, ’CoffeeTable’, ’DiningTable’, ’RoundTable’, ’Table.’

Original: Then we evaluateon 166 unseen classes.

Original: The first model outperforms the second in reconstruction quality, validatingthat the diversity in the training set is more important than the raw number of classes.

Original: We do notethat the difference in CD is noticeable but not very significant.

Original: This validates the effectiveness of ourmeta-learning approach: even with less diverse data, our model can still produce generalized priors.

Original: We provide quantitative results in Tab.

Original: 5 and training curves in Fig.

Original: [Figure]

Original: Six Diverse Classes Six

Original: [Figure]

Original: CD 0.972 / 0.

Original: [Table]

Original: [Table]

Original: Training only with the supervised loss We

Original: train two separate models for a prior.

Original: Both train onsix classes: ’Bench’, ’QueenBed’, ’EndTable’, ’FloorLamp’, ’Monitor’, ’PottedPlant,’ with a total of600 meshes.

Original: The first model is trained using our two-stage learning approach.

Original: The second model is trained with only the supervised loss, but introduces dropout (20%) and small amounts of Gaussiannoise perturbations to the point clouds to reduce overfitting.

Original: Then, we use both priors to train our second stage in exactly the same fashion.

Original: With our prior, ourmodel performs significantly better when reconstructing unseen classes.

Original: We provide quantitativeresults on 166 unseen classes in Tab. 6.

Original: We highlight that after training stage 1, both methods performon par on unseen classes.

Original: However, our prior that emulates semi-supervised training is able tosignificantly outperform in the second stage, where we introduce true unlabeled data samples.

Original: [Table]