Original: Neural Shape Deformation Priors
Revised: Neural Shape Deformation Priors

Original: [Figure]

Original: AffiliationAddress email

Original: Abstract
Revised: Abstract

Original: We present Neural Shape Deformation Priors , a novel method for shape manipulation that predicts mesh deformations of non-rigid objects from user-providedhandle movements.
Revised: We present Neural Shape Deformation Priors , a novel method for shape manipulation that predicts mesh deformations of non-rigid objects from user-provided handle movements.

Original: State-of-the-art methods cast this problem as an optimizationtask, where the input source mesh is iteratively deformed to minimize an objectivefunction according to hand-crafted regularizers such as ARAP [1].
Revised: State-of-the-art methods cast this problem as an optimization task, where the input source mesh is iteratively deformed to minimize an objective function according to hand-crafted regularizers such as ARAP [1].

Original: In this work,we learn the deformation behavior based on the underlying geometric properties ofa shape, while leveraging a large-scale dataset containing a diverse set of non-rigiddeformations.
Revised: In this work, we learn the deformation behavior based on the underlying geometric properties of a shape, while leveraging a large-scale dataset containing a diverse set of non-rigid deformations.

Original: Specifically, given a source mesh and desired target locations ofhandles that describe the partial surface deformation, we predict a continuousdeformation field that is defined in 3D space to describe the space deformation.
Revised: Specifically, given a source mesh and desired target locations of handles that describe the partial surface deformation, we predict a continuous deformation field that is defined in 3D space to describe the space deformation.

Original: To this end, we introduce transformer-based deformation networks that representa shape deformation as a composition of local surface deformations.
Revised: To this end, we introduce transformer-based deformation networks that represent a shape deformation as a composition of local surface deformations.

Original: It learns aset of local latent codes anchored in 3D space, from which we can learn a set ofcontinuous deformation functions for local surfaces.
Revised: It learns a set of local latent codes anchored in 3D space, from which we can learn a set of continuous deformation functions for local surfaces.

Original: Our method can be applied tochallenging deformations and generalizes well to unseen deformations.
Revised: Our method can be applied to challenging deformations and generalizes well to unseen deformations.

Original: We validateour approach in experiments using the DeformingThing4D dataset, and compare toboth classic optimization-based and recent neural network-based methods.
Revised: We validate our approach in experiments using the DeformingThing4D dataset, and compare to both classic optimization-based and recent neural network-based methods.

Original:  Introduction
Revised:  Introduction

Original: Editing and deforming 3D shapes is a key component in animation creation and computer aideddesign pipelines.
Revised: Editing and deforming 3D shapes is a key component in animation creation and computer aided design pipelines.

Original: Given as little user input as possible, the goal is to create new deformed instancesof the original 3D shape which look natural and behave like real objects or animals.
Revised: Given as little user input as possible, the goal is to create new deformed instances of the original 3D shape which look natural and behave like real objects or animals.

Original: The user input isassumed to be very sparse, such as vertex handles that can be dragged around.
Revised: The user input is assumed to be very sparse, such as vertex handles that can be dragged around.

Original: For example, userscan animate a 3D model of an animal by dragging its feet forward.
Revised: For example, users can animate a 3D model of an animal by dragging its feet forward.

Original: This problem is severely ill-posedand typically under-constrained, as there are many possible deformations that can be matched withthe provided partial surface deformations of handles, especially for large surface deformations.
Revised: This problem is severely ill-posed and typically under-constrained, as there are many possible deformations that can be matched with the provided partial surface deformations of handles, especially for large surface deformations.

Original: Thus,strong priors encoding deformation regularity are necessary to tackle this problem.
Revised: Thus, strong priors encoding deformation regularity are necessary to tackle this problem.

Original: Physics and differential geometry provide solutions that use various analytical priors which define natural-lookingmesh deformations, such as elasticity [2, 3], Laplacian smoothness [4, 5, 6], and rigidity [1, 7, 8]priors.
Revised: Physics and differential geometry provide solutions that use various analytical priors which define natural-looking mesh deformations, such as elasticity [2, 3], Laplacian smoothness [4, 5, 6], and rigidity [1, 7, 8] priors.

Original: They update mesh vertex coordinates by iteratively optimizing energy functions that satisfyconstraints from both the pre-defined deformation priors and given handle locations.
Revised: They update mesh vertex coordinates by iteratively optimizing energy functions that satisfy constraints from both the pre-defined deformation priors and given handle locations.

Original: Although thesealgorithms can preserve geometric details of the original source model, they still have limited capacityto model realistic deformations, since the deformation priors are region independent, e.g., the headregion deforms in a similar way as the tail of an animal, resulting in unrealistic deformation states.
Revised: Although these algorithms can preserve geometric details of the original source model, they still have limited capacity to model realistic deformations, since the deformation priors are region independent, e.g., the head region deforms in a similar way as the tail of an animal, resulting in unrealistic deformation states.

Original: Hence, motivated by the recent success of deep neural networks for 3D shape modeling [9, 10,11, 12, 13, 14, 15, 16, 17, 18, 19, 20], we propose to learn shape deformation priors of a specificobject class, e.g., quadruped animals, to complete surface deformations beyond observed handles.
Revised: Hence, motivated by the recent success of deep neural networks for 3D shape modeling [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], we propose to learn shape deformation priors of a specific object class, e.g., quadruped animals, to complete surface deformations beyond observed handles.

Original: We formulate the following properties of such a learned model; (1) it should be robust to differentmesh quality and number of vertices, (2) the source mesh is not limited to canonical pose (i.e.,the input mesh can have arbitrary pose), and (3) it should generalize well to new deformations.
Revised: We formulate the following properties of such a learned model; (1) it should be robust to different mesh quality and number of vertices, (2) the source mesh is not limited to canonical pose (i.e., the input mesh can have arbitrary pose), and (3) it should generalize well to new deformations.

Original: Towards these goals, we represent deformations as a continuous deformation field which is definedin the near-surface region to describe the space deformation caused by the corresponding surfacedeformation.
Revised: Towards these goals, we represent deformations as a continuous deformation field which is defined in the near-surface region to describe the space deformation caused by the corresponding surface deformation.

Original: The continuity property enables us to manipulate meshes with infinite number ofvertices and disconnected components.
Revised: The continuity property enables us to manipulate meshes with infinite number of vertices and disconnected components.

Original: To handle source meshes in arbitrary poses, we learn shapedeformations via canonicalization.
Revised: To handle source meshes in arbitrary poses, we learn shape deformations via canonicalization.

Original: Specifically, the overall deformation process consists of twostages: arbitrary-to-canonical transformation and canonical-to-arbitrary transformation.
Revised: Specifically, the overall deformation process consists of two stages: arbitrary-to-canonical transformation and canonical-to-arbitrary transformation.

Original: To obtainmore detailed surface deformations and better generalization capabilities to unseen deformations,we propose to learn local deformation fields conditioned on local latent codes encoding geometrydependent deformation priors, instead of global deformation fields conditioned on a single latentcode.
Revised: To obtain more detailed surface deformations and better generalization capabilities to unseen deformations, we propose to learn local deformation fields conditioned on local latent codes encoding geometrydependent deformation priors, instead of global deformation fields conditioned on a single latent code.

Original: To this end, we propose Transformer-based Deformation Networks (TD-Nets), which learnsencoder-based local deformation fields on point cloud approximations of the input mesh.
Revised: To this end, we propose Transformer-based Deformation Networks (TD-Nets), which learns encoder-based local deformation fields on point cloud approximations of the input mesh.

Original: Concretely,
Revised: Concretely,

Original: TD-Nets encode an input point cloud with surface geometry information and incomplete deformationflow into a sparse set of local latent codes and a global feature vector by using the vector attentionblocks proposed in [21].
Revised: TD-Nets encode an input point cloud with surface geometry information and incomplete deformation flow into a sparse set of local latent codes and a global feature vector by using the vector attention blocks proposed in [23].

Original: The deformation vectors of spatial points are estimated by an attentivedecoder, which aggregates the information of neighboring local latent codes of a spatial point basedon the feature similarity relationships.
Revised: The deformation vectors of spatial points are estimated by an attentive decoder, which aggregates the information of neighboring local latent codes of a spatial point based on the feature similarity relationships.

Original: The aggregated feature vectors are finally passed to a multilayer-perceptron (MLP) to predict displacement vectors which can be applied to the source mesh tocompute the final output mesh.
Revised: The aggregated feature vectors are finally passed to a multilayer-perceptron (MLP) to predict displacement vectors which can be applied to the source mesh to compute the final output mesh.

Original: To summarize, we introduce transformer-based local deformation field networks which are capableto learn shape deformation priors for the task of user-driven shape manipulation.
Revised: To summarize, we introduce transformer-based local deformation field networks which are capable to learn shape deformation priors for the task of user-driven shape manipulation.

Original: The deformationnetworks learn a set of anchor features based on a vector attention mechanism, enhancing theglobal deformation context, and selecting the most informative local deformation descriptors fordisplacement vector estimations, leading to an improved generalization ability to new deformations.
Revised: The deformation networks learn a set of anchor features based on a vector attention mechanism, enhancing the global deformation context, and selecting the most informative local deformation descriptors for displacement vector estimations, leading to an improved generalization ability to new deformations.

Original: Incomparison to classical hand-crafted deformation priors as well as recent learning-based deformationpredictors, our method achieves more accurate and natural shape deformations.
Revised: In comparison to classical hand-crafted deformation priors as well as recent neural network-based deformation predictors, our method achieves more accurate and natural shape deformations.

Original:  Related Work
Revised:  Related Work

Original: User-guided shape manipulation lies at the intersection of computer graphics and computer vision.
Revised: User-guided shape manipulation lies at the intersection of computer graphics and computer vision.

Original: Our proposed method is related to polygonal mesh geometry processing, neural field representations,as well as vision transformers.
Revised: Our proposed method is related to polygonal mesh geometry processing, neural field representations, as well as vision transformers.

Original: Optimization-based Shape Manipulation.
Revised: Optimization-based Shape Manipulation.

Original: Classical methods formulate shape manipulation asa mathematical optimization problem.
Revised: Classical methods formulate shape manipulation as a mathematical optimization problem.

Original: They perform mesh deformations by either deforming thevertices [22, 23] or the 3D space [24, 25, 8, 26, 27].
Revised: They perform mesh deformations by either deforming the vertices [24, 25] or the 3D space [26, 27, 8, 28, 29].

Original: Performing mesh deformation without any otherinformation about the target shape, but only using limited user-provided correspondences is an underconstrained problem.
Revised: Performing mesh deformation without any other information about the target shape, but only using limited user-provided correspondences is an underconstrained problem.

Original: To this end, the optimization methods require deformation priors to constraintthe deformation regularity as well as the smoothness of the deformed surface.
Revised: To this end, the optimization methods require deformation priors to constraint the deformation regularity as well as the smoothness of the deformed surface.

Original: Various analytic priorshave been proposed which encourage smooth surface deformations, such as elasticity [2, 3], Laplaciansmoothness [4, 5, 6], and rigidity [1, 7, 8].
Revised: Various analytic priors have been proposed which encourage smooth surface deformations, such as elasticity [2, 3], Laplacian smoothness [4, 5, 6], and rigidity [1, 7, 8].

Original: These methods use efficient linear solvers to iterativelyoptimize energy functions that satisfy constraints from both the pre-defined deformation prior andprovided handle movements.
Revised: These methods use efficient linear solvers to iteratively optimize energy functions that satisfy constraints from both the pre-defined deformation prior and provided handle movements.

Original: Recently, NFGP [28] was proposed to optimize neural networks withnon-linear deformation regularizations.
Revised: Recently, NFGP [30] was proposed to optimize neural networks with non-linear deformation regularizations.

Original: Specifically, it performs shape deformations by warping theneural implicit fields of the source model through a deformation vector field, which is constrained by modeling implicitly represented surfaces as elastic shells.
Revised: Specifically, it performs shape deformations by warping the neural implicit fields of the source model through a deformation vector field, which is constrained by modeling implicitly represented surfaces as elastic shells.

Revised: NeuralMLS [31] learned a geometry-aware weight function of a shape and given control points for moving least squares(MLS) deformations, which smoothly interpolates the control point displacements over space.

Original: Although they can preserve manygeometric details of the source shape, they struggle to model complex deformations, as local surfacesare simply constrained to be transformed in a similar manner.
Revised: Although they can preserve many geometric details of the source shape, they struggle to model complex deformations, as local surfaces are simply constrained to be transformed in a similar manner.

Original: In contrast, we aim to learn deformationpriors based on local geometries to infer hidden surface deformations.
Revised: In contrast, we aim to learn deformation priors based on local geometries to infer hidden surface deformations.

Original: Learning-based Shape Reconstruction and Manipulation.
Revised: Learning-based Shape Reconstruction and Manipulation.

Original: Learning-based shape manipulationhas been studied to learn shape priors based on shape auto-encoding and auto-decoding.
Revised: Learning-based shape manipulation has been studied to learn shape priors based on shape auto-encoding or auto-decoding.

Original: [29, 30,31, 32] map a class of shapes into a latent space.
Revised: [32, 33, 34, 35] map a class of shapes into a latent space.

Original: During inference, given handle positions as input,they find an optimal latent code whose 3D interpretation is the most similar to the observation.
Revised: During inference, given handle positions as input, they find an optimal latent code whose 3D interpretation is the most similar to the observation.

Original: Incontrast, we learn explicit deformation priors to directly predict 3D surface deformations.
Revised: In contrast, we learn explicit deformation priors to directly predict 3D surface deformations.

Original: Jakab etal.
Revised: Jakab et al.

Original: [33] proposed to control shapes via unsupervised 3D keypoint discovery.
Revised: [36] proposed to control shapes via unsupervised 3D keypoint discovery.

Original: Instead, we use partialsurface deformations represented by handle displacements as input observations, rather than keypointdisplacements.
Revised: Instead, we use partial surface deformations represented by handle displacements as input observations, rather than keypoint displacements.

Original: There exist a series of methods that use deep neural networks to complete non-rigidshapes [32, 34, 35, 36, 37, 38, 39, 40] from partial scans.
Revised: There exist a series of methods that use deep neural networks to complete non-rigid shapes [35, 37, 38, 39, 40, 41, 42, 43] from partial scans.

Original: Our task is partially related to this task,but our shape manipulation task from user input requires completion of the deformation field.
Revised: Our task is partially related to this task, but our shape manipulation task from user input requires completion of the deformation field.

Original: Incontrast to shape completion, our setting is more under-constrained, as the user-provided handlecorrespondences are very sparse and more incomplete than partial point clouds from scans.
Revised: In contrast to shape completion, our setting is more under-constrained, as the user-provided handle correspondences are very sparse and more incomplete than partial point clouds from scans.

Original: Recentmethods for clothed-human body reconstruction choose to canonicalize the captured scan into a predefined T-pose [41, 42, 43] using the skeletal deformation model of SMPL [44] or STAR [45] whichcan also be used to later animate the human.
Revised: Recent methods for clothed-human body reconstruction choose to canonicalize the captured scan into a predefined T-pose [44, 45, 46] using the skeletal deformation model of SMPL [47] or STAR [48] which can also be used to later animate the human.

Original: Inspired by this, we also perform a canonicalization toenable editing of source meshes with arbitrary poses, before applying the actual deformation towardsthe target pose handles.
Revised: Inspired by this, we also perform a canonicalization to enable editing of source meshes with arbitrary poses, before applying the actual deformation towards the target pose handles.

Original: Continuous Neural Fields.
Revised: Continuous Neural Fields.

Original: Continuous neural field representations have been widely used in 3Dshape modeling [9, 11, 10] and 4D dynamics capture [46, 37, 34, 35, 36].
Revised: Continuous neural field representations have been widely used in 3D shape modeling [9, 11, 10] and 4D dynamics capture [49, 40, 38, 37, 39].

Original: Recent work that represents3D shapes as continuous signed distance fields [15, 16, 17, 18, 19] or occupancy fields [9, 11,12, 47,13, 14, 20, 48] can theoretically obtain volumetric reconstructions with infinite resolutions, as they arenot bound to the resolution of a discrete grid structure.
Revised: Recent work that represents 3D shapes as continuous signed distance fields [17, 12, 18, 19, 20] or occupancy fields [9, 11, 14, 50, 15, 16, 51, 21, 52, 53] can theoretically obtain volumetric reconstructions with infinite resolutions, as they are not bound to the resolution of a discrete grid structure.

Original: Similarly, we learn continuous deformationfields defined in 3D space for shape deformations.
Revised: Similarly, we learn continuous deformation fields defined in 3D space for shape deformations [13, 35, 30, 54].

Original: Due to the continuity of the deformation fields,our method is not limited by the number of mesh vertices, or disconnected components.
Revised: Due to the continuity of the deformation fields, our method is not limited by the number of mesh vertices, or disconnected components.

Original: Differentfrom ShapeFlow [32], OFlow [46], and NPMs [34] that learn a deformation field from a single latentcode, inspired by local implicit field learning [12, 13, 20, 48], we model the deformation field as acomposition of local deformation functions, improving the representation capability of describingcomplex deformations as well as generalization to new deformations.
Revised: Different from ShapeFlow [35], OFlow [49], LPDC-Net [40] and NPMs [37] that learn a deformation field from a single latent code, inspired by local implicit field learning [14, 15, 21, 52, 55], we model the deformation field as a composition of local deformation functions, improving the representation capability of describing complex deformations as well as generalization to new deformations.

Original: Visual Transformers.
Revised: Visual Transformers.

Original: Recently, transformer architectures [49] from natural language processinghave revolutionized many computer vision tasks, including image classification [50, 51], objectrecognition [52], semantic segmentation [53], or 3D reconstruction [54, 55, 48].
Revised: Recently, transformer architectures [56] from natural language processing have revolutionized many computer vision tasks, including image classification [57, 58], object recognition [59], semantic segmentation [60], or 3D reconstruction [61, 62, 52, 55, 63].

Original: We refer the readerto [56] for a detailed survey of visual transformers.
Revised: We refer the reader to [64] for a detailed survey of visual transformers.

Original: In this work, we propose the usage of atransformer architecture to learn deformation fields.
Revised: In this work, we propose the usage of a transformer architecture to learn deformation fields.

Original: Given the input point cloud sampled from thesource mesh with partial deformation flow (defined by the user handles), we employ the vectorattention blocks from Point Transformer [21] as a main point cloud processing module to extract asparse set of local latent codes, enhancing the global understanding of deformation behaviours.
Revised: Given the input point cloud sampled from the source mesh with partial deformation flow (defined by the user handles), we employ the vector attention blocks from Point Transformer [23] as a main point cloud processing module to extract a sparse set of local latent codes, enhancing the global understanding of deformation behaviours.

Original: Basedon the obtained local deformation descriptors, our attentive deformation decoder learns to attend tothe most informative features from near-by local codes to predict a deformation field.
Revised: Based on the obtained local deformation descriptors, our attentive deformation decoder learns to attend to the most informative features from near-by local codes to predict a deformation field.

Original:  Approach
Revised:  Approach

Original: Given a source mesh S = {V , F} where V and F denote the set of vertices and the set of faces,respectively, we aim to deform S to obtain a target mesh T by selecting a sparse set of mesh vertices
Revised: Given a source mesh S = {V , F} where V and F denote the set of vertices and the set of faces, respectively, we aim to deform S to obtain a target mesh T by selecting a sparse set of mesh vertices

Original: H =
Revised: H =

Original: { h i } ℓi =1 as handles, and dragging them to target locations
Revised: { h i } ℓi =1 as handles, and dragging them to target locations

Original: O =
Revised: O =

Original: { o i } ℓi =1 .
Revised: { o i } ℓi =1 .

Original: The key idea in thiswork is to use deformation priors to complete hidden surface deformations.
Revised: The key idea in this work is to use deformation priors to complete hidden surface deformations.

Original: Specifically, the goalis to learn a continuous deformation field D defined in 3D space, from which we can obtain thedeformed mesh T ′ =
Revised: Specifically, the goal is to learn a continuous deformation field D defined in 3D space, from which we can obtain the deformed mesh T ′ =

Original: {V + D ( V ) , F} through vertex deformations of the source mesh S .
Revised: {V + D ( V ) , F} through vertex deformations of the source mesh S .

Original: The overallpipeline of the proposed approach is shown in Figure 2.
Revised: The overall pipeline of the proposed approach is shown in Figure 2.

Original: Our method can be applied to input meshesin arbitrary poses by leveraging learned shape deformation via canonicalization (see Section 3.1). To represent the underlying deformation prior, we propose neural deformation fields as described in Section 3.2 which can be learned from large deformation datasets (see Section 3.3).
Revised: Our method can be applied to input meshes

Original: U s e
Revised: U s e

Original: r
Revised: r

Original: I npu t
Revised: I npu t

Original: Source Mesh Target Handle Locations
Revised: Source Mesh Target Handle Locations

Original: BackwardDeformationNetworks
Revised: BackwardDeformationNetworks

Original: ForwardDeformationNetworks Shape Deformation via Canonicalization
Revised: ForwardDeformationNetworks Shape Deformation via Canonicalization

Original: Target Mesh
Revised: Target Mesh

Original: [Figure]
Revised: [Figure]

Revised: in arbitrary poses by leveraging learned shape deformation via canonicalization (see Section 3.1).

Revised: To represent the underlying deformation prior, we propose neural deformation fields as described in

Revised: Section 3.2 which can be learned from large deformation datasets (see Section 3.3).

Original: 3.1 Learning Shape Deformations via Canonicalization
Revised: 3.1 Learning Shape Deformations via Canonicalization

Original: To ensure robustness w.r.t.
Revised: To ensure robustness w.r.t.

Original: varying input mesh quality (topology and resolution) , we operate onpoint clouds instead of meshes.
Revised: varying input mesh quality (topology and resolution), we operate on point clouds instead of meshes.

Original: Specifically, we sample a point cloud P S
Revised: Specifically, we sample a point cloud P S

Original: = { p i } ni =0 ∈
Revised: = { p i } ni =0 ∈

Original: R n × 3 from
Revised: R n × 3 from

Original: S of size n = 5000 .
Revised: S of size n = 5000 .

Original: We define the target handle point locations P O =
Revised: We define the target handle point locations P O =

Original: { o i } ni =

Revised: { o i } ni =

Original: ∈ R n × 3 , wherewe use zeros to represent unknown point flows.
Revised: ∈ R n × 3 , where we use zeros to represent unknown point flows.

Original: Further, to avoid the ambiguity of zero point flow,we define the corresponding binary user handle masks M = { b i } ni =0 ∈ R n where b i = 1 if p i is ahandle or otherwise b i = 0 .
Revised: Further, to avoid the ambiguity of zero point flow, we define the corresponding binary user handle masks M = { b i } ni =0 ∈ R n where b i = 1 if p i is a handle or otherwise b i = 0 .

Original: To learn the shape transformation between two arbitrary non-rigidly deformed poses, one can learndeformation fields that directly map the source deformed space to target space.
Revised: To learn the shape transformation between two arbitrary non-rigidly deformed poses, one can learn deformation fields that directly map the source deformed space to target space.

Original: However, it would bedifficult to learn the deformation priors well, as there could be infinite deformation state transformationpairs.
Revised: However, it would be difficult to learn the deformation priors well, as there could be infinite deformation state transformation pairs.

Original: To decrease the learning complexity, we introduce a canonical space as an intermediate state.
Revised: To decrease the learning complexity, we introduce a canonical space as an intermediate state.

Original: We divide the shape transformation process into two steps; a backward deformation that aligns thesource deformed space to canonical space, and a forward deformation that maps the canonical space tothe target deformation space.
Revised: We divide the shape transformation process into two steps; a backward deformation that aligns the source deformed space to canonical space, and a forward deformation that maps the canonical space to the target deformation space.

Original: Concretely, P S is passed into the backward transformation network Ω bto learn the backward deformation field D b which transforms the input shape P S into a canonical pose
Revised: Concretely, P S is passed into the backward transformation network Ω b to learn the backward deformation field D b which transforms the input shape P S into a canonical pose

Original: P ′C .
Revised: P ′C .

Original: Similarly, the querying non-surface point set Q S =
Revised: Similarly, the querying non-surface point set Q S =

Original: { q i } mi =0 ∈
Revised: { q i } mi =0 ∈

Original: R m × 3 , m = 5000 randomlysampled in the 3D space of S is also mapped to canonical space through Q ′C = Q S + D b ( Q S ) .
Revised: R m × 3 , m = 5000 randomly sampled in the 3D space of S is also mapped to canonical space through Q ′C = Q S + D b ( Q S ) .

Original: Lastly, given P ′C , M , and P O as input, a forward transformation network Ω f is learned to representthe forward deformation field D f that predicts final locations Q ′T =
Revised: Lastly, given P ′C , M , and P O as input, a forward transformation network Ω f is learned to represent the forward deformation field D f that predicts final locations Q ′T =

Original: Q ′C + D f ( Q ′C ) .
Revised: Q ′C + D f ( Q ′C ) .

Original: 3.2 Transformer-based Deformation Networks (TD-Nets)
Revised: 3.2 Transformer-based Deformation Networks (TD-Nets)

Original: The deformation via canonicalization is based on two deformation field predictors (forward andbackward deformations).
Revised: The deformation via canonicalization is based on two deformation field predictors (forward and backward deformations).

Original: Both networks share the same architecture, thus, in the following, wewill only describe the forward deformation network as visualized in Figure 3 while the backwarddeformation network is analogous.
Revised: Both networks share the same architecture, thus, in the following, we will only describe the forward deformation network as visualized in Figure 3 while the backward deformation network is analogous.

Original: It consists of a transformer-based deformation encoder and avector cross attention-based decoder network.
Revised: It consists of a transformer-based deformation encoder and a vector cross attention-based decoder network.

Original: Point transformer encoder.
Revised: Point transformer encoder.

Original: Given a point set P C with handle locations P O and a binary mask M asinputs, we use point transformer layers from [21] to build our encoder modules.
Revised: Given a point set P C with handle locations P O and a binary mask M as inputs, we use point transformer layers from [23] to build our encoder modules.

Original: The point transformerlayer is based on the vector attention mechanism [57].
Revised: The point transformer layer is based on the vector attention mechanism [65].

Original: Let X
Revised: Let X

Original: = { x i , f i } i and Y =
Revised: = { x i , f i } i and Y =

Original: { y i , g i } i be thequery and key-value sequences, where x i and y i denote the coordinates of query and key-value pointswith corresponding feature vectors
Revised: { y i , g i } i be the query and key-value sequences, where x i and y i denote the coordinates of query and key-value points with corresponding feature vectors

Original: f i and g i .
Revised: f i and g i .

Original: The vector cross attention operator VCA is defined as:
Revised: The vector cross attention operator VCA is defined as:

Original: [Equation]
Revised: [Equation]

Revised: U s e

Original:  where f ′ i are the aggregated features, φ , ψ , and α are linear projections implemented by a fullyconnected layer.
Revised: r I npu t [Figure] where f ′ i are the aggregated features, φ , ψ , and α are linear projections implemented by a fullyconnected layer.

Revised: γ is a mapping function implemented by a two-layer MLP to predict attention vectors.

Original: γ is the attention weight normalization function, in our case softmax .
Revised: ρ is the attention weight normalization function, in our case softmax .

Original: δ :
Revised: δ :

Original: = θ ( x i − y j )is the positional embedding module [49, 58] implemented by a two linear layers with a single ReLU [59].
Revised: = θ ( x i − y j ) is the positional embedding module [56, 66] implemented by a two linear layers with a single ReLU [67].

Original: It leverages relatively positional information of x i and y j to benefit the network training.
Revised: It leverages relatively positional information of x i and y j to benefit the network training.

Original: [Figure] r I npu [Figure] Then, with the definition of VCA, the vector self-attention operator VSA can be defined as:
Revised: Then, with the definition of VCA, the vector self-attention operator VSA can be defined as:

Original: [Equation]
Revised: [Equation]

Original: Based on VCA and VSA, we can define two basic modules to build our encoder network, i.e. thepoint transformer block (PTB) and the point abstraction block (PAB).
Revised: Based on VCA and VSA, we can define two basic modules to build our encoder network, i.e. the point transformer block (PTB) and the point abstraction block (PAB).

Original: The definition of the pointtransformer block PTB is a combination of the BatchNorm (BN) layer [60], VSA, and residualconnections, formulated as:
Revised: The definition of the point transformer block PTB is a combination of the BatchNorm (BN) layer [68], VSA, and residual connections, formulated as:

Original: [Equation]
Revised: [Equation]

Original: For each point X i , it encapsulates the information from k enc = 16 nearest neighborhoods whilekeeping the point’s position x i unchanged.
Revised: For each point X i , it encapsulates the information from k enc = 16 nearest neighborhoods while keeping the point’s position x i unchanged.

Original: The point abstraction block PAB consists of farthestpoint sampling (FPS), BN, VCA, and VSA, which is defined as follow:[Equation] ( X ) , X )) .
Revised: The point abstraction block PAB consists of farthest point sampling (FPS), BN, VCA, and VSA, which is defined as follow:

Original: [Equation]
Revised: [Equation]

Original: The point cloud P C with handle mask M and flow P O as additional channels are passed to a pointtransformer block (PTB) to obtain a feature point cloud Z 

Revised: The point cloud P C with handle mask M and flow P O as additional channels are passed to a point transformer block (PTB) to obtain a feature point cloud Z

Original: = { c 0 i , z 0 i } ni =1 .
Revised: = { c 0 i , z 0 i } ni =1 .

Original: By using two consecutivepoint abstraction blocks (PABs) with intermediate set size of n 1 = 500 and n 2 = 100 , we obtain
Revised: By using two consecutive point abstraction blocks (PABs) with intermediate set size of n 1 = 500 and n 2 = 100 , we obtain

Original: Z 1 = { c 1 i , z 1 i } n 

Revised: Z 1 = { c 1 i , z 1 i } n

Original: i
Revised: i

Original: =1 and Z 2 = { c 2 i , z 2 i } n 

Revised: =1 and Z 2 = { c 2 i , z 2 i } n

Original: i
Revised: i

Original: =1 .
Revised: =1 .

Original: To enhance global deformation priors, we stack 4 pointtransformer blocks with full self-attention whose k enc is set to 100 to exchange the global informationin the whole set of Z 2 .
Revised: To enhance global deformation priors, we stack 4 point transformer blocks with full self-attention whose k enc is set to 100 to exchange the global information in the whole set of Z 2 .

Original: By doing so, we can obtain a sparse set of local deformation descriptors
Revised: By doing so, we can obtain a sparse set of local deformation descriptors

Original: Z = { c i , z i } 100 i =1 that are anchored in { c i } .
Revised: Z = { c i , z i } 100 i =1 that are anchored in { c i } .

Original: Finally, we perform a global max-pooling operationfollowed by two linear layers to obtain the global latent vector z glo .
Revised: Finally, we perform a global max-pooling operation followed by two linear layers to obtain the global latent vector z glo .

Original: Attentive deformation decoder.
Revised: Attentive deformation decoder.

Original: Based on the learned local latent codes Z = { c i , z i } 100 i =1 and globallatent vector z glo , the deformation decoder defines the forward deformation function D f : R 3 −→ R 3 ,which maps a point q from the canonical space of C to the 3D space of T .
Revised: Based on the learned local latent codes Z = { c i , z i } 100 i =1 and global latent vector z glo , the deformation decoder defines the forward deformation function D f : R 3 −→ R 3 , which maps a point q from the canonical space of C to the 3D space of T .

Original: Similar to tri-linearinterpolation operations in grid-based implicit field learning, a straightforward way to find thecorresponding feature vector z q is to use the weighted combination of k dec = 16 nearby localcodes Z q = { c k , z k } k dec k =1 .
Revised: Similar to tri-linear interpolation operations in grid-based implicit field learning, a straightforward way to find the corresponding feature vector z q is to use the weighted combination of k dec = 16 nearby local codes Z q = { c k , z k } k dec k =1 .

Original: Intuitively, the weight is inversely proportional to the euclidean distancebetween q and the anchoring location c k [13].
Revised: Intuitively, the weight is inversely proportional to the euclidean distance between q and the anchoring location c k [15].

Original: However, distance-based feature queries ignorethe relationships between deformation descriptors.
Revised: However, distance-based feature queries ignore the relationships between deformation descriptors.

Original: Thus, we propose to obtain z q by adaptivelyaggregating information of Z q based on the vector cross-attention operator:
Revised: Thus, we propose to obtain z q by adaptively aggregating information of Z q based on the vector cross-attention operator:

Original: [Equation]
Revised: [Equation]

Original: The local information aggregation enables us to flexibly search the local deformation priors, thus,improving the generalizability to new deformations.
Revised: The local information aggregation enables us to flexibly search the local deformation priors, thus, improving the generalizability to new deformations.

Original: Finally, the z q is fed into an MLP composed offive Res-FC blocks to estimate the associate location q ′ =
Revised: Finally, the z q is fed into an MLP composed of five Res-FC blocks to estimate the associate location q ′ =

Original: q + D f ( q ; z q ) in the target space.
Revised: q + D f ( q ; z q ) in the target space.

Original: 3.3 Training Objectives
Revised: 3.3 Training Objectives

Original: For training, we need a set of triplets ( S , C , T ) with dense correspondences, from which we canrandomly sample surface point clouds ( P S , P C , P T ) of size n and querying non-surface points( Q S , Q C , Q T ) of size m in the 3D space.
Revised: For training, we need a set of triplets ( S , C , T ) with dense correspondences, from which we can randomly sample surface point clouds ( P S , P C , P T ) of size n and querying non-surface points ( Q S , Q C , Q T ) of size m in the 3D space.

Original: To optimize the backward deformation networks, weemploy the mean ℓ 2 distance error that measures the difference between deformed points from sourcespace and their ground-truths in the canonical space:[Equation]
Revised: To optimize the backward deformation networks, we employ the mean ℓ 2 distance error that measures the difference between deformed points from source space and their ground-truths in the canonical space:

Original: [Equation]
Revised: [Equation]

Original: Similarly, to optimize the forward deformation networks, we use the following loss function:
Revised: Similarly, to optimize the forward deformation networks, we use the following loss function:

Original: [Equation]

Original: [Equation]
Revised: [Equation]

Original: The total loss function for source-target shape deformations is defined as:
Revised: The total loss function for source-target shape deformations is defined as:

Original: [Equation]
Revised: [Equation]

Original:  Experiments
Revised:  Experiments

Original: Dataset.
Revised: Dataset.

Original: Our experiments are performed on the DeformingThing4D-Animals [36] dataset whichcontains 1494 non-rigidly deforming animations with various motions comprising 40 identities of24 categories.
Revised: Our experiments are performed on the DeformingThing4D-Animals [39] dataset which contains 1494 non-rigidly deforming animations with various motions comprising 40 identities ofcategories.

Original: For the train/test split, we divide all animations into training (1296) and test (198).
Revised: For the train/test split, we divide all animations into training (1296) and test (198).

Original: The test set is composed of two subsets: (S1) contains 143 sequences of new motions for seen trainidentities, and (S2) contains 55 sequences of unseen individuals (and thus also new motions).
Revised: Similar to the D-FAUST [69] used in OFlow [49], the test set is composed of two subsets: (S1) contains 143 sequences of new motions for seen train identities, and (S2) contains 55 sequences of unseen individuals (and thus also new motions).

Original: Duringtraining, we randomly sample two frames from an identity as source-target deformation pairs.
Revised: During training, we randomly sample two frames from an identity as source-target deformation pairs.

Original: Duringinference, we consider the first frame of an animation as source mesh, and other frames as targetmeshes.
Revised: During inference, we consider the first frame of an animation as source mesh, and other frames as target meshes.

Revised: To evaluate the generalization ability to unseen identities, we evaluate the pre-trained models on the animal dataset used in Deformation

Revised: Transfer [70].

Original: For the quantitative comparison on each test subset, we compute evaluation metrics for 300randomly sampled pairs.
Revised: For the quantitative comparison on each test subset, we compute evaluation metrics for 300 randomly sampled pairs.

Revised: In addition, we also include comparisons on another animal dataset used in TOSCA [71].

Revised: TOSCA [71] does not have correspondences between different poses of the same animal, and hence does not easily provide handle displacements as input.

Revised: Thus, we provide a qualitative comparison under the setting of using user-specified handles as inputs.

Original: Implementation details.
Revised: Implementation details.

Original: Our approach is built on the PyTorch library [61].
Revised: Our approach is built on the PyTorch library [72].

Original: Please refer to thesupplementary material for the details of our network architecture.
Revised: Please refer to the supplementary material for the details of our network architecture.

Original: Our model consists of two trainingstages.
Revised: Our model consists of two training stages.

Original: We use an Adam [62] optimizer with β 1 = 0 .
Revised: We use an Adam [73] optimizer with β 1 = 0 .

Original: 9 , β 2 = 0 .
Revised: 9 , β 2 = 0 .

Original: 999 , and ϵ = 

Revised: 999 , and ϵ =

Original: − 8 .
Revised: − 8 .

Original: In the first stage,we train the forward and backward deformation networks individually.
Revised: In the first stage, we train the forward and backward deformation networks individually.

Original: Specifically, the backward andforward deformation networks are respectively optimized by the objective described in Equations 6or 7 using a batch size of 16 with the learning rate of 5e-4 for 100 epochs.
Revised: Specifically, the backward and forward deformation networks are respectively optimized by the objective described in Equationsor 7 using a batch size of 16 with the learning rate of 5e-4 for 100 epochs.

Original: In the second stage, thewhole model is trained according to Equation 8 in an end-to-end manner using a batch size of 6 witha learning rate of 5e-5 for 20 epochs.[Figure] [Table] [Table]
Revised: In the second stage, the whole model is trained according to Equation 8 in an end-to-end manner using a batch size of 6 with a learning rate of 5e-5 for 20 epochs.

Original: Baselines.
Revised: Baselines.

Original: We conduct comparisons against classical optimization-based and recent neural networkoptimization-based methods.
Revised: We conduct comparisons against classical optimization-based and recent neural networkbased methods.

Original: For the former, we select a representative work, ARAP [1], thatconstrains each local surface to be rigidly transformed as much as possible.
Revised: For the former, we select a representative work, ARAP [1], that constrains each local surface to be rigidly transformed as much as possible.

Original: For the latter, we use arecent state-of-the-art method, NFGP [28], which constrains the implicitly represented surfaces aselastic shells during the deformation process.It overfits the neural network to each input.
Revised: For the latter, we compare our method with the learning-based deformation predictor ShapeFlow [35] that embeds each shape into a latent space and learns flow-based deformations among 3D shapes. We also compare to NFGP [30], a deep optimization method, which constrains the implicitly represented surfaces as elastic shells during the deformation process.

Original: Evaluation metrics.
Revised: Evaluation metrics.

Original: We consider ℓ 2 distance error of mesh vertices ( ℓ 2 × 0 . 001 ), Chamfer Distance(CD × 0 . 01 ) of sampled point clouds of 30k points, and Face Normal Consistency (FNC × 0 . 01 ) asprimary evaluation metrics.
Revised: We consider ℓ 2 distance error of mesh vertices ( ℓ 2 × 0 . 001 ), Chamfer Distance (CD × 0 . 01 ) of sampled point clouds of 30k points, and Face Normal Consistency (FNC × 0 . 01 ) as primary evaluation metrics.

Original: Please refer to the supplementary material for a detailed explanation ofthese metrics.
Revised: Please refer to the supplementary material for a detailed explanation of these metrics.

Original: Note that for ℓ 2 and CD, lower is better, while for FNC, higher is better.
Revised: Note that for ℓ 2 and CD, lower is better, while for FNC, higher is better.

Original: 4.1 Comparisons
Revised: 4.1 Comparisons

Original: For a qualitative comparison, we visualize the vertex ℓ 1 distance error maps of deformed meshesin Figure 5 and Figure 6.
Revised: For a qualitative comparison, we visualize the vertex ℓ 1 distance error maps of deformed meshes in Figure 4 and Figure 5.

Original: As can be seen, our method has lower vertex errors in the hidden surface
Revised: As can be seen, our method has lower vertex errors in the hidden surface

Original: [Figure]
Revised: [Figure]

Revised: [Figure]

Original: regions since we use data-driven deformation priors, instead of employing hand-crafted regularizersto enforce surface smoothness.
Revised: regions since we use data-driven deformation priors, instead of employing hand-crafted regularizers to enforce surface smoothness.

Revised: The generalization ability to unseen deformations is improved by learning deformation fields for local surfaces, instead of modeling global deformations.

Original: Compared to ARAP [1] and NFGP [28], we can produce morerealistic results for complicated actions in the 3rd and 4th rows of Figure 5.
Revised: Compared to ARAP, ShapeFlow, and NFGP, we can produce more realistic results for complicated actions in the 3rd and 4th rows of Figure 4.

Original: The deformation resultspresented in Figure 6 demonstrate that our method can generalize to unseen identities, and is alsoverified quantitatively in Table 1, where our method consistently outperforms all baselines.
Revised: The deformation results presented in Figure 5 demonstrate that our method can generalize to unseen identities, and is also verified quantitatively in Table 1, where our method consistently outperforms all baselines.

Original: User-specified handles.
Revised: User-specified handles.

Original: To evaluate the generalization performance of our approach on userprovided handle displacements that are used in interactive editing applications, we use randomtranslations of handles  as input.
Revised: To evaluate the generalization performance of our approach on unseen identities using user-provided handle displacements that are used in interactive editing applications, we use random translations of handles applied to animals from TOSCA [71] as input.

Original: As depicted  in Figure 4, our approach is able to produce naturallylooking deformation results, and shows its advantages compared to ARAP [1] and NFGP [28].
Revised: As depicted [Table] in Figure 6, our approach is able to produce naturally-looking deformation results, and shows its advantages compared to ARAP, ShapeFlow, and NFGP.

Original: Notethat for this demonstration of user-specified handles there exists no corresponding ground-truth.
Revised: Note that for this demonstration of user-specified handles there exists no corresponding ground-truth.

Revised: Source mesh, handles and target handles

Revised: [Figure]

Revised: Ours

Original: 4.2 Ablation Studies
Revised: 4.2 Ablation Studies

Original: To verify our final model choice, we conducted a series of ablation studies, where we analyse severalvariants of our deformation fields (see Table 1).
Revised: To verify our final model choice, we conducted a series of ablation studies, where we analysed several variants of our deformation fields (see Table 1 and Figure 7). [Figure]

Original: Volumetric grids vs continuous fields.
Revised: Volumetric grids vs continuous fields.

Original: As continuous fields are not bound to the resolution of adiscrete grid structure, it can better represent complex deformations.
Revised: As continuous fields are not bound to the resolution of a discrete grid structure, it can better represent complex deformations.

Original: The performance degrades whenwe learn grid-based volumetric deformation fields.
Revised: The performance degrades when we learn grid-based volumetric deformation fields.

Original: This can be seen in the experiment “Ours-VDF"which uses a 3D U-Net [63] to generate volumetric deformation fields of a fixed resolution 64 3 .
Revised: This can be seen in the experiment “Ours-VDF" which uses a 3D U-Net [74] to generate volumetric deformation fields of a fixed resolution 64 3 .

Original: Global vs local deformation fields.
Revised: Global vs local deformation fields.

Original: “Ours-global" learns a global continuous field only conditioned on the global latent code.
Revised: “Ours-global" learns a global continuous field only conditioned on the global latent code.

Original: This variant tends to lose detailed information about local surfacedeformations, and is more difficult to generalize to new motions or identities, leading to inferiorresults in comparison to our  deformation fields.
Revised: This variant tends to lose detailed information about local surface deformations, and is more difficult to generalize to new motions or identities, leading to inferior results in comparison to our local deformation fields.

Original: Network Architectures (3D U-Net vs PointNet++ vs Point Transformer).
Revised: Network Architectures (3D U-Net vs PointNet++ vs Point Transformer).

Original: Compared to gridbased and point-based local deformation descriptors learning, the point transformer-based encodercaptures strong global contexts that enforce more global consistency constraints.
Revised: Compared to gridbased and point-based local deformation descriptors learning, the point transformer-based encoder captures strong global contexts that enforce more global consistency constraints.

Original: This provides performance improvements on surface accuracy of deformed meshes.
Revised: This provides performance improvements on surface accuracy of deformed meshes.

Original: To verify this, we conductedan experiment with “Ours-3D-UNet," which learns a volumetric feature map through a 3D U-Net,and then predicts deformation fields based on queried features via tri-linear interpolation operations.
Revised: To verify this, we conducted an experiment with “Ours-3D-UNet," which learns a volumetric feature map through a 3D U-Net, and then predicts deformation fields based on queried features via tri-linear interpolation operations.

Original: Additionally, we compare with “Ours-PointNet++," which replaces the point transformer encoderwith PointNet++ [64].
Revised: Additionally, we compare with “Ours-PointNet++," which replaces the point transformer encoder with PointNet++ [75].

Original: With vs without Attention-based feature querying.
Revised: With vs without Attention-based feature querying.

Original: The attention-based feature query mechanismcan flexibly and effectively select the most relevant deformation descriptors for a query point,resulting in improved performance over feature interpolation purely based on euclidean distances.
Revised: The attention-based feature query mechanism can flexibly and effectively select the most relevant deformation descriptors for a query point, resulting in improved performance over feature interpolation purely based on euclidean distances.

Original: Adeformation decoder that for example uses an interpolation with weights that are purely based oneuclidean distance instead (“Ours-w/o atten.
Revised: A deformation decoder that for example uses an interpolation with weights that are purely based on euclidean distance instead (“Ours-w/o atten.

Original: dec."), leading to significantly higher errors, particularlyin terms of the ℓ 2 vertex error.
Revised: dec."), leading to significantly higher errors, particularly in terms of the ℓ 2 vertex error.

Original: With vs without canonical poses.
Revised: With vs without canonical poses.

Original: Learning shape deformations via canonicalization improves thegeneralization to source meshes in different poses.
Revised: Learning shape deformations via canonicalization improves the generalization to source meshes in different poses.

Original: Learning without canonicalization ("Ours-w/ocano."), i.e., learning shape deformations directly between two arbitrary poses, results in considerablyhigher surface errors.
Revised: Learning without canonicalization ("Ours-w/o cano."), i.e., learning shape deformations directly between two arbitrary poses, results in considerably higher surface errors.

Revised: 4.3 Intermediate results of canonicalization

Revised: In Figure 8, we visualize our intermediate results of canonicalization.

Revised: As can be seen, our method can project source meshes with arbitrary poses into a canonical space with a same pose.

Revised: [Figure]

Original: 4.3 Limitations
Revised: 4.4 Limitations

Original: While compelling results have been demonstrated for shape manipulation, a few limitations still existin our approach that can be addressed in future work.
Revised: While compelling results have been demonstrated for shape manipulation, a few limitations still exist in our approach that can be addressed in future work.

Original: Our approach only needs sparse user input inform of handles which can be moved to create a new deformation state.
Revised: Our approach only needs sparse user input in form of handles which can be moved to create a new deformation state.

Original: While this allows for quickediting, a possible extension is to add rotations to the handles.
Revised: While this allows for quick editing, a possible extension is to add rotations to the handles.

Original: This could be done by leveraging adifferent deformation representation such as a SE(3) field which is composed of a displacement and arotation field.
Revised: This could be done by leveraging a different deformation representation such as a SE(3) field which is composed of a displacement and a rotation field.

Original: Note that our displacement representation is able to represent general deformations,but might require more user handles.
Revised: Note that our displacement representation is able to represent general deformations, but might require more user handles.

Original: Due to the limitations of the DeformingThing4D-Animals [36]dataset in terms of available models and poses, our approach may suffer from the generalization toout-of-distribution models and extreme poses.
Revised: Due to the limitations of the DeformingThing4D-Animals [39] dataset in terms of available models and poses, our approach may suffer from the generalization to out-of-distribution models and extreme poses.

Original: must add one limitation : a drawback since availabilityof such data is scarce.

Original: Additionally, the output of our model, as with other learning-based methods,may be affected by biases in the training dataset that can limit generalization.
Revised: Additionally, the output of our model, as with other learning-based methods, may be affected by biases in the training dataset that can limit generalization.

Original: We believe this issuecan be relieved by a larger training dataset and a richer data augmentation strategy in future work.
Revised: We believe this issue can be relieved by a larger training dataset and a richer data augmentation strategy in future work.

Original: Lastly, our training scheme only considers handles that are selected from a set of candidate parts ofthe models, thus, limiting the regions the user can interact with.
Revised: Lastly, our training scheme only considers handles that are selected from a set of candidate parts of the models, thus, limiting the regions the user can interact with.

Original: Enriching the candidate handlesduring training is potentially helpful for allowing free handle placement.
Revised: Enriching the candidate handles during training is potentially helpful for allowing free handle placement.

Original:  Conclusion
Revised:  Conclusion

Original: In this work, we introduced Neural Shape Deformation Priors , a novel approach that learns meshdeformations of non-rigid objects from user-provided handles based on the underlying geometricproperties of shapes.
Revised: In this work, we introduced Neural Shape Deformation Priors , a novel approach that learns mesh deformations of non-rigid objects from user-provided handles based on the underlying geometric properties of shapes.

Original: To enable shape manipulation for source meshes with different poses, wechoose to learn shape deformations via canonicalization where the source mesh is first transformedto the canonical space through a backward deformation field and then deformed to the target spacethrough a forward deformation field.
Revised: To enable shape manipulation for source meshes with different poses, we choose to learn shape deformations via canonicalization where the source mesh is first transformed to the canonical space through a backward deformation field and then deformed to the target space through a forward deformation field.

Original: For deformation field learning, we propose Transformer-based
Revised: For deformation field learning, we propose Transformer-based

Original: Deformation Networks (TD-Net) that represent a shape deformation as a composition of local surfacedeformations.
Revised: Deformation Networks (TD-Net) that represent a shape deformation as a composition of local surface deformations.

Original: Our experiments and ablation studies demonstrate that our method can be applied tochallenging new deformations, outperforming classical optimization-based methods such as ARAP [1]and neural networks-based methods such as  NFGP [28], while showing a good generalization topreviously unseen identities.
Revised: Our experiments and ablation studies demonstrate that our method can be applied to challenging new deformations, outperforming classical optimization-based methods such as ARAP [1] and neural networks-based methods such as ShapeFlow [35] and NFGP [30], while showing a good generalization to previously unseen identities.

Original: We see our method as an important step in the development of 3Dmodeling algorithms and softwares and hope to inspire more research in learning-based shapemanipulation.
Revised: We see our method as an important step in the development of 3D modeling algorithms and softwares and hope to inspire more research in learning-based shape manipulation.

Original: Societal impact.
Revised: Societal impact.

Original: Our work provides an algorithm for natural-looking shape editing, which cansimplify tedious procedures in 3D content creation and empower artists in the movie and gameindustries.
Revised: Our work provides an algorithm for natural-looking shape editing, which can simplify tedious procedures in 3D content creation and empower artists in the movie and game industries.

Original: It further has the potential to enrich 3D data with additional deformed shapes, andcould thus help improve the performance of other practical application techniques that rely on largequantities of 3D ground-truth for training.
Revised: It further has the potential to enrich 3D data with additional deformed shapes, and could thus help improve the performance of other practical application techniques that rely on large quantities of 3D ground-truth for training.

Original: Yet, misuse of our shape manipulation algorithm couldenable fraud or offensive content generation. 
Revised: Yet, misuse of our shape manipulation algorithm could enable fraud or offensive content generation. Acknowledgement.

Revised: This work is supported by a TUM-IAS Rudolf Mößbauer Fellowship, the ERC

Revised: Starting Grant Scan2CAD (804724), and Sony Semiconductor Solutions Corporation.

Revised: We would also like to thank Angela Dai for the video voice over.

Original: Checklist
Revised: Checklist

Original: For all authors... • Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope?
Revised: For all authors... • Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope?

Original: [Yes] See abstract and Section 1.
Revised: [Yes] See abstract and Section 1.

Original: • Did you describe the limitations of your work?
Revised: • Did you describe the limitations of your work?

Original: [Yes] See Section 4.3.
Revised: [Yes] See Section 4.4.

Original: • Did you discuss any potential negative societal impacts of your work?
Revised: • Did you discuss any potential negative societal impacts of your work?

Original: [Yes] SeeSection 5.• Have you read the ethics review guidelines and ensured that your paper conforms to them?
Revised: [Yes] See Section 5. • Have you read the ethics review guidelines and ensured that your paper conforms to them?

Original: [Yes] 
Revised: [Yes] 2.

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

Original: [N/A] (b) Did you include complete proofs of all theoretical results?
Revised: [N/A] (b) Did you include complete proofs of all theoretical results?

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

Original: If you ran experiments...[Table] (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: If you ran experiments... (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] See thesupplemental material.
Revised: [Yes] See the supplemental material.

Original: [Table] (b) Did you specify all the training details (e.g., data splits, hyperparameters, how theywere chosen)?
Revised: (b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)?

Original: [Yes] See Implementation details in Section 4.
Revised: [Yes] See Implementation details in Section 4.

Original: [Table] (c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)?[No]
Revised: (c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)?

Original: [Table] (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: [No] (d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)?

Original: [Yes] See Implementation details inSection 4.[Table]
Revised: [Yes] See Implementation details in Section 4.

Original: If you are using existing assets (e.g., code, data, models) or curating/releasing new assets... (a) If your work uses existing assets, did you cite the creators?
Revised: If you are using existing assets (e.g., code, data, models) or curating/releasing new assets... (a) If your work uses existing assets, did you cite the creators?

Original: [Yes] We use and citeDeformingThing4D [Table]
Revised: [Yes] We use and cite DeformingThing4D [39].

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

Original: [Yes] See the data section of the supplemental material.[Table]
Revised: [Yes] See the data section of the supplemental material.

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: [No][Table] (d) Did you discuss whether and how consent was obtained from people whose data you’reusing/curating?
Revised: [No] (d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating?

Original: [Yes] See the data section of the supplemental material.
Revised: [Yes] See the data section of the supplemental material.

Original: [Table] (e) Did you discuss whether the data you are using/curating contains personally identifiable[Table] information or offensive content?
Revised: (e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content?

Original: [Yes] See the data section of the supplementalmaterial.
Revised: [Yes] See the data section of the supplemental material.

Original: [Table] If you used crowdsourcing or conducted research with human subjects...[Table] (a) Did you include the full text of instructions given to participants and screenshots, ifapplicable?
Revised: If you used crowdsourcing or conducted research with human subjects... (a) Did you include the full text of instructions given to participants and screenshots, if applicable?

Original: [N/A](b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable?
Revised: [N/A] (b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable?

Original: [N/A]( c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation?
Revised: [N/A] (c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation?

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