SHREC'20: Non-rigid Shape Correspondence of Physically-Based Deformations

Full text

Eurographics Workshop on 3D Object Retrieval (2020)
T. Schreck and T. Theoharis (Editors)
SHREC’20: Non-rigid Shape Correspondence of Physically-Based
Deformations
R. M. Dyke†1F. Zhou†2Y-K. Lai†1P. L. Rosin†1D. Guo3K. Li3R. Marin4J. Yang3
1School of Computer Science & Informatics, Cardiff University, Wales
2Beihang University, Bejing, China
3Tianjin University, Tianjin, China
4Department of Computer Science, University of Verona, Italy
Abstract
Commonly, novel non-rigid shape correspondence techniques focus on particular matching challenges. This can lead to the
potential trade-off of poorer performance in other scenarios. An ideal dataset would provide a granular means for degrees
of evaluation. In this paper, we propose a novel dataset of real scans that contain challenging non-isometric deformations to
evaluate non-rigid point-to-point correspondence and registration algorithms. The deformations included in our dataset cover
extreme types of physically-based contortions of a toy rabbit. Furthermore, shape pairs contain incrementally different types
and amounts of deformation, this enables performance to be systematically evaluated with respect to the nature of the defor-
mation. A brief investigation into different methods for initialising correspondence was undertaken, and a series of experiments
were subsequently conducted to investigate the performance of state-of-the-art methods on the proposed dataset. We find that
methods that rely on initial correspondences and local descriptors that are sensitive to local surface changes perform poorly in
comparison to other strategies, and that a template-based approach performs the best.
CCS Concepts
•Computing methodologies →Shape analysis; Mesh models;
1. Introduction
Shape correspondence is a fundamental problem in geometry pro-
cessing with numerous applications, e.g., texture transfer, shape
morphing, and statistical shape analysis. However, accurately iden-
tifying correspondences between two or more surfaces continues
to be a challenging problem, and scenarios in which contemporary
approaches fail persist.
Many potential challenges occur when estimating a correspon-
dence between surfaces: deformations such as non-isometry (i.e.,
stretching between shapes); ambiguities (e.g., mapping features
with little geometric detail); shape incompatibility [MMR∗19]
(e.g., varying connectivity and vertex density); partial corre-
spondence (e.g., registering two incomplete scans); and semi-
compatible shapes (e.g., matching a human and a centaur).
State-of-the-art techniques aim to address challenges such as
missing data and non-isometry. However, evaluative datasets fail
to provide an appropriate means of identifying precisely where a
method’s performance degrades. Therefore it may be difficult to
determine what degree of robustness a method has for a particular
†Track organisers
correspondence challenge. This is crucial for understanding what
scenarios a method may be useful in.
We seek to address this problem by designing a structured, incre-
mentally challenging dataset. We focus on inducing non-rigid de-
formations on a real-world object and use texture markers to estab-
lish ground-truths. Various internal properties and drastic poses of
the shape were selected, causing complex deformations, and vary-
ing degrees of local protrusions and indentations on the surface.
A subset of deformations were selected—twist, indent, inflate &
stretch—from those identified by [SPF19], whose work focuses on
how humans interpret deformation of an unknown object.
The organisers briefly investigate the problem of correspondence
initialisation in Section 3.1, the results of which are discussed in
Section 6.1. Participants were asked to estimate the correspondence
between each partial scan in the dataset and one watertight scan of
the rabbit. Section 4details the correspondence methods evaluated
using this dataset. Participant results are presented in Section 6.2.
2. Related work
There are many different possible approaches to estimating cor-
respondences between non-rigid shapes. These may be classified
as extrinsic approaches (e.g., iterative closest point), intrinsic or
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R. M. Dyke et al. / SHREC’20: Non-rigid Shape Correspondence of Physically-Based Deformations
spectral techniques (e.g., Gaussian kernels [VLR∗17], heat ker-
nels [VLB∗17] and functional maps [EBC17]), and methods that
use a combination of both [DLRT19]. Data-driven methods can
perform well in benchmarks [DSL∗19], but may fail in scenarios
where training data is insufficient or no comparable model is avail-
able. Many other methods have been proposed for computing shape
correspondence, which are further discussed in the following sur-
veys [vKZHCO11,TCL∗13,BCBB16,BBL∗17,Sah19].
Many recent works have focused on addressing the problem of
non-isometric deformations [VLR∗17,VLB∗17,EBC17,DLRT19,
JYZ∗19,EHA∗19,EEBC20]— [Sah19] provides a comprehensive
overview of many methods. However, the resources available to
evaluate the performance of such methods are insufficient.
Previous SHape REtrieval Contests (SHREC) have produced in-
sightful benchmark datasets. Many use synthetic objects [BBC∗10,
LRB∗16,RCB∗17,RCL∗17]. While these synthetic datasets may
have certain advantages, such as easily established ground-truths,
they also produce deformations that are not necessarily realistic.
Human body scan datasets [RDP99,ASK∗05,BRLB14] capture
real-world scans of humans undergoing realistic deformations. This
is useful for understanding how well a method may perform on hu-
man subjects. However, the range of motion of a human is naturally
constrained, thus the degree of non-rigid deformation is relatively
limited. Whilst significant non-isometric deformation does occur
between persons, features like the head, hands and feet, are particu-
larly distinct, enabling correspondences between distinctive surface
regions to be established through smooth interpolations.
3. Dataset
For this paper, 3D scans of a real-world object were captured using
a high-precision 3D scanner (Artec3D Space Spider). The scanner
is accurate up to 0.05mm. Each scan exhibits one or more types
of deformation. Scans were classified into four distinct groups by
the type of deformation primarily exhibited by a given pose: twist,
indent, inflate, &stretch. The challenge of the dataset was fur-
ther increased by varying the internal properties of the object by
filling it with different materials: couscous, risotto, &chickpea.
Using different internal materials changed the local appearance of
the shape’s surface, as well as its deformation properties. For each
pose, the object was filled, and then scanned, with three different
internal materials. This caused incremental changes to the surface
and overall deformation exhibited, as illustrated in Fig. 1.
(a) Couscous (b) Risotto (c) Chickpea
Figure 1: Illustrations of the surfaces of meshes with different in-
ternal materials coloured by the surface normals.
The dataset consists of a stuffed soft toy rabbit made out of
a stretchy jersey material with no type of internal skeleton that
could otherwise restrict its movement, see Fig. 2. The rabbit had
590 coloured markers drawn on the surface, which allowed numer-
ous accurate ground-truth correspondences to be established, see
Fig. 3. Note that our purpose is to investigate how different types
of physically-based deformations affect non-rigid shape correspon-
dence, so a carefully chosen object with different material fillings
is sufficient and makes data capture and analysis more manageable.
(a) (b) (c) (d) (e)
Figure 3: Examples of texture transfer using the ground-truth cor-
respondences. (a) Target shape. (b-e) Source shapes. Correspon-
dences were transferred and interpolated using a landmark-based
correspondence method [EBC17]. The original texture was pro-
jected onto the coronal (frontal) plane of the rabbit in (a).
Figure 2: A photo of
the model used for the
dataset with markers.
The poses and materials used were
carefully selected to incrementally vary
the deformation challenge so that al-
gorithm deficiencies—with respect to
these varying properties—may be iden-
tified. Some examples of challenging
problems are shown in Fig. 4.
A key point about the proposed
dataset is that the exaggerated nature of
the deformations, such as twisting, of-
ten contradicts the underlying assump-
tions of state-of-the-art approaches.
Due to changes of the internal mate-
rial and surface creases, geometry is
often locally non-isometric, which is
problematic for many shape descrip-
tors. The model has intrinsic symme-
tries and, with the exception of the target scan, all scans are partial.
Information about the data underpinning the results presented
here, including how to access them, can be found in the Cardiff
University data catalogue (here).
3.1. Initial correspondences
Most correspondence methods require an initial set of sparse or
dense correspondences that are subsequently refined. Due to the
challenging variations in both the local and global appearance,
three sets of initial correspondences using different methods were
produced to find an optimal approach. The following methods
were used to acquire the initial sets of correspondences: diffusion
pruning [TMRL14], region-level correspondence [KO19], and non-
rigid iterative closest point (N-ICP) [BP13]. All methods took a
similar amount of time to compute. Where possible these initial
correspondences have been used for fairer comparisons.
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R. M. Dyke et al. / SHREC’20: Non-rigid Shape Correspondence of Physically-Based Deformations
(a) (b) (c)
Figure 4: Illustrations of some of the challenges in the dataset. (a) Partial scans (green indicates the boundary). (b) Complex deformations.
(c) Missing geometry caused by self-occlusion.
The diffusion pruning method of [TMRL14] was used to pro-
duce a set of globally consistent correspondences from an initial
set of point-wise descriptors. Due to the significant deformation, lo-
cal geometry is often non-isometric and thus local descriptors that
rely on near-isometries performed poorly. Signature of histograms
of orientations (SHOT) [TSDS10] signatures were computed with
10 bins at two scales, which covered 2% & 5% of the surface area
square rooted. Due to memory limitations and computation time,
diffusion pruning was performed with the default parameters, ex-
cept K=5 and d=25%.
The region-level correspondence method of [KO19] was used to
produce a set of correspondences between segmented shapes. The
method is capable of finding region-based matches using a shape
graph that describes the connectivity of consistently segmented
shapes. The method was run using nearly all default parameters,
with numComponentsRange ={10,9,8,7}. A dense point-to-
point mapping was subsequently recovered using nearest neigh-
bours of a functional map from a state-of-the-art approach [NO17].
The non-rigid registration method of [BP13] was used to register
the shapes together. Point-to-point correspondences were computed
using nearest neighbour between the vertices of the two surfaces.
The method’s parameters were set to w1 =1 (point-to-plane term),
w2 =1 (point-to-point term), w3 =1 (global rigidity term), w4 =
1000 (local rigidity term) and iter =100.
4. Correspondence methods
This section presents the methods that are examined in this work.
Eight methods were evaluated using the benchmark; namely: non-
rigid registration with re-weighted sparsities [LYLG19], non-rigid
partial functional maps [RCB∗17], anisotropic non-rigid registra-
tion [DLRT19], non-rigid partial functional maps [VLB∗17], pre-
cise recovery of non-isometric functional maps [EBC17], continu-
ous and orientation-preserving functional maps [RPWO18], data-
driven non-rigid registration FARM+, and a commercial non-rigid
registration tool R3DS Wrap 3.4.
4.1. Robust Non-Rigid Registration with Reweighted Position
and Transformation Sparsity
To cope with non-rigid deformation with large motion, [LYLG19]
proposes a robust non-rigid registration method using re-weighted
sparsities on position and transformation to estimate deformations
between 3D shapes. The energy function is formulated with posi-
tion and transformation sparsity on both the data and smoothness
terms, and a smoothness constraint is defined using local rigidity.
The double sparsity-based non-rigid registration model is enhanced
with a re-weighting scheme, and solved by transferring the model
into four alternately-optimised sub-problems which have exact so-
lutions and guaranteed convergence. Experimental results on both
public datasets and real scanned datasets show that the method out-
performs other state-of-the-art approaches [LYLG19,DSL∗19], and
is more robust to noise and outliers than conventional non-rigid reg-
istration methods.
The set of pruned and N-ICP correspondences were provided,
and was run using parameters optimised by the authors.
4.2. Partial Functional Correspondence
[RCB∗17] extends the functional mapping framework to address
the problem of partial input data. The authors discovered that it is
possible to estimate a partial correspondence with functional maps.
Computation of a partial functional map C
C
Cis formulated as an alter-
nating minimisation problem with two steps. In the first step, corre-
spondences are regularised based on assumptions about the overlap
of the source mesh. The slope, orthogonality, and rank of C
C
C⊤C
C
C
are incorporated to help regularise this step. In the second step,
the mapping is regularised by the part. Solutions with a dissimi-
lar area and long boundaries are penalised. This method assumes
the deformation to be near-isometric. While this is not necessarily
the case, being able to effectively handle partial data is critical for
this dataset, and is typically sufficient. SHOT was used to compute
dense point-wise descriptors.
For the experiments, shapes were re-scaled—as described in the
method’s code. All parameters remained default, with the exception
of n_eigen =100.
4.3. Non-rigid Registration under Anisotropic Deformations
[DLRT19] proposes a non-rigid registration pipeline that estimates
a correspondence between two surfaces in two steps. First, diffu-
sion pruning is used to compute an initial sparse set of globally
consistent correspondences. An implementation of N-ICP with an
as-rigid-as-possible regularisation term that is generalised to sup-
port r-ring neighbourhoods is then used to find a dense set of corre-
spondences. Finally, the dense correspondence is used to estimate
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R. M. Dyke et al. / SHREC’20: Non-rigid Shape Correspondence of Physically-Based Deformations
local anisotropy on the source surface. For subsequent iterations,
the original geodesics used for diffusion pruning are replaced with
anisotropic geodesics.
The described pipeline is fully automatic. However, for compar-
ative purposes, our pre-computed correspondences are used for ini-
tialisation. All other parameters remain as described in the original
paper.
4.4. Efficient Deformable Shape Correspondence via Kernel
Matching
[VLB∗17] proposes an algorithm to compute vertex-to-vertex
correspondence between non-isometric shapes. The work ex-
tends [VLR∗17], primarily incorporating the use of heat kernels
and a method to handle partial matching cases. A linear assign-
ment problem (LAP) is solved using a multi-scale approach for
cases where objects have a high number of vertices to relieve the
quadratic memory requirements of solving the LAP. In the original
paper SHOT and heat kernel signatures (HKS) [SOG09] were used
as point-wise descriptors.
Based on the discussions and experimental results in the
original paper, the parameters αand twere set to 10−7and
{500,323,209,135,88,57,37,24,15,10}respectively. Only SHOT
is used to compute point-wise descriptors, as HKS is sensitive to
changes in topology. Optimal results were achieved by scaling in-
put shapes with respect to the unit area of the source shape. Since
all shapes were captured using the same device, the original scale
was the same.
4.5. Deblurring and Denoising of Maps between Shapes
[EBC17] observes that functional maps typically lack speci-
ficity, moreover recovering vertex-to-vertex correspondences from
a functional map leads to undesirable noise. The authors propose
a method to refine a functional map, which is capable of recover-
ing vertex-to-point correspondences. This is desirable when trans-
porting high frequency information between surfaces—such as tex-
tures. The authors incorporate a correspondence regulariser that
favours smooth maps. The method removes noise by first blurring
the map, and then applying their proposed smoothness term. Point-
wise correspondences are subsequently recovered from the map-
ping, projected to a facet.
This method was run in three configurations, using each respec-
tive set of pre-computed initial correspondences. Due to memory
limitations caused by computing the wave kernel map, all configu-
rations used a subset of 200 correspondences—selected using far-
thest point sampling (FPS) based on geodesic distances. The fol-
lowing parameters were modified k1=120 & k2=120.
4.6. Continuous and Orientation-preserving Correspondences
via Functional Maps
[RPWO18] proposes a method that attempts to address the prob-
lem of symmetric ambiguity for functional mapping methods. The
method also attempts to ensure that the mapping remains bijective
and continuous when recovering point-wise correspondences from
a given functional map. The wave kernel signature (WKS) is used
as a point-wise descriptor. WKS was shown to be robust to some
topological changes in the seminal paper [ASC11], although the
descriptor is known to be strictly invariant only under isometric de-
formation. Due to the symmetrical appearance of the shape used
in this dataset, distinguishing such ambiguity is beneficial. How-
ever, the authors remark that the method is not designed to directly
handle partial cases.
The method was run both with and without our sets of initial
correspondences. Similarly to [EBC17], due to memory limitations
of computing the wave kernel map, 200 correspondences were se-
lected using geodesic-based FPS. Parameters were configured to
the default settings used in the paper, with num_iters =10.
The parameters for computing WKS were numTimes =100 and
skipSize =10.
4.7. FARM+: Functional Automatic Registration Method for
3D Human Bodies
FARM+ a variant of [MMRC20] is used. This method relies on the
registration of a morphable model exploiting the functional map
framework [OBCS∗12]. In the original paper, automatic landmarks
are detected on protrusions relying only on geometrical information
of the discrete-time evolution process (DEP) [MOR∗18] descriptor.
These landmarks are used to initialise a dense correspondence in
the functional domain, and also to retrieve finer local correspon-
dence over hands and heads. Then, a learned deformable template
of humans bodies is optimised to fit the target model. Finally, a
local refinement is applied to align the template to the target us-
ing an as-rigid-as-possible regularisation. The correspondence be-
tween the template and target is achieved using nearest-neighbour
between vertices. This method has been refined by [MMRC19],
removing some iterative steps and using ZoomOut [MRR∗19] re-
finement for functional maps. In this challenge, we start from
[MMRC19]. Since the provided template is not capable of defor-
mation, it is animated using Mixamo [Ado20] and some deforma-
tion basis is defined to inflate or shrink the template along the di-
rection of the surface normals. To compute landmarks, the mini-
mum and maximum of the first Laplacian eigenfunctions are used,
and six landmarks are classified over extremal points of the rabbit’s
ears, arms, and legs. Another main change of the original methods
of [MMRC19] and [MMRC20] is that no local correspondence is
used. All parameters were left unchanged from the original method,
which were tuned for the specific domain of human bodies.
4.8. R3DS Wrap 3.4
[Rus19] develops a commercial software product with functional-
ity to non-rigidly register surfaces called Wrap 3. The method uses
landmark points to compute an optimal alignment between two
non-rigid surfaces. The method uses a multiple-step sub-division
surface approach with N-ICP in a coarse-to-fine manner to establish
an approximate non-rigid alignment, which is subsequently refined
in further steps.
Wrap 3 was used to register the scans both with and without our
initial pruned correspondences. Better results were achieved by set-
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R. M. Dyke et al. / SHREC’20: Non-rigid Shape Correspondence of Physically-Based Deformations
ting the final weight of control points (the initial correspondences)
to zero, all other settings remained as per default.
5. Evaluation
The quality of correspondences is measured following the protocol
described by [KLF11] using the sparse texture markers as ground-
truths. For convenience, we describe the protocol for computing
the geodesic error of correspondences here. For an estimated cor-
respondence (x,y)∈X×Yand the respective ground-truth corre-
spondence (x,y∗)∈X×Y. The geodesic distance between the cor-
responding points on Yis dY(y,y∗)
ε(x) = dY(y,y∗)
area(Y)1/2.(1)
6. Results
In this section we discuss the performance achieved by correspon-
dence methods on our dataset. We examine how different initialisa-
tion techniques impact the performance of a selection of methods.
Then the affects of variations in pose and internal material are scru-
tinised. It should be noted that the density of the correspondences
acquired is not wholly reported because all methods report a dense
mapping of ≈100% in most cases.
6.1. Initial correspondences
In Fig. 5the performance of the initial correspondence methods de-
scribed in Section 3.1 is reported. The methods are abbreviated as
follows: N-ICP [BP13] refers to [BP13], Pruning [TMRL14] refers
to the diffusion pruning method of [TMRL14], and SEG [KO19]
refers to the region-level correspondence method of [KO19]. N-
ICP [BP13] performed the best. This may be due to the shapes hav-
ing a reasonable initial rigid alignment, which is necessary when
using N-ICP. All deformations are largely locally non-isometric,
this causes point-wise descriptors that methods use on unreliable.
0 0.2 0.40.60.8 1
0
20
40
60
80
100
Geodesic error
% Correspondences
N-ICP [BP13]
Pruning [TMRL14]
SEG [KO19]
Figure 5: Error curves for the methods used to establish an ini-
tial correspondence. Note, Pruning [TMRL14] only estimated ≈
7.4250% of correspondences.
These initial correspondences were subsequently used to ini-
tialise the relevant shape correspondence and registration meth-
ods. In Fig. 6, a comparison of the performance of a selection of
methods using different initial correspondences is reported. The re-
sults show that using the initial correspondences of N-ICP [BP13]
greatly reduces the resulting error of the subsequent methods.
R3DS Wrap 3 + N-ICP [EBC17] + N-ICP
R3DS Wrap 3 + Pruning [EBC17] + Pruning
R3DS Wrap 3 + SEG [EBC17] + SEG
R3DS Wrap 3 (none) [RPWO18] + N-ICP
[DLRT19] + N-ICP [RPWO18] + Pruning
[DLRT19] + Pruning [RPWO18] + SEG
[DLRT19] + SEG [RPWO18] (none)
0 0.2 0.40.60.8 1
0
20
40
60
80
100
Geodesic error
% Correspondences
(a) R3DS Wrap 3
0 0.2 0.40.60.8 1
0
20
40
60
80
100
Geodesic error
(b) [EBC17]
0 0.2 0.40.60.8 1
0
20
40
60
80
100
Geodesic error
% Correspondences
(c) [DLRT19]
0 0.2 0.40.60.8 1
0
20
40
60
80
100
Geodesic error
(d) [RPWO18]
Figure 6: Comparison of the error of methods initialised with
different initial correspondence techniques (N-ICP [BP13], Prun-
ing [TMRL14], SEG [KO19], or none).
Table 1summarises the same performance measurements nu-
merically by reporting the area under the curve AUC of each
method for each set of initial correspondences. All methods per-
form best using N-ICP [BP13] for initialisation, with the excep-
tion of R3DS Wrap 3, which achieved its best results using none.
This slight improvement may be a consequence of the coarse-to-
fine strategy being able to converge to a more optimal solution.
[RPWO18] achieve better results using no correspondence initiali-
sation compared to Pruning [TCL∗13] or SEG [KO19], or just us-
ing WKS [ASC11] descriptors. In all cases, using SEG [KO19]
produced better results than using Pruning [TMRL14].
6.2. Track results
Hereafter, methods initialised with N-ICP [BP13] correspondences
are qualified by an asterisk (∗). Comprehensive results—measured
by AUC—of running each method on each scan—grouped by pose
or by internal material—are reported in Table 2. Error curves that
complement Table 2are given in Figs. 7&8. Scans that are
members of a given column were examined collectively. FARM+
achieved the highest overall accuracy of any method using a semi-
automatic approach. Of the fully-automatic methods, [RPWO18]
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R. M. Dyke et al. / SHREC’20: Non-rigid Shape Correspondence of Physically-Based Deformations
Table 1: (left) The AUCs are calculated from the cumulative error curves of the initial correspondence methods reported in Fig. 5. (right) The
resulting AUCs of methods using each set of initial correspondences—reported in Fig. 6. Note, [TMRL14] reports an average of 7.4250%
vertex correspondences.
Initial correspondences
Initialisation method AUC Method N-ICP
[BP13]
Pruning
[TMRL14]SEG
[KO19] None
N-ICP [BP13] 0.8736 R3DS Wrap 3 0.8763 0.5869 0.6050 0.8837
Pruning [TMRL14] 0.6151 [EBC17] 0.8829 0.5430 0.5891 N/A
SEG [KO19] 0.5323 [DLRT19] 0.8771 0.5812 0.6290 N/A
[RPWO18] 0.9015 0.5480 0.6347 0.7609
performed the best. The pose that all methods performed the
best on, on average, was the indented pose. The sporadic non-
isometry, limited deformation, and slight topological change may
have helped. Conversely, twist was the most challenging pose. The
most challenging internal material was the risotto. This is likely to
be due to the subtle variations induced on local geometry and how
the risotto grains affected the way the rabbit bent in the distinct
poses. However, excluding the results of [RCB∗17] and [VLB∗17],
all methods achieve a particularly high accuracy on the stretch pose.
Although there is a large amount of non-rigid motion, the topology
remains consistent, and the non-isometric deformation is relatively
simple.
R3DS Wrap 3 [EBC17]∗[RCB∗17]
[RPWO18]∗[LYLG19]∗[VLB∗17]
[DLRT19]∗FARM+
0 0.2 0.40.60.8 1
0
20
40
60
80
100
Geodesic error
% Correspondences
(a) Twist
0 0.2 0.40.60.8 1
0
20
40
60
80
100
Geodesic error
(b) Indent
0 0.2 0.40.60.8 1
0
20
40
60
80
100
Geodesic error
% Correspondences
(c) Inflate
0 0.2 0.40.60.8 1
0
20
40
60
80
100
Geodesic error
(d) Stretch
Figure 7: Cumulative error curves with scans grouped by the pose
exhibited.
R3DS Wrap 3 performed unexpectedly poorly on the indent
pose, with the worst performance of any method on scan no. 5.
[RCB∗17] performed poorly in most scenarios, especially in cases
R3DS Wrap 3 [EBC17]∗[RCB∗17]
[RPWO18]∗[LYLG19]∗[VLB∗17]
[DLRT19]∗FARM+
0 0.2 0.40.60.8 1
0
20
40
60
80
100
Geodesic error
% Correspondences
(a) Couscous
0 0.2 0.40.60.8 1
0
20
40
60
80
100
Geodesic error
(b) Risotto
0 0.2 0.40.60.8 1
0
20
40
60
80
100
Geodesic error
% Correspondences
(c) Chickpea
Figure 8: Cumulative error curves with scans grouped by the in-
ternal material selected.
where a pose exhibited greater non-isometry. For all poses, ex-
cept inflate, FARM+ converges to 100% correspondence within the
smallest geodesic error. [RPWO18] performs the worst on the twist
pose, this is understandable as the fused geometry caused by twist-
ing contradicts the assumption of continuity.
As shown in Fig. 9, overall, FARM+ performed the best of
all methods. [RPWO18] performed the best of all the fully-
automatic approaches. The performance of [DLRT19] is compa-
rable to [LYLG19], with only a slight improvement over the initial
N-ICP [BP13] correspondences.
7. Conclusions
We consider the problem of establishing correspondence between
shapes with different internal materials in challenging poses. A new
dataset was created with high quality texture-based ground-truths.
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Table 2: The total area under the curve of scans grouped by the type of pose exhibited, scans grouped by material, and the overall perfor-
mance of each method over all scans is reported. The method that achieved the best results in each configuration is emphasised in bold, and
the second best in bold italics. In the final two rows the mean and standard deviation of each column is reported.
Pose Internal material
Method Twist Indent Inflate Stretch Couscous Risotto Chickpea Overall
R3DS Wrap 3 0.9025 0.8129 0.9005 0.9418 0.9265 0.8071 0.9277 0.8837
[EBC17]∗0.8730 0.8830 0.8689 0.9195 0.8944 0.8591 0.8979 0.8829
[RCB∗17] 0.5249 0.6247 0.6136 0.5778 0.5840 0.5570 0.6170 0.5863
[RPWO18]∗0.8708 0.9004 0.9070 0.9420 0.8956 0.8950 0.9122 0.9015
[BP13] 0.8620 0.8713 0.8646 0.9087 0.8842 0.8579 0.8813 0.8736
[LYLG19]∗0.8598 0.8719 0.8651 0.9088 0.8822 0.8581 0.8816 0.8733
[VLB∗17] 0.6369 0.7610 0.6827 0.5521 0.7660 0.5966 0.6695 0.6692
[DLRT19]∗0.8616 0.8796 0.8712 0.9058 0.8886 0.8604 0.8850 0.8771
FARM+ 0.8999 0.9338 0.8780 0.9438 0.9281 0.9111 0.8992 0.9113
Mean 0.7636 0.8023 0.7967 0.7932 0.8126 0.7623 0.8008
Std. 0.1698 0.1318 0.1307 0.2040 0.1484 0.1581 0.1551
0 0.2 0.40.60.8 1
0
20
40
60
80
100
Geodesic error
% Correspondences
R3DS Wrap 3
[EBC17]∗
[RCB∗17]
[RPWO18]∗
[LYLG19]∗
[VLB∗17]
[DLRT19]∗
FARM+
Figure 9: Overall performance of methods.
The resulting accuracy achieved by using different correspondence
initialisation techniques was investigated. We discover that in this
scenario, N-ICP [BP13] performed the best for correspondence ini-
tialisation. Of all the methods, FARM+ achieved the greatest accu-
racy using a semi-automatic approach, while [RPWO18] performed
the best of the fully-automatic approaches.
Further work would include an extended investigation into the
performance of different shape descriptors and initial correspon-
dence techniques on this dataset.
For many of the methods evaluated, it is unclear how to best op-
timise the parameters. It was possible to incrementally change the
parameters to achieve better results, however this is a time consum-
ing strategy and not necessarily possible in cases where ground-
truths are not available. Further investigation into optimal parame-
ters on a range of benchmark datasets is required to give a greater
overview of what parameters should be selected in a given scenario.
Acknowledgements
We thank the authors of methods that did not participate but made
their code available online [VLB∗17,EBC17,RCB∗17,RPWO18,
Rus19]. We also thank Seana Dykes for helping to fabricate the
toy rabbit. This work has been supported by the Cardiff University
EPSRC Doctoral Training Partnership [grant ref. EP/N509449/1].
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