
\section{Datasets}
\label{sec:datasets}



\begin{figure*}
 \includegraphics[width=\linewidth]{figures/nafie/teaser_datasets_compressed.jpg}
 \centering
  \caption{\textbf{The BeCoS dataset}~\cite{ehm2025beyond} connects seven existing 3D shape matching datasets~\cite{bogo_faust_2014,zuffi2017small,anguelov_scape_2005,bronstein2008numerical,li20214dcomplete,rodola2014dense,dyke2020shrec}, enabling the propagation of dense correspondences across a wide range of categories, including humanoids, cats, elephants, and others. Furthermore, it provides annotations for partial correspondences, supporting both partial-to-full (\textbf{P2F}) and partial-to-partial (\textbf{P2P}) matching settings. Image source: \cite{ehm2025beyond}.
  }
  \label{fig:becos_teaser}
\end{figure*}


\input{tables/tab_datasets}


While large-scale 3D shape datasets such as ShapeNet~\cite{chang_shapenet_2015} and Objaverse~\cite{objaverse} have enabled progress in general shape understanding, they typically lack the dense ground-truth correspondences required for evaluating deformable shape matching.
In line with prior work in this domain, we instead focus on datasets that contain deformable objects annotated with consistent correspondences across shape instances. 

\paragraph{Near-isometric.}
Early 3D shape matching datasets such as the CAESER dataset \cite{robinette1999caeser} provided thousands of human body scans annotated with hand-placed landmarks, offering an important benchmark but with limited ground-truth correspondences. To address this limitation, the SCAPE dataset \cite{anguelov_scape_2005} introduced 71 registered meshes of a single subject in a single pose, providing dense correspondences but restricting variability since all shapes originate from one individual. The TOSCA dataset \cite{bronstein2008numerical} expanded diversity by including multiple object categories (e.g., humans, cats and dogs), yet its synthetic nature with fixed topology introduced a domain gap between real-world scans and artist-crafted meshes. Subsequent datasets such as FAUST~\cite{bogo_faust_2014} improved diversity with 10 individuals captured in multiple poses, using registrations to a common template to establish dense correspondences, while DFAUST extended FAUST to dynamic sequences, yielding over 40,000 aligned meshes, though its focus on adults limited generalisation to children. To address this gap, the KIDS dataset \cite{rodola2014dense} introduced eight high-resolution synthetic models (80K vertices) of a child in near-isometric poses.

Other datasets emerged from parametric models such as SMPL~\cite{loper2015smpl}, its variants~\cite{romero2017mano,pavlakos2019smplx}, and the COMA model~\cite{ranjan2018coma}, enabling the creation of very large collections such as SURREAL \cite{varol_learning_2017}, which contains 230,000 meshes. However, these datasets suffer from biases introduced by repeated use of identical triangulations across thousands of meshes. More recent efforts, such as DT4D~\cite{li20214dcomplete}, extend diversity by providing animatable shapes from multiple categories, such as different animal species, with consistent triangulations across meshes of the same class. Despite these advances, nearly all of these datasets remain constrained to the near-isometric case and, therefore, fail to fully capture the complexities of real-world shape variability. This highlights the need for datasets that provide reliable correspondences under non-isometric deformations.



\paragraph{Beyond isometry.}
A more general and challenging setting for 3D shape matching arises in the non-isometric regime, where datasets need to provide correspondences across fundamentally different object categories, such as establishing mappings between a cat and a horse. Constructing such datasets is particularly difficult because non-isometric correspondences are inherently ill-defined. While one may attempt to align overall body structures, it is unclear how to meaningfully associate, for example, the trunk of an elephant with the body of a cat. Early efforts in this direction include the SMAL dataset \cite{zuffi2017small}, which introduced a parametric model for multiple animal categories trained on 41 scans. While this dataset offers cross-category representations, it relies on fitting a single parametric model across all meshes, which limits its expressiveness and its ability to capture the fine geometric details unique to each class of shapes. Another step forward is SHREC’20 \cite{dyke2020shrec}, which explicitly defines correspondences across different animal categories, such as elephants and cats. However, it only provides sparse correspondences, thereby limiting its utility for dense shape analysis. 
More recently, Magnet et al.~\cite{magnet2022smooth} addressed this gap by manually establishing dense correspondences across most categories in the DT4D dataset~\cite{li20214dcomplete}, thereby creating the first dataset to offer dense non-isometric mappings.
Building on this idea, BeCoS~\cite{ehm2025beyond} further expanded the scope by leveraging seven existing isometric datasets. Instead of introducing new shapes, BeCoS builds upon seven existing isometric datasets and manually generates dense correspondences between a set of selected template meshes, effectively enabling cross-category mappings. This extension expands deformable shape analysis to the non-isometric setting, resulting in a large, interconnected collection of shapes, as illustrated in Fig.~\ref{fig:becos_teaser}.




\paragraph{Challenging connectivity and topological noise.}
Another line of research in 3D shape matching has focused on datasets designed to introduce specific challenges, particularly related to mesh connectivity and topological noise. Variations in mesh connectivity can arise from anisotropy, where parts of the same surface are represented with coarse triangulation, while others use much finer discretisation, making correspondence estimation substantially more difficult. To evaluate generalisation to such scenarios, SHREC’19~\cite{melzi2019shrec} introduced human scans with altered mesh connectivity. Similarly, Donati et al.~\cite{donati_deep_2022} created a challenging setting by remeshing both the SCAPE~\cite{anguelov_scape_2005} and FAUST~\cite{bogo_faust_2014} datasets anisotropically. 

A related challenge is topological noise, which includes the presence of holes, self-intersections, or other surface artefacts. SHREC’10~\cite{bronstein2010shrec} addressed this by extending TOSCA with artificially injected topological noise, though it inherited TOSCA’s broader limitations. Building on this idea, TOPKIDS~\cite{laehner2016topkids} extended the KIDS dataset \cite{rodola2014dense} by synthetically introducing topological perturbations, while TACO~\cite{pedico_taco_2024} extended TOSCA using a non-connectivity-preserving remeshing strategy. In TOCA~\cite{pedico_taco_2024}, mesh connectivities were intentionally altered, even among shapes of the same class. Leveraging the 3D alignment between original and remeshed shapes as well as TOSCA’s ground-truth correspondences, the authors generated new ground-truth correspondences across the perturbed surfaces. 
Using a different approach, SCAPET~\cite{yusuf2023scapet} and ExtFAUST~\cite{basset2021extFaust,Merrouche_2023_BMVC} build upon existing datasets, SCAPE~\cite{anguelov_scape_2005} and FAUST~\cite{bogo_faust_2014}, respectively. These methods modify the topology of the shapes by either adding shortcut tunnels or by merging nearby surface regions, effectively connecting previously separate parts of the mesh.
Together, these datasets emphasise the importance of evaluating shape matching methods under realistic noise and connectivity variations, moving beyond the simplified settings of earlier benchmarks.









\paragraph{Partial 3D shapes datasets.}
Beyond the full-to-full (F2F) setting discussed so far, the availability of datasets for the other two key settings, partial-to-full (P2F) and partial-to-partial (P2P), as described in Sec.~\ref{sub:partial-to-full}, is equally important.
The first benchmark in this direction was SHREC’16~\cite{cosmo2016shrec}, which extended the TOSCA dataset \cite{bronstein2008numerical} to include partial shapes. This was later followed by PFAUST~\cite{bracha_partial_2023} and PFARM~\cite{attaiki2021dpfm}, based respectively on the FAUST~\cite{bogo_faust_2014} and FARM~\cite{kirgo2021wavelet} datasets, while SHREC’20~\cite{dyke2020shrec} also included a subset of partial-to-full correspondence pairs. 

In contrast, P2P shape matching is considerably more challenging, as it requires establishing correspondences between two partial shapes with unknown overlap. The first benchmark for this setting, CP2P~\cite{attaiki2021dpfm}, was introduced by extending the SHREC’16 CUTS dataset \cite{cosmo2016shrec}. More recently, PSMAL~\cite{ehm_partial--partial_2024} extended the SMAL dataset~\cite{zuffi2017small} to incorporate partial-to-partial correspondences across animal categories. However, in both P2F and P2P settings, partiality has traditionally been simulated by artificially removing mesh parts or introducing holes, which does not accurately reflect the challenges of real-world partial observations. To address this limitation, BeCoS~\cite{ehm2025beyond} introduces a more realistic framework for generating partial shapes through ray-casting, enabling the creation of P2F, P2P, and F2F correspondence pairs within a unified framework.









\paragraph{Performance of 3D shape matching methods.}
Over the past few years, performance on well-established benchmarks has largely saturated, as indicated by the marginal improvements achieved by recent methods (e.g.~the mean geodesic error (×100) on FAUST~\cite{bogo_faust_2014} has remained at approximately 1.6~\cite{cao2024synchronous, bastian2024hybrid}). This stagnation highlights the need for more challenging benchmarks, preferably based on real-world shapes obtained from 3D scans, in order to further drive methodological progress. In addition, the reliability of ground-truth annotations in several commonly used datasets, including DT4D~\cite{li20214dcomplete}, BeCoS~\cite{ehm2025beyond}, and SHREC’19~\cite{melzi_shrec19_2019}, may contain errors, suggesting that improvements in numerical accuracy do not necessarily reflect genuine advances in correspondence quality~\cite{li_learning_2022}. These challenges are even more pronounced in the partial shape setting, where benchmarks and dedicated methods remain scarce, despite this scenario being the most representative of real-world data. 
At the time of writing, state-of-the-art results in full-to-full, partial-to-full and partial-to-partial matching scenarios, were obtained by~\cite{bastian2024hybrid}, ~\cite{cao2024synchronous} and~\cite{xie_echomatch_2025}, respectively.




