Unlike image or text domains that benefit from an abundance of large-scale datasets, point cloud learning techniques frequently encounter limitations due to the scarcity of extensive datasets. To overcome this limitation, we present Symmetria, a formula-driven dataset that can be generated at any arbitrary scale. By construction, it ensures the absolute availability of precise ground truth, promotes data-efficient experimentation by requiring fewer samples, enables broad generalization across diverse geometric settings, and offers easy extensibility to new tasks and modalities. Using the concept of symmetry, we create shapes with known structure and high variability, enabling neural networks to learn point cloud features effectively. Our results demonstrate that this dataset is highly effective for point cloud self-supervised pre-training, yielding models with strong performance in downstream tasks such as classification and segmentation, which also show good few-shot learning capabilities. Additionally, our dataset can support fine-tuning models to classify real-world objects, highlighting our approach’s practical utility and application. We also introduce a challenging task for symmetry detection and provide a benchmark for baseline comparisons. A significant advantage of our approach is the public availability of the dataset, the accompanying code, and the ability to generate very large collections, promoting further research and innovation in point cloud learning.

Partial retrieval is a long-standing problem in the 3D Object Retrieval community. Its main difficulties arise from how to define 3D local descriptors in a way that makes them effective for partial retrieval and robust to common real-world issues, such as occlusion, noise, or clutter, when dealing with 3D data. This SHREC track is based on the newly proposed ShapeBench benchmark to evaluate the matching performance of local descriptors. We propose an experiment consisting of three increasing levels of difficulty, where we combine different filters to simulate real-world issues related to the partial retrieval task. Our main findings show that classic 3D local descriptors like Spin Image are robust to several of the tested filters (and their combinations), but more recent learned local descriptors like GeDI can be competitive for some specific filters. Finally, no 3D local descriptor was able to successfully handle the hardest level of difficulty. • We evaluate the robustness of local 3D descriptors for partial shape retrieval using a novel benchmark—ShapeBench—under progressively challenging conditions simulating real-world degradations (e.g., clutter, occlusion, noise, remeshing). • Our analysis shows that classic hand-crafted descriptors like Spin Image consistently outperform more recent learned descriptors under high levels of occlusion and noise. • No existing local 3D descriptor was found to be reliably effective under the most challenging scenarios combining multiple perturbations, highlighting an open problem in robust partial 3D retrieval.

This SHREC 2025 track dedicated to protein surface shape retrieval involved 9 participating teams. We evaluated the performance in retrieval of 15 proposed methods on a large dataset of 11,555 protein surfaces with calculated electrostatic potential (a key molecular surface descriptor). The performance in retrieval of the proposed methods was evaluated through different metrics (Accuracy, Balanced accuracy, F1 score, Precision and Recall). The best retrieval performance was achieved by the proposed methods that used the electrostatic potential complementary to molecular surface shape. This observation was also valid for classes with limited data which highlights the importance of taking into account additional molecular surface descriptors.

Given a 3D point cloud, we propose a method for suitably resampling the cloud while reconstructing and preserving the feature curves to which some points are identified to belong. The first phase of our strategy enriches the cloud by approximating the curvilinear profiles outlined by the feature points with piece-wise polynomial parametric space curves through the use of the Hough transform. The second phase describes how the removal of a point or its insertion can be performed without affecting the approximated profiles and preserving the enriched structure of the cloud. The combination of the two steps provides multiple possibilities for processing a point cloud by varying its size or improving its density homogeneity without affecting the retrieved feature curves. The various capabilities of our approach are investigated to produce simplification, refinement, and resampling techniques whose effectiveness is evaluated through experiments and comparisons.

Feature curves are space curves identified by color or curvature variations in a shape, which are crucial for human perception (Biederman, 1995). Detecting these characteristic lines in 3D digital models becomes important for recognition and representation processes. For recognizing plane curves in images, the Hough transform (HT) provided a very good solution to the problem. It selects the best-fitting curve in a dictionary of families of curves through a voting procedure that makes it robust to noise and missing parts. Since 3D digital models are often obtained by scanning real objects and may have many defects, the HT has been extended to recognize and approximate space curves in 3D models that correspond to relevant features This work overviews three HT-based different approaches for identifying and approximating spatial profiles of points extracted from point clouds or meshes. A first attempt at this extension involved projecting the spatial points onto the regression plane, thus reducing the problem to planar recognition and using families of plane curves. A second approach has been proposed to recognize spatial profiles that cannot be projected onto the regression plane, using two types of space curve families. Unfortunately, the main drawback of methods based on traditional HT is that it requires prior knowledge of which family of curves to look for. To overcome this limitation, a third method has been developed that provides a piecewise space curve approximation using specific parametric polynomial curves. Additionally, free-form curves that a parametric or implicit form cannot express can be represented using this technique. In the paper, we also analyze the pros and cons of the various approaches and how they managed and reduced the HT's computational cost, given the large number of parameters introduced when families of space curves are considered.

Urban simulations that involve disaster prevention, urban design, and assisted navigation heavily rely on urban geometric models. While large urban areas need a lot of time to be acquired terrestrially, government organizations have already conducted massive aerial LiDAR surveys, some even at the national level. This work aims to provide a pipeline for extracting multi-scale point clouds from 2D building footprints and airborne LiDAR data, which depends on whether the points represent buildings, vegetation, or ground. We denoise the roof slopes, match the vegetation, and roughly recreate the building façades frequently hidden to aerial acquisition using a parametric representation of geometric primitives. We then carry out multiple-scale samplings of the urban geometry until a 3D urban representation can be achieved because we annotate the new version of the original point cloud with the parametric equations representing each part. We mainly tested our methodology in a real-world setting – the city of Genoa – which includes historical buildings and is heavily characterized by irregular ground slopes. Moreover, we present the results of urban reconstruction on part of two other cities, Matera, which has a complex morphology like Genoa, and Rotterdam.

Abstract We propose CurveML, a benchmark for evaluating and comparing methods for the classification and identification of plane curves represented as point sets. The dataset is composed of 520k curves, of which 280k are generated from specific families characterised by distinctive shapes, and 240k are obtained from Bézier or composite Bézier curves. The dataset was generated starting from the parametric equations of the selected curves making it easily extensible. It is split into training, validation, and test sets to make it usable by learning-based methods, and it contains curves perturbed with different kinds of point set artefacts. To evaluate the detection of curves in point sets, our benchmark includes various metrics with particular care on what concerns the classification and approximation accuracy. Finally, we provide a comprehensive set of accompanying demonstrations, showcasing curve classification, and parameter regression tasks using both ResNet-based and PointNet-based networks. These demonstrations encompass 14 experiments, with each network type comprising 7 runs: 1 for classification and 6 for regression of the 6 defining parameters of plane curves. The corresponding Jupyter notebooks with training procedures, evaluations, and pre-trained models are also included for a thorough understanding of the methodologies employed.

The problem faced in this paper concerns the recognition of simple and complex geometric primitives in point clouds resulting from scans of mechanical CAD objects. A large number of points, the presence of noise, outliers, missing or redundant parts and uneven distribution are the main problems to be addressed to meet this need. In this article we propose a solution, based on the Hough transform, that can recognize simple and complex geometric primitives and is robust to noise, outliers, and missing parts. Additionally, we can extract a series of geometric descriptors that uniquely characterize a primitive and, based on them, aggregate the output into maximal or compound primitives, thus reducing oversegmentation. The results presented in the paper demonstrate the robustness of the method and its competitiveness with respect to other solutions proposed in the literature.

Voltage-gated sodium (Nav) channels constitute a prime target for drug design and discovery, given their implication in various diseases such as epilepsy, migraine and ataxia to name a few. In this regard, performing morphological analysis is a crucial step in comprehensively understanding their biological function and mechanism, as well as in uncovering subtle details of their mechanism that may be elusive to experimental observations. Despite their tremendous therapeutic potential, drug design resources are deficient, particularly in terms of accurate and comprehensive geometric information. This paper presents a geometric dataset of molecular surfaces that are representative of Nav channels in mammals. For each structure we provide three representations and a number of geometric measures, including length, volume and straightness of the recognized channels. To demonstrate the effective use of GEO-Nav, we have tested it on two methods belonging to two different categories of approaches: a sphere-based and a tessellation-based method.

Abstract We analyze the joint efforts made by the geometry processing and the numerical analysis communities in the last decades to define and measure the concept of “mesh quality”. Researchers have been striving to determine how, and how much, the accuracy of a numerical simulation or a scientific computation (e.g., rendering, printing, modeling operations) depends on the particular mesh adopted to model the problem, and which geometrical features of the mesh most influence the result. The goal was to produce a mesh with good geometrical properties and the lowest possible number of elements, able to produce results in a target range of accuracy. We overview the most common quality indicators, measures, or metrics that are currently used to evaluate the goodness of a discretization and drive mesh generation or mesh coarsening/refinement processes. We analyze a number of local and global indicators, defined over two‐ and three‐dimensional meshes with any type of elements, distinguishing between simplicial, quadrangular/hexahedral, and generic polytopal elements. We also discuss mesh optimization algorithms based on the above indicators and report common libraries for mesh analysis and quality‐driven mesh optimization.

In this paper we investigate a local surface approximation, the Weighted Quasi Interpolant Spline Approximation (wQISA), specifically designed for large and noisy point clouds. We briefly describe the properties of the wQISA representation and introduce a novel data-driven implementation, which combines prediction capability and complexity efficiency. We provide an extended comparative analysis with other continuous approximations on real data, including different types of surfaces and levels of noise, such as 3D models, terrain data and digital environmental data.

Abstract The recent introduction of 3D shape analysis frameworks able to quantify the deformation of a shape into another in terms of the variation of real functions yields a new interpretation of the 3D shape similarity assessment and opens new perspectives. Indeed, while the classical approaches to similarity mainly quantify it as a numerical score, map‐based methods also define (dense) shape correspondences. After presenting in detail the theoretical foundations underlying these approaches, we classify them by looking at their most salient features, including the kind of structure and invariance properties they capture, as well as the distances and the output modalities according to which the similarity between shapes is assessed and returned. We also review the usage of these methods in a number of 3D shape application domains, ranging from matching and retrieval to annotation and segmentation. Finally, the most promising directions for future research developments are discussed.

Abstract In this paper we target the problem of textured 3D object retrieval. As a first contribution, we show how to include photometric information in the persistence homology setting, also proposing a novel theoretical result about multidimensional persistence spaces. As a second contribution, we introduce a generalization of the integral geodesic distance which fuses shape and color properties. Finally, we adopt a purely geometric description based on the selection of geometric functions that are mutually independent. The photometric, hybrid and geometric descriptions are combined into a signature, whose performance is tested on a benchmark dataset.

In this work we evaluate purely structural graph measures for 3D objects classification. We extract spectral features from different Reeb graph representations. Information-theoretic feature selection gives an insight on which are the most relevant features.

We present the results of a project aimed to evaluate 2D and 3D face recognition algorithms. In particular, we focused on the potentialities of 3D-based techniques to overcome typical limitations of 2D methods in non-controlled situations. According to the reference scenario of people identification at airport check points, we built a representative database on which we tested different face recognition algorithms. We implemented and tested an improved version of a well-known state-of-the-art 3D approach, and verified that on our dataset it performs better than a widely used commercial system.

In this report we present the results of the Stability on Watertight Models Track. The aim of this track is to evaluate the stability of algorithms with respect to input perturbations that modify the representation of the object without changing its overall shape significantly. Examples of these perturbations include geometric noise, varying sampling patterns, small shape deformations and topological noise.

Reeb graphs can be used in many applications to construct simple graph-like sketches of shapes, which retain the topology/connectivity of the original shape. In this paper, our Reeb graph representation is extended to generic surfaces with boundary.

The paper investigates the main issues related to the definition of abstraction tools for deriving high-level descriptions of complex geometric models. Among the wide range of shape descriptors, topological graph-like representations not only give a powerful and synthetic sketch of the object, but also capture its inner structure, that is how features connect together to give the overall shape. This aspect makes them useful to describe complex 3D objects in various applications like modeling, morphing, matching and recognition. The paper surveys the main properties of skeletons developed in shape modeling for representing objects.

A method for the extraction of the extended Reeb graph (ERG) from a closed 3D triangular mesh is presented. The ERG encodes the relationships among critical points of the height function associated to the mesh, and it can represent isolated as well as degenerate critical points. The extraction process is based on a re-meshing strategy of the original mesh, which is forced to follow contour levels. The occurrence and configuration of flat areas in the re-triangulated model identify critical areas of the shape, and their relationships allow the reconstruction of the global topological structure of the shape.