We propose two algorithms for 3D symmetry detection based on enhanced back-projection of vision features extracted from foundation vision models such as DINOv2. Our method enhances back-projection by rendering multiple views of 3D objects, extracting features, and projecting them onto the geometry with two key improvements—Fibonacci view sampling and view rotations—that increase robustness and accuracy. Using these features, we detect symmetry planes and axes through two dedicated algorithms. Experiments on ShapeNet show that our plane detection approach outperforms both traditional geometric and learning-based methods by a wide margin. The method is also efficient, running in seconds on a single 8GB GPU, making it practical for large-scale or real-world applications. Overall, our results demonstrate that enhanced back-projection of vision features offers a simple yet effective framework for solving fundamental 3D geometric problems such as symmetry detection. Code is available at https://github.com/Spulp/EnhancedBackProjection.

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.

Abstract In digital archaeology, a large research area is concerned with the computer‐aided analysis of 3D captured ancient pottery objects. A key aspect thereby is the analysis of motifs and patterns that were painted on these objects' surfaces. In particular, the automatic identification and segmentation of repetitive patterns is an important task serving different applications such as documentation, analysis and retrieval. Such patterns typically contain distinctive geometric features and often appear in repetitive ornaments or friezes, thus exhibiting a significant amount of symmetry and structure. At the same time, they can occur at varying sizes, orientations and irregular placements, posing a particular challenge for the detection of similarities. A key prerequisite to develop and evaluate new detection approaches for such repetitive patterns is the availability of an expressive dataset of 3D models, defining ground truth sets of similar patterns occurring on their surfaces. Unfortunately, such a dataset has not been available so far for this particular problem. We present an annotated dataset of 82 different 3D models of painted ancient Peruvian vessels, exhibiting different levels of repetitiveness in their surface patterns. To serve the evaluation of detection techniques of similar patterns, our dataset was labeled by archaeologists who identified clearly definable pattern classes. Those given, we manually annotated their respective occurrences on the mesh surfaces. Along with the data, we introduce an evaluation benchmark that can rank different recognition techniques for repetitive patterns based on the mean average precision of correctly segmented 3D mesh faces. An evaluation of different incremental sampling‐based detection approaches, as well as a domain specific technique, demonstrates the applicability of our benchmark. With this benchmark we especially want to address the geometry processing community, and expect it will induce novel approaches for pattern analysis based on geometric reasoning like 2D shape and symmetry analysis. This can enable novel research approaches in the Digital Humanities and related fields, based on digitized 3D Cultural Heritage artifacts. Alongside the source code for our evaluation scripts we provide our annotation tools for the public to extend the benchmark and further increase its variety.

We introduce a data-driven approach to aid the repairing and conservation of archaeological objects: ORGAN, an object reconstruction generative adversarial network (GAN). By using an encoder-decoder 3D deep neural network on a GAN architecture, and combining two loss objectives: a completion loss and an Improved Wasserstein GAN loss, we can train a network to effectively predict the missing geometry of damaged objects. As archaeological objects can greatly differ between them, the network is conditioned on a variable, which can be a culture, a region or any metadata of the object. In our results, we show that our method can recover most of the information from damaged objects, even in cases where more than half of the voxels are missing, without producing many errors.

We present a new method for the completion of partial globally-symmetric 3D objects, based on the detection of partial and approximate symmetries in the incomplete input dataset. In our approach, symmetry detection is formulated as a constrained sparsity maximization problem, which is solved efficiently using a robust RANSAC-based optimizer. The detected partial symmetries are then reused iteratively, in order to complete the missing parts of the object. A global error relaxation method minimizes the accumulated alignment errors and a non-rigid registration approach applies local deformations in order to properly handle approximate symmetry. Unlike previous approaches, our method does not rely on the computation of features, it uniformly handles translational, rotational and reflectional symmetries and can provide plausible object completion results, even on challenging cases, where more than half of the target object is missing. We demonstrate our algorithm in the completion of 3D scans with varying levels of partiality and we show the applicability of our approach in the repair and completion of heavily eroded or incomplete cultural heritage objects.

Abstract Symmetry is a common characteristic in natural and man‐made objects. Its ubiquitous nature can be exploited to facilitate the analysis and processing of computational representations of real objects. In particular, in computer graphics, the detection of symmetries in 3D geometry has enabled a number of applications in modeling and reconstruction. However, the problem of symmetry detection in incomplete geometry remains a challenging task. In this paper, we propose a vote‐based approach to detect symmetry in 3D shapes, with special interest in models with large missing parts. Our algorithm generates a set of candidate symmetries by matching local maxima of a surface function based on the heat diffusion in local domains, which guarantee robustness to missing data. In order to deal with local perturbations, we propose a multi‐scale surface function that is useful to select a set of distinctive points over which the approximate symmetries are defined. In addition, we introduce a vote‐based scheme that is aware of the partiality, and therefore reduces the number of false positive votes for the candidate symmetries. We show the effectiveness of our method in a varied set of 3D shapes and different levels of partiality. Furthermore, we show the applicability of our algorithm in the repair and completion of challenging reassembled objects in the context of cultural heritage.

This paper presents a hierarchical method for finding correspondences in non-rigid shapes. We propose a new representation for 3D meshes: the decomposition tree. This structure characterizes the recursive decomposition process of a mesh into regions of interest and key points. The internal nodes contain regions of interest (which may be recursively decomposed) and the leaf nodes contain the key points to be matched. We also propose a hierarchical matching algorithm that performs in a level-wise manner. The matching process is guided by the similarity between regions in high levels of the tree, until reaching the key points stored in the leaves. This allows us to reduce the search space of correspondences, making also the matching process efficient. We evaluate the effectiveness of our approach using the SHREC'2010 robust correspondence benchmark. In addition, we show that our results outperform the state of the art.

In this paper, we present a new approach for generic 3D shape retrieval based on a mesh partitioning scheme. Our method combines a mesh global description and mesh partition descriptions to represent a 3D shape. The partitioning is useful because it helps us to extract additional information in a more local sense. Thus, part descriptions can mitigate the semantic gap imposed by global description methods. We propose to find spatial agglomerations of local features to generate mesh partitions. Hence, the definition of a distance function is stated as an optimization problem to find the best match between two shape representations. We show that mesh partitions are representative and therefore it helps to improve the effectiveness in retrieval tasks. We present exhaustive experimentation using the SHREC'09 Generic Shape Retrieval Benchmark.

This PhD thesis proposal is focused on proposing solutions to the problem of Partial Shape Retrieval which is part of the Three-Dimensional Object Retrieval problem and represents a very challenging problem. Given a shape (or a part of a shape) as query, one wants to retrieve from a collection of 3D models those objects which contain parts visually similar to the query. Difficulties can arise due to the need of representing a model in a compact way with local information, where the extent of the locality is unknown a priori. In addition, the matching becomes an expensive task because of the large amount of possible memberships of the partial query in the shapes. Typically, assumptions are made to constrain the problem in order to solve it effectively. Therefore, partial shape retrieval is a challenging and open problem. In this document, we provide proposals to address this problem and furthermore, we discuss the open problems and the important issues that should be tackled in order to solve the problem of Partial Shape Matching and Retrieval.