Ivan Sipiran

Approximate Symmetry Detection in Partial 3D Meshes

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.

Towards automated 3D reconstruction of defective cultural heritage objects

Due to recent improvements in 3D acquisition and shape processing technology, the digitization of Cultural Heritage (CH) artifacts is gaining increased application in context of archival and archaeological research. This increasing availability of acquisition technologies also implies a need for intelligent processing methods that can cope with imperfect object scans. Specifically for Cultural Heritage objects, besides imperfections given by the digitization process, also the original artifact objects may be imperfect due to deterioration or fragmentation processes. Currently, the reconstruction of previously digitized CH artifacts is mostly performed manually by expert users reassembling fragment parts and completing imperfect objects by modeling. However, more automatic methods for CH object repair and completion are needed to cope with increasingly large data becoming available. In this conceptual paper, we first provide a brief survey of typical imperfections in CH artifact scan data and in turn motivate the need for respective repair methods. We survey and classify a selection of existing reconstruction methods with respect to their applicability for CH objects, and then discuss how these approaches can be extended and combined to address various types of physical defects that are encountered in CH artifacts by proposing a flexible repair workflow for 3D digitizations of CH objects. The workflow accommodates an automatic reassembly step which can deal with fragmented input data. It also includes the similarity-based retrieval of appropriate complementary object data which is used to repair local and global object defects. Finally, we discuss options for evaluation of the effectiveness of such a CH repair workflow.

A benchmark of simulated range images for partial shape retrieval

In this paper, we address the evaluation of algorithms for partial shape retrieval using a large-scale simulated benchmark of partial views which are used as queries. Since the scanning of real objects is a time-consuming task, we create a simulation that generates a set of views from a target model and at different levels of complexity (amount of missing data). In total, our benchmark contains 7,200 partial views. Furthermore, we propose the use of weighted effectiveness measures based on the complexity of a query. With these characteristics, we aim at jointly evaluating the effectiveness, efficiency and robustness of existing algorithms. As a result of our evaluation, we found that a combination of methods provides the best effectiveness, mainly due to the complementary information that they deliver. The obtained results open new questions regarding the difficulty of the partial shape retrieval problem. As a consequence, potential future directions are also identified.

From Reassembly to Object Completion: A Complete Systems Pipeline

The problem of the restoration of broken artifacts, where large parts could be missing, is of high importance in archaeology. The typical manual restoration can become a tedious and error-prone process, which also does not scale well. In recent years, many methods have been proposed for assisting the process, most of which target specialized object types or operate under very strict constraints. We propose a digital shape restoration pipeline consisting of proven, robust methods for automatic fragment reassembly and shape completion of generic three-dimensional objects of arbitrary type. In this pipeline, first we introduce a novel unified approach for handling the reassembly of objects from heavily damaged fragments by exploiting both fracture surfaces and salient features on the intact sides of fragments, when available. Second, we propose an object completion procedure based on generalized symmetries and a complementary part extraction process that is suitable for driving the fabrication of missing geometry. We demonstrate the effectiveness of our approach using real-world fractured objects and software implemented as part of the European Union--funded PRESIOUS project, which is also available for download from the project site.

Scalability of non-rigid 3D shape retrieval

Due to recent advances in 3D acquisition and modeling, increasingly large amounts of 3D shape data become available in many application domains. This rises not only the need for effective methods for 3D shape retrieval, but also efficient retrieval and robust implementations. Previous 3D retrieval challenges have mainly considered data sets in the range of a few thousands of queries. In the 2015 SHREC track on Scalability of 3D Shape Retrieval we provide a benchmark with more than 96 thousand shapes. The data set is based on a non-rigid retrieval benchmark enhanced by other existing shape benchmarks. From the baseline models, a large set of partial objects were automatically created by simulating a range-image acquisition process. Four teams have participated in the track, with most methods providing very good to near-perfect retrieval results, and one less complex baseline method providing fair performance. Timing results indicate that three of the methods including the latter baseline one provide near- interactive time query execution. Generally, the cost of data pre-processing varies depending on the method.

Object Completion using k-Sparse Optimization

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.

Guiding the Exploration of Scatter Plot Data Using Motif-Based Interest Measures

Finding interesting patterns in large scatter plot spaces is a challenging problem and becomes even more difficult with increasing number of dimensions. Previous approaches for exploring large scatter plot spaces like e.g., the well-known Scagnostics approach, mainly focus on ranking scatter plots based on their global properties. However, often local patterns contribute significantly to the interestingness of a scatter plot. We are proposing a novel approach for the automatic determination of interesting views in scatter plot spaces based on analysis of local scatter plot segments. Specifically, we automatically classify similar local scatter plot segments, which we call scatter plot motifs. Inspired by the well-known tf-idf approach from information retrieval, we compute local and global quality measures based on certain frequency properties of the local motifs. We show how we can use these to filter, rank and compare scatter plots and their incorporated motifs. We demonstrate the usefulness of our approach with synthetic and real-world data sets and showcase our corresponding data exploration tool that visualizes the distribution of local scatter plot motifs in relation to a large overall scatter plot space.

Guiding the exploration of scatter plot data using motif-based interest measures

Finding interesting patterns in large scatter plot spaces is a challenging problem and becomes even more difficult with increasing number of dimensions. Previous approaches for exploring large scatter plot spaces like e.g., the well-known Scagnostics approach, mainly focus on ranking scatter plots based on their global properties. However, often local patterns contribute significantly to the interestingness of a scatter plot. We are proposing a novel approach for the automatic determination of interesting views in scatter plot spaces based on analysis of local scatter plot segments. Specifically, we automatically classify similar local scatter plot segments, which we call scatter plot motifs. Inspired by the well-known tf × idf -approach from information retrieval, we compute local and global quality measures based on frequency properties of the local motifs. We show how we can use these to filter, rank and compare scatter plots and their incorporated motifs. We demonstrate the usefulness of our approach with synthetic and real-world data sets and showcase our data exploration tools that visualize the distribution of local scatter plot motifs in relation to a large overall scatter plot space.

Fractured 3D object restoration and completion

The problem of object restoration from eroded fragments where large parts could be missing is of high relevance in archaeology. Manual restoration is possible and common in practice but it is a tedious and error-prone process, which does not scale well. Solutions for specific parts of the problem have been proposed but a complete reassembly and repair pipeline is absent from the bibliography. We propose a shape restoration pipeline consisting of appropriate methods for automatic fragment reassembly and shape completion. We demonstrate the effectiveness of our approach using real-world fractured objects.

Automatic 3D object fracturing for evaluation of partial retrieval and object restoration tasks: benchmark and application to 3D cultural heritage data

Recently, 3D digitization and printing hardware have seen rapidly increasing adoption. High-quality digitization of real-world objects is becoming more and more efficient. In this context, growing amounts of data from the cultural heritage (CH) domain such as columns, tombstones or arches are being digitized and archived in 3D repositories. In many cases, these objects are not complete, but fragmented into several pieces and eroded over time. As manual restoration of fragmented objects is a tedious and error-prone process, recent work has addressed automatic reassembly and completion of fragmented 3D data sets. While a growing number of related techniques are being proposed by researchers, their evaluation currently is limited to smaller numbers of high-quality test fragment sets. We address this gap by contributing a methodology to automatically generate 3D fragment data based on synthetic fracturing of 3D input objects. Our methodology allows generating large-scale fragment test data sets from existing CH object models, complementing manual benchmark generation based on scanning of fragmented real objects. Besides being scalable, our approach also has the advantage to come with ground truth information (i.e. the input objects), which is often not available when scans of real fragments are used. We apply our approach to the Hampson collection of digitized pottery objects, creating and making available a first, larger restoration test data set that comes with ground truth. Furthermore, we illustrate the usefulness of our test data for evaluation of a recent 3D restoration method based on symmetry analysis and also outline how the applicability of 3D retrieval techniques could be evaluated with respect to 3D restoration tasks. Finally, we discuss first results of an ongoing extension of our methodology to include object erosion processes by means of a physiochemical model simulating weathering effects.