Partial Shape Retrieval Research Articles

Unsupervised Learning of 3-D Local Features From Raw Voxels Based on a Novel Permutation Voxelization Strategy.

Effective 3-D local features are significant elements for 3-D shape analysis. Existing hand-crafted 3-D local descriptors are effective but usually involve intensive human intervention and prior knowledge, which burdens the subsequent processing procedures. An alternative resorts to the unsupervised learning of features from raw 3-D representations via popular deep learning models. However, this alternative suffers from several significant unresolved issues, such as irregular vertex topology, arbitrary mesh resolution, orientation ambiguity on the 3-D surface, and rigid and slightly nonrigid transformation invariance. To tackle these issues, we propose an unsupervised 3-D local feature learning framework based on a novel permutation voxelization strategy to learn high-level and hierarchical 3-D local features from raw 3-D voxels. Specifically, the proposed strategy first applies a novel voxelization which discretizes each 3-D local region with irregular vertex topology and arbitrary mesh resolution into regular voxels, and then, a novel permutation is applied to permute the voxels to simultaneously eliminate the effect of rotation transformation and orientation ambiguity on the surface. Based on the proposed strategy, the permuted voxels can fully encode the geometry and structure of each local region in regular, sparse, and binary vectors. These voxel vectors are highly suitable for the learning of hierarchical common surface patterns by stacked sparse autoencoder with hierarchical abstraction and sparse constraint. Experiments are conducted on three aspects for evaluating the learned local features: 1) global shape retrieval; 2) partial shape retrieval; and 3) shape correspondence. The experimental results show that the learned local features outperform the other state-of-the-art 3-D shape descriptors.

BoSCC: Bag of Spatial Context Correlations for Spatially Enhanced 3D Shape Representation.

Highly discriminative 3D shape representations can be formed by encoding the spatial relationship among virtual words into the Bag of Words (BoW) method. To achieve this challenging task, several unresolved issues in the encoding procedure must be overcome for 3D shapes, including: 1) arbitrary mesh resolution; 2) irregular vertex topology; 3) orientation ambiguity on the 3D surface; and 4) invariance to rigid and non-rigid shape transformations. In this paper, a novel spatially enhanced 3D shape representation called bag of spatial context correlations (BoSCCs) is proposed to address all these issues. Adopting a novel local perspective, BoSCC is able to describe a 3D shape by an occurrence frequency histogram of spatial context correlation patterns, which makes BoSCC become more compact and discriminative than previous global perspective-based methods. Specifically, the spatial context correlation is proposed to simultaneously encode the geometric and spatial information of a 3D local region by the correlation among spatial contexts of vertices in that region, which effectively resolves the aforementioned issues. The spatial context of each vertex is modeled by Markov chains in a multi-scale manner, which thoroughly captures the spatial relationship by the transition probabilities of intra-virtual words and the ones of inter-virtual words. The high discriminability and compactness of BoSCC are effective for classification and retrieval, especially in the scenarios of limited samples and partial shape retrieval. Experimental results show that BoSCC outperforms the state-of-the-art spatially enhanced BoW methods in three common applications: global shape retrieval, shape classification, and partial shape retrieval.

Unsupervised 3D Local Feature Learning by Circle Convolutional Restricted Boltzmann Machine.

Extracting local features from 3D shapes is an important and challenging task that usually requires carefully designed 3D shape descriptors. However, these descriptors are hand-crafted and require intensive human intervention with prior knowledge. To tackle this issue, we propose a novel deep learning model, namely circle convolutional restricted Boltzmann machine (CCRBM), for unsupervised 3D local feature learning. CCRBM is specially designed to learn from raw 3D representations. It effectively overcomes obstacles such as irregular vertex topology, orientation ambiguity on the 3D surface, and rigid or slightly non-rigid transformation invariance in the hierarchical learning of 3D data that cannot be resolved by the existing deep learning models. Specifically, by introducing the novel circle convolution, CCRBM holds a novel ring-like multi-layer structure to learn 3D local features in a structure preserving manner. Circle convolution convolves across 3D local regions via rotating a novel circular sector convolution window in a consistent circular direction. In the process of circle convolution, extra points are sampled in each 3D local region and projected onto the tangent plane of the center of the region. In this way, the projection distances in each sector window are employed to constitute a novel local raw 3D representation called projection distance distribution (PDD). In addition, to eliminate the initial location ambiguity of a sector window, the Fourier transform modulus is used to transform the PDD into the Fourier domain, which is then conveyed to CCRBM. Experiments using the learned local features are conducted on three aspects: global shape retrieval, partial shape retrieval, and shape correspondence. The experimental results show that the learned local features outperform other state-of-the-art 3D shape descriptors.

Mesh Convolutional Restricted Boltzmann Machines for Unsupervised Learning of Features With Structure Preservation on 3-D Meshes.

Discriminative features of 3-D meshes are significant to many 3-D shape analysis tasks. However, handcrafted descriptors and traditional unsupervised 3-D feature learning methods suffer from several significant weaknesses: 1) the extensive human intervention is involved; 2) the local and global structure information of 3-D meshes cannot be preserved, which is in fact an important source of discriminability; 3) the irregular vertex topology and arbitrary resolution of 3-D meshes do not allow the direct application of the popular deep learning models; 4) the orientation is ambiguous on the mesh surface; and 5) the effect of rigid and nonrigid transformations on 3-D meshes cannot be eliminated. As a remedy, we propose a deep learning model with a novel irregular model structure, called mesh convolutional restricted Boltzmann machines (MCRBMs). MCRBM aims to simultaneously learn structure-preserving local and global features from a novel raw representation, local function energy distribution. In addition, multiple MCRBMs can be stacked into a deeper model, called mesh convolutional deep belief networks (MCDBNs). MCDBN employs a novel local structure preserving convolution (LSPC) strategy to convolve the geometry and the local structure learned by the lower MCRBM to the upper MCRBM. LSPC facilitates resolving the challenging issue of the orientation ambiguity on the mesh surface in MCDBN. Experiments using the proposed MCRBM and MCDBN were conducted on three common aspects: global shape retrieval, partial shape retrieval, and shape correspondence. Results show that the features learned by the proposed methods outperform the other state-of-the-art 3-D shape features.

Algorithm BOSS (Bag-of-Salient local Spectrums) for non-rigid and partial 3D object retrieval

The aim of the proposed algorithm is to expedite three-dimensional objects indexing and retrieval. Investigating the Bag-of-Features (BoF) paradigm, we focus on a set of extracted local descriptors from 3D objects. Using scalar function calculated on the surface mesh, the algorithm extracts the salient points, and then associates each of these points with a local Fourier descriptor. The descriptor is computed on the neighboring salient points by projecting the geometry onto the first eigenvectors of Laplace–Beltrami operator. Additionally, through an offline learning step, a visual dictionary is built by clustering a large set of feature descriptors. Then, each 3D shape is described by a histogram of these visual words occurrences weighted using the number of their local descriptors. Experimental results show the highly discriminative capability of the proposed approach against rigid and non-rigid transformations, noise and geometry changes. The performance of our algorithm is also demonstrated on global and partial shape retrieval.

Efficient descriptor for full and partial shape matching

In this paper we present a new approach for full and partial shape retrieval based on a shape descriptor invariant to geometric transformations, reflection and deformation. The proposed description...

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.

Sampling Strategies for 3D Partial Shape Matching and Retrieval Using Bag-of-Words Model

This paper investigates the feature sampling strategies for 3D partial shape retrieval using bag-of-words model. The SHREC 09’ parts query models [3] are tested for comparison. These parts models are obtained by cutting parts from complete models, which are different from range scans. Dense sampling and pyramid sampling are proposed to extract local salient features from the depth images of the 3D models. Bag-of-words model is used to represent of both of parts query and complete target models. The optimal sampling configurations for the proposed feature extraction strategies are obtained by comparing the retrieval accuracy using maximum histogram intersection distance (MHID). The results suggest that extracting more features does not guarantee better retrieval accuracy using the bag-of-words model. The feature sampling configurations also have significant impacts on the retrieval accuracy.

A Survey on Partial Retrieval of 3D Shapes

Content-based shape retrieval techniques can facilitate 3D model resource reuse, 3D model modeling, object recognition, and 3D content classification. Recently more and more researchers have attempted to solve the problems of partial retrieval in the domain of computer graphics, vision, CAD, and multimedia. Unfortunately, in the literature, there is little comprehensive discussion on the state-of-the-art methods of partial shape retrieval. In this article we focus on reviewing the partial shape retrieval methods over the last decade, and help novices to grasp latest developments in this field. We first give the definition of partial retrieval and discuss its desirable capabilities. Secondly, we classify the existing methods on partial shape retrieval into three classes by several criteria, describe the main ideas and techniques for each class, and detailedly compare their advantages and limits. We also present several relevant 3D datasets and corresponding evaluation metrics, which are necessary for evaluating partial retrieval performance. Finally, we discuss possible research directions to address partial shape retrieval.

Combination of bag-of-words descriptors for robust partial shape retrieval

This paper presents a 3D shape retrieval algorithm based on the Bag of Words (BoW) paradigm. For a given 3D shape, the proposed approach considers a set of feature points uniformly sampled on the surface and associated with local Fourier descriptors. This descriptor is computed in the neighborhood of each feature point by projecting the geometry onto the eigenvectors of the Laplace–Beltrami operator; it is very informative, robust to connectivity and geometry changes, and also fast to compute. In a preliminary step, a visual dictionary is built by clustering a large set of feature descriptors, then each 3D shape is described by an histogram of occurrences of these visual words, hence discarding any spatial information. A spatially-sensitive algorithm is also presented where the 3D shape is described by an histogram of pairs of visual words. We show that these two approaches are complementary and can be combined to improve the performance and the robustness of the retrieval. The performances have been compared against very recent state-of-the-art methods on several different datasets. For global shape retrieval, our combined approach is comparable to these recent works, however, it clearly outperforms them in the case of partial shape retrieval.

Retrieving Reusable 3D CAD Models Using Knowledge-Driven Dependency Graph Partitioning

Abstract3D design retrieval works, which focus on geometric representations, can hardly obtain reusable CAD models. We propose a novel method to retrieve reusable CAD models using knowledge-driven partitioning based on modeling dependency graphs. In order to retrieve reusable results, two dependency-graph partitionings are given based on design knowledge. The first is a horizontal partitioning scheme to simplify CAD models and preserve their essential shapes. In order to support partial shape retrieval and reuse, another vertical partitioning segments sub-parts in a meaningful way. The main contributions include (1) a graph-based modeling knowledge representation; (2) knowledge-driven graph partitioning strategies for improving reusability of retrieved results; and (3) redesign supports by utilizing modeling expertise. The validity of the method is demonstrated with several retrieval cases of realistic CAD models.

Learning Robust Similarity Measures for 3D Partial Shape Retrieval

In this paper, we propose a novel approach to learning robust ground distance functions of the Earth Mover's distance to make it appropriate for quantifying the partial similarity between two feature-sets. First, we define the ground distance as a monotonic transformation of commonly used feature-to-feature base distance (or similarity) measures, so that in computing the Earth Mover's distance, the algorithm could better turn its focus on the feature pairs that are correctly matched, while being less affected by irrelevant ones. As a result, the proposed method is especially suited for 3D partial shape retrieval where occlusion and clutter are serious problems. We prove that when the transformation satisfies certain conditions, the metric property of the base distance is sufficient to guarantee the ground distance is a metric (and so is the Earth Mover's distance), which makes fast shape retrieval on large databases technically possible. Second, we propose a discriminative learning framework to optimize the transformation function based on the real Adaboost algorithm. The optimization is performed in the space of the piecewise constant approximations of the transformation without making any parametric assumption. Finally, extensive experiments on 3D partial shape retrieval convincingly demonstrate the effectiveness of the proposed techniques.

Partial 3D Shape Retrieval by Reeb Pattern Unfolding

Abstract This paper presents a novel approach for fast and efficient partial shape retrieval on a collection of 3D shapes. Each shape is represented by a Reeb graph associated with geometrical signatures. Partial similarity between two shapes is evaluated by computing a variant of their maximum common sub‐graph. By investigating Reeb graph theory, we take advantage of its intrinsic properties at two levels. First, we show that the segmentation of a shape by a Reeb graph provides charts with disk or annulus topology only. This topology control enables the computation of concise and efficient sub‐part geometrical signatures based on parameterisation techniques. Secondly, we introduce the notion of Reeb pattern on a Reeb graph along with its structural signature. We show this information discards Reeb graph structural distortion and still depicts the topology of the related sub‐parts. The number of combinations to evaluate in the matching process is then dramatically reduced by only considering the combinations of topology equivalent Reeb patterns. The proposed framework is invariant against rigid transformations and robust against non‐rigid transformations and surface noise. It queries the collection in interactive time (from 4 to 30 seconds for the largest queries). It outperforms the competing methods of the SHREC 2007 contest in term of NDCG vector and provides, respectively, a gain of 14.1% and 40.9% on the approaches by Biasotti et al.[BMSF06]and Cornea et al.[CDS*05]. As an application, we present an intelligent modelling‐by‐example system which enables a novice user to rapidly create new 3D shapes by composing shapes of a collection having similar sub‐parts.