Shape Classification using Spectral Graph Wavelets

Spectral shape descriptors have been used extensively in a broad spectrum of geometry processing applications ranging from shape retrieval and segmentation to classification. In this pa- per, we propose a spectral graph wavelet approach for 3D shape classification using the bag-of-features paradigm. In an effort to capture both the local and global geometry of a 3D shape, we present a three-step feature description framework. First, local descriptors are extracted via the spectral graph wavelet transform having the Mexican hat wavelet as a generating ker- nel. Second, mid-level features are obtained by embedding lo- cal descriptors into the visual vocabulary space using the soft- assignment coding step of the bag-of-features model. Third, a global descriptor is constructed by aggregating mid-level fea- tures weighted by a geodesic exponential kernel, resulting in a matrix representation that describes the frequency of appearance of nearby codewords in the vocabulary. Experimental results on two standard 3D shape benchmarks demonstrate the effective- ness of the proposed classification approach in comparison with state-of-the-art methods

3D Shape Classification Using Collaborative Representation based Projections

A novel 3D shape classification scheme, based on collaborative representation learning, is investigated in this work. A data-driven feature-extraction procedure, taking the form of a simple projection operator, is in the core of our methodology. Provided a shape database, a graph encapsulating the structural relationships among all the available shapes, is first constructed and then employed in defining low-dimensional sparse projections. The recently introduced method of CRPs (collaborative representation based projections), which is based on L2-Graph, is the first variant that is included towards this end. A second algorithm, that particularizes the CRPs to shape descriptors that are inherently nonnegative, is also introduced as potential alternative. In both cases, the weights in the graph reflecting the database structure are calculated so as to approximate each shape as a sparse linear combination of the remaining dataset objects. By way of solving a generalized eigenanalysis problem, a linear matrix operator is designed that will act as the feature extractor. Two popular, inherently high dimensional descriptors, namely ShapeDNA and Global Point Signature (GPS), are employed in our experimentations with SHREC10, SHREC11 and SCHREC 15 datasets, where shape recognition is cast as a multi-class classification problem that is tackled by means of an SVM (support vector machine) acting within the reduced dimensional space of the crafted projections. The results are very promising and outperform state of the art methods, providing evidence about the highly discriminative nature of the introduced 3D shape representations.Comment: 16 pages, 6 Figures, 3 Tables Statement including that an updated version of this manuscript is under condiseration at Pattern Recognition Letters, is adde

Augmented Semantic Signatures of Airborne LiDAR Point Clouds for Comparison

LiDAR point clouds provide rich geometric information, which is particularly useful for the analysis of complex scenes of urban regions. Finding structural and semantic differences between two different three-dimensional point clouds, say, of the same region but acquired at different time instances is an important problem. A comparison of point clouds involves computationally expensive registration and segmentation. We are interested in capturing the relative differences in the geometric uncertainty and semantic content of the point cloud without the registration process. Hence, we propose an orientation-invariant geometric signature of the point cloud, which integrates its probabilistic geometric and semantic classifications. We study different properties of the geometric signature, which are an image-based encoding of geometric uncertainty and semantic content. We explore different metrics to determine differences between these signatures, which in turn compare point clouds without performing point-to-point registration. Our results show that the differences in the signatures corroborate with the geometric and semantic differences of the point clouds.Comment: 18 pages, 6 figures, 1 tabl

Global spectral graph wavelet signature for surface analysis of carpal bones

In this paper, we present a spectral graph wavelet approach for shape analysis of carpal bones of human wrist. We apply a metric called global spectral graph wavelet signature for representation of cortical surface of the carpal bone based on eigensystem of Laplace-Beltrami operator. Furthermore, we propose a heuristic and efficient way of aggregating local descriptors of a carpal bone surface to global descriptor. The resultant global descriptor is not only isometric invariant, but also much more efficient and requires less memory storage. We perform experiments on shape of the carpal bones of ten women and ten men from a publicly-available database. Experimental results show the excellency of the proposed GSGW compared to recent proposed GPS embedding approach for comparing shapes of the carpal bones across populations.Comment: arXiv admin note: substantial text overlap with arXiv:1705.0625

Local Geometry Inclusive Global Shape Representation

Knowledge of shape geometry plays a pivotal role in many shape analysis applications. In this paper we introduce a local geometry-inclusive global representation of 3D shapes based on computation of the shortest quasi-geodesic paths between all possible pairs of points on the 3D shape manifold. In the proposed representation, the normal curvature along the quasi-geodesic paths between any two points on the shape surface is preserved. We employ the eigenspectrum of the proposed global representation to address the problems of determination of region-based correspondence between isometric shapes and characterization of self-symmetry in the absence of prior knowledge in the form of user-defined correspondence maps. We further utilize the commutative property of the resulting shape descriptor to extract stable regions between isometric shapes that differ from one another by a high degree of isometry transformation. We also propose various shape characterization metrics in terms of the eigenvector decomposition of the shape descriptor spectrum to quantify the correspondence and self-symmetry of 3D shapes. The performance of the proposed 3D shape descriptor is experimentally compared with the performance of other relevant state-of-the-art 3D shape descriptors.Comment: 11 pages, 5 figure

A Fusion of Labeled-Grid Shape Descriptors with Weighted Ranking Algorithm for Shapes Recognition

Retrieving similar images from a large dataset based on the image content has been a very active research area and is a very challenging task. Studies have shown that retrieving similar images based on their shape is a very effective method. For this purpose a large number of methods exist in literature. The combination of more than one feature has also been investigated for this purpose and has shown promising results. In this paper a fusion based shapes recognition method has been proposed. A set of local boundary based and region based features are derived from the labeled grid based representation of the shape and are combined with a few global shape features to produce a composite shape descriptor. This composite shape descriptor is then used in a weighted ranking algorithm to find similarities among shapes from a large dataset. The experimental analysis has shown that the proposed method is powerful enough to discriminate the geometrically similar shapes from the non-similar ones

Geodesic convolutional neural networks on Riemannian manifolds

Feature descriptors play a crucial role in a wide range of geometry analysis and processing applications, including shape correspondence, retrieval, and segmentation. In this paper, we introduce Geodesic Convolutional Neural Networks (GCNN), a generalization of the convolutional networks (CNN) paradigm to non-Euclidean manifolds. Our construction is based on a local geodesic system of polar coordinates to extract "patches", which are then passed through a cascade of filters and linear and non-linear operators. The coefficients of the filters and linear combination weights are optimization variables that are learned to minimize a task-specific cost function. We use GCNN to learn invariant shape features, allowing to achieve state-of-the-art performance in problems such as shape description, retrieval, and correspondence

Multi-feature Distance Metric Learning for Non-rigid 3D Shape Retrieval

In the past decades, feature-learning-based 3D shape retrieval approaches have been received widespread attention in the computer graphic community. These approaches usually explored the hand-crafted distance metric or conventional distance metric learning methods to compute the similarity of the single feature. The single feature always contains onefold geometric information, which cannot characterize the 3D shapes well. Therefore, the multiple features should be used for the retrieval task to overcome the limitation of single feature and further improve the performance. However, most conventional distance metric learning methods fail to integrate the complementary information from multiple features to construct the distance metric. To address these issue, a novel multi-feature distance metric learning method for non-rigid 3D shape retrieval is presented in this study, which can make full use of the complimentary geometric information from multiple shape features by utilizing the KL-divergences. Minimizing KL-divergence between different metric of features and a common metric is a consistency constraints, which can lead the consistency shared latent feature space of the multiple features. We apply the proposed method to 3D model retrieval, and test our method on well known benchmark database. The results show that our method substantially outperforms the state-of-the-art non-rigid 3D shape retrieval methods

PointHop: An Explainable Machine Learning Method for Point Cloud Classification

An explainable machine learning method for point cloud classification, called the PointHop method, is proposed in this work. The PointHop method consists of two stages: 1) local-to-global attribute building through iterative one-hop information exchange, and 2) classification and ensembles. In the attribute building stage, we address the problem of unordered point cloud data using a space partitioning procedure and developing a robust descriptor that characterizes the relationship between a point and its one-hop neighbor in a PointHop unit. When we put multiple PointHop units in cascade, the attributes of a point will grow by taking its relationship with one-hop neighbor points into account iteratively. Furthermore, to control the rapid dimension growth of the attribute vector associated with a point, we use the Saab transform to reduce the attribute dimension in each PointHop unit. In the classification and ensemble stage, we feed the feature vector obtained from multiple PointHop units to a classifier. We explore ensemble methods to improve the classification performance furthermore. It is shown by experimental results that the PointHop method offers classification performance that is comparable with state-of-the-art methods while demanding much lower training complexity.Comment: 13 pages with 9 figure

Diffusion framework for geometric and photometric data fusion in non-rigid shape analysis

In this paper, we explore the use of the diffusion geometry framework for the fusion of geometric and photometric information in local and global shape descriptors. Our construction is based on the definition of a diffusion process on the shape manifold embedded into a high-dimensional space where the embedding coordinates represent the photometric information. Experimental results show that such data fusion is useful in coping with different challenges of shape analysis where pure geometric and pure photometric methods fail