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We propose a unified 3D flow framework for joint learning of shape embedding and deformation for different categories. Our goal is to recover shapes from imperfect point clouds by fitting the best shape template in a shape repository after deformation. Accordingly, we learn a shape embedding for template retrieval and a flow-based network for robust deformation. We note that the deformation flow can be quite different for different shape categories. Therefore, we introduce a novel multi-hub module to learn multiple modes of deformation to incorporate such variation, providing a network which can handle a wide range of objects from different categories. The shape embedding is designed to retrieve the best-fit template as the nearest neighbor in a latent space. We replace the standard fully connected layer with a tiny structure in the embedding that significantly reduces network complexity and further improves deformation quality. Experiments show the superiority of our method to existing state-of-the-art methods via qualitative and quantitative comparisons. Finally, our method provides efficient and flexible deformation that can further be used for novel shape design. [ABSTRACT FROM AUTHOR]

Object retrieval systems measure the degree of similarity of the shape of 3D models. They search for the elements of the 3D model databases that resemble the query model. In structural bioinformatics, the query model is a protein tertiary/quaternary structure and the objective is to find similarly shaped molecules in the Protein Data Bank. With the ever-growing size of the PDB, a direct atomic coordinate comparison with all its members is impractical. To overcome this problem, the shape of the molecules can be encoded by fixed-length feature vectors. The distance of a protein to the entire PDB can be measured in this low-dimensional domain in linear time. The state-of-the-art approaches utilize Zernike–Canterakis moments for the shape encoding and supply the retrieval process with geometric data of the input structures. The BioZernike descriptors are a standard utility of the PDB since 2020. However, when trying to calculate the ZC moments locally, the issue of the deficiency of libraries readily available for use in custom programs (i.e., without relying on external binaries) is encountered, in particular programs written in Python. Here, a fast and well-documented Python implementation of the Pozo–Koehl algorithm is presented. In contrast to the more popular algorithm by Novotni and Klein, which is based on the voxelized volume, the PK algorithm produces ZC moments directly from the triangular surface meshes of 3D models. In particular, it can accept the molecular surfaces of proteins as its input. In the presented PK-Zernike library, owing to Numba's just-in-time compilation, a mesh with 50,000 facets is processed by a single thread in a second at the moment order 20. Since this is the first time the PK algorithm is used in structural bioinformatics, it is employed in a novel, simple, but efficient protein structure retrieval pipeline. The elimination of the outlying chain fragments via a fast PCA-based subroutine improves the discrimination ability, allowing for this pipeline to achieve an 0.961 area under the ROC curve in the BioZernike validation suite (0.997 for the assemblies). The correlation between the results of the proposed approach and of the 3D Surfer program attains values up to 0.99. [ABSTRACT FROM AUTHOR]

Porous structures are essential in a variety of fields such as materials science and chemistry. To retrieve porous materials efficiently, novel descriptors are required to quantify the geometric and topological features. In this paper, we present a novel framework to create a descriptor that incorporates both topological and geometric information of a porous structure. To capture geometric information, we keep track of the birthtime and deathtime of the persistentfeatures of a real-valued function on the surface that evolves with a parameter. Then, we generate the corresponding persistentfeaturediagram (DgmPF) and convert it into a vector called persistencefeaturedescriptor (PFD). To extract topological information, we sample points from the pore surface and compute the corresponding persistence diagram, which is then transformed into the Persistence B-Spline Grids (PBSG). Our proposed descriptor, namely persistentgeometry−topologydescriptor (PGTD), is obtained by concatenating PFD with PBSG. In our experiments, we use the heat kernel signature (HKS) as the real-valued function to compute the descriptor. We test the method on a synthetic porous dataset and a zeolite dataset and find that it is competitive compared to other descriptors based on HKS and advanced topological descriptors.

Transforming assemblies are products that alter their shapes by re-assembling their parts. This idea is applied to a wide range of objects from folding gadgets as outdoor gear aimed at saving space, to robotic characters fighting in Hollywood films which drastically change their appearance. While the former type falls into a folding or packing problems, the latter requires a different viewpoint to be solved since the destination shape is not necessarily aiming at minimizing the occupation space. As a possible solution, this kind of deformation can be decomposed into segmentation of the shape to parts and parts matching. Segmentation is a general problem in shape modeling and numerous algorithms have been proposed for this. On the other hand, matching simultaneously multiple parts (many-to-many matching) has hardly been explored. This study develops a many-to-many matching algorithm for surface meshes of parts from two distinct destination shapes of a single transforming assembly. The proposed algorithm consists of a local geometry analysis and a global optimization of parts combination based on such analysis. For the local geometry analysis, the surface geometric feature is described by a local shape descriptor. Some vertices are detected as feature points by intrinsic shape signature (ISS) and the geometry at the feature points is expressed by the signature of histogram of orientation (SHOT). For all the combination of pairs from each destination shape, the number of feature points with similar descriptor values is counted. In the global optimization, the final matching is determined by the maximum weight matching on a complete bipartite graph whose nodes are the parts, and edges are weighted by the number of the feature points with similar descriptors. We present successful results for several examples to empirically show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The shape encoding of geospatial objects is a key problem in the fields of cartography and geoscience. Although traditional geometric-based methods have made great progress, deep learning techniques offer a development opportunity for this classical problem. In this study, a shape encoding framework based on a deep encoder–decoder architecture was proposed, and three different methods for encoding planar geospatial shapes, namely GraphNet, SeqNet, and PixelNet methods, were constructed based on raster-based, graph-based, and sequence-based modeling for shape. The three methods were compared with the existing deep learning-based shape encoding method and two traditional geometric methods. Quantitative evaluation and visual inspection led to the following conclusions: (1) The deep encoder–decoder methods can effectively compute shape features and obtain meaningful shape coding to support the shape measure and retrieval task. (2) Compared with the traditional Fourier transform and turning function methods, the deep encoder–decoder methods showed certain advantages. (3) Compared with the SeqNet and PixelNet methods, GraphNet performed better due to the use of a graph to model the topological relations between nodes and efficient graph convolution and pooling operations to process the node features. [ABSTRACT FROM AUTHOR]

In recent years, with the rapid development of the computer aided design and computer graphics, a large number of 3D models have emerged, making it a challenge to quickly find models of interest. As a concise and informative representation of 3D models, shape descriptors are a key factor in achieving effective retrieval. In this paper, we propose a novel global descriptor for 3D models that incorporates both geometric and topological information. We refer to this descriptor as the persistent heat kernel signature descriptor (PHKS). Constructed by concatenating our isometry-invariant geometric descriptor with topological descriptor, PHKS possesses high recognition ability, while remaining insensitive to noise and can be efficiently calculated. Retrieval experiments of 3D models on the benchmark datasets show considerable performance gains of the proposed method compared to other descriptors based on HKS and advanced topological descriptors. • A descriptor incorporating both geometric and topological information is proposed. • The stability of the proposed descriptor is proved. • The proposed descriptor outperforms state-of-the-art descriptors in shape retrieval. [ABSTRACT FROM AUTHOR]

Point cloud learning has lately attracted increasing attention due to its wide applications in many areas, such as computer vision, autonomous driving, and robotics. As a dominating technique in AI, deep learning has been successfully used to solve various 2D vision problems. However, deep learning on point clouds is still in its infancy due to the unique challenges faced by the processing of point clouds with deep neural networks. Recently, deep learning on point clouds has become even thriving, with numerous methods being proposed to address different problems in this area. To stimulate future research, this paper presents a comprehensive review of recent progress in deep learning methods for point clouds. It covers three major tasks, including 3D shape classification, 3D object detection and tracking, and 3D point cloud segmentation. It also presents comparative results on several publicly available datasets, together with insightful observations and inspiring future research directions. [ABSTRACT FROM AUTHOR]

Feature analysis plays a significant role in computer vision and computer graphics. In the task of shape retrieval, shape descriptor is indispensable. In recent years, feature extraction based on deep learning becomes very popular, but the design of geometric shape descriptor is still meaningful due to the contained intrinsic information and interpretability. This paper proposes an effective and robust descriptor of 3D models. The descriptor is constructed based on the probability distribution of the normalized eigenfunctions of the Laplace–Beltrami operator on the surface, and a spectrum method for dimensionality reduction. The distance metric of the descriptor space is learned by utilizing the joint Bayesian model, and we introduce a matrix regularization in the training stage to re-estimate the covariance matrix. Finally, we apply the descriptor to 3D shape retrieval on a public benchmark. Experiments show that our method is robust and has good retrieval performance.

The shape encoding of geospatial objects is a key problem in the fields of cartography and geoscience. Although traditional geometric-based methods have made great progress, deep learning techniques offer a development opportunity for this classical problem. In this study, a shape encoding framework based on a deep encoder–decoder architecture was proposed, and three different methods for encoding planar geospatial shapes, namely GraphNet, SeqNet, and PixelNet methods, were constructed based on raster-based, graph-based, and sequence-based modeling for shape. The three methods were compared with the existing deep learning-based shape encoding method and two traditional geometric methods. Quantitative evaluation and visual inspection led to the following conclusions: (1) The deep encoder–decoder methods can effectively compute shape features and obtain meaningful shape coding to support the shape measure and retrieval task. (2) Compared with the traditional Fourier transform and turning function methods, the deep encoder–decoder methods showed certain advantages. (3) Compared with the SeqNet and PixelNet methods, GraphNet performed better due to the use of a graph to model the topological relations between nodes and efficient graph convolution and pooling operations to process the node features.

Due to the growing number of 3D objects in digital libraries, the task of searching and browsing models in an extensive 3D database has been the focus of considerable research in the area. In the last decade, several approaches to retrieve 3D models based on shape similarity have been proposed. The majority of the existing methods addresses the problem of similarity between objects as a global matching problem. Consequently, most of these techniques do not support a part of the object as a query, in addition to their poor performance for classes with globally non-similar shape models and also for articulated objects. The partial matching technique seems to be a suitable solution to these problems. In this paper, we address the problem of shape matching and retrieval. We propose a new approach based on partial matching in which each 3D object is segmented into its constituent parts, and shape descriptors are computed from these elements to compare similarities. Several experiments investigated that our technique enables fast computing for content-based 3D shape retrieval and significantly improves the results of our method based on Data Envelopment Analysis descriptor for global matching.

The availability of dummy-atom modelling programs to determine the shape of monodisperse globular particles from small-angle solution scattering data has led to outstanding scientific advances. However, there is no equivalent procedure that allows modelling of stacked, seemingly endless structures, such as helical systems. This work presents a bead-modelling algorithm that reconstructs the structural motif of helical and rod-like systems. The algorithm is based on a `projection scheme': by exploiting the recurrent nature of stacked systems, such as helices, the full structure is reduced to a single building-block motif. This building block is fitted by allowing random dummy-atom movements without an underlying grid. The proposed method is verified using a variety of analytical models, and examples are presented of successful shape reconstruction from experimental data sets. To make the algorithm available to the scientific community, it is implemented in a graphical computer program that encourages user interaction during the fitting process and also includes an option for shape reconstruction of globular particles.

Object retrieval systems measure the degree of similarity of the shape of 3D models. They search for the elements of the 3D model databases that resemble the query model. In structural bioinformatics, the query model is a protein tertiary/quaternary structure and the objective is to find similarly shaped molecules in the Protein Data Bank. With the ever-growing size of the PDB, a direct atomic coordinate comparison with all its members is impractical. To overcome this problem, the shape of the molecules can be encoded by fixed-length feature vectors. The distance of a protein to the entire PDB can be measured in this low-dimensional domain in linear time. The state-of-the-art approaches utilize Zernike-Canterakis moments for the shape encoding and supply the retrieval process with geometric data of the input structures. The BioZernike descriptors are a standard utility of the PDB since 2020. However, when trying to calculate the ZC moments locally, the issue of the deficiency of libraries readily available for use in custom programs (i.e., without relying on external binaries) is encountered, in particular programs written in Python. Here, a fast and well-documented Python implementation of the Pozo-Koehl algorithm is presented. In contrast to the more popular algorithm by Novotni and Klein, which is based on the voxelized volume, the PK algorithm produces ZC moments directly from the triangular surface meshes of 3D models. In particular, it can accept the molecular surfaces of proteins as its input. In the presented PK-Zernike library, owing to Numba's just-in-time compilation, a mesh with 50,000 facets is processed by a single thread in a second at the moment order 20. Since this is the first time the PK algorithm is used in structural bioinformatics, it is employed in a novel, simple, but efficient protein structure retrieval pipeline. The elimination of the outlying chain fragments via a fast PCA-based subroutine improves the discrimination ability, allowing for this pipeline to achieve an 0.961 area under the ROC curve in the BioZernike validation suite (0.997 for the assemblies). The correlation between the results of the proposed approach and of the 3D Surfer program attains values up to 0.99.

• A method for extracting short descriptors from lengthy descriptors is developed. • The dimension reduction results are strengthened by an attraction/repulsion model. • A deep residual network is trained for generating the short descriptors. • The short descriptors improve the retrieval speed greatly. The state-of-the-art shape descriptors are usually lengthy for gaining high retrieval precision. With the rapidly growing number of 3-dimensional models, the retrieval speed becomes a prominent problem in shape retrieval. In this paper, by exploiting the capabilities of the dimensionality reduction methods and the deep convolutional residual network (ResNet), we developed a method for extracting short shape descriptors (with just 2 real numbers, named 2- descriptors) from lengthy descriptors, while keeping or even improving the retrieval precision of the original lengthy descriptors. Specifically, an attraction and repulsion model is devised to strengthen the direct dimensionality reduction results. In this way, the dimensionality reduction results turn into desirable labels for the ResNet. Moreover, to extract the 2-descriptors using ResNet, we transformed it as a classification problem. For this purpose, the range of each component of the dimensionality reduction results (including two components in total) is uniformly divided into n intervals corresponding to n classes. Experiments on 3D shape retrieval show that our method not only accelerates the retrieval speed greatly but also improves the retrieval precisions of the original shape descriptors. [ABSTRACT FROM AUTHOR]

Highlights • We present a geometric framework for 3D shape retrieval using geodesic moments. • We propose an unsupervised approach for learning shape descriptors using sparse autoencoders. • We demonstrate the superior performance of our approach on standard shape benchmarks. Graphical abstract Abstract Shape representations provide compact, parsimonious shape descriptions that are often used in object recognition and retrieval tasks. In light of the increased processing power of graphics cards and the availability of large-scale datasets, deep neural networks have shown a remarkable performance in numerous computer vision and geometry processing applications. In this paper, we present a deep learning framework for unsupervised 3D shape retrieval with geodesic moments. The proposed method learns deep shape representations using stacked sparse autoencoders in an unsupervised manner. Such discriminative shape descriptors can then be used to compute pairwise dissimilarities between shapes in a dataset, and to find the retrieved set of the most relevant shapes to a given shape query. Experimental evaluation on four standard 3D shape benchmarks demonstrate the competitive performance of our approach, showing that it leads to improved retrieval results in comparison with state-of-the-art techniques. [ABSTRACT FROM AUTHOR]

This paper proposes a new computational method for retrieving shapes under unpredictable conditions such as when occlusion, geometric distortion, and differences in image resolution occur simultaneously. The human visual system retrieves shapes from incomplete information in the real world, and it has inspired a lot of computational methods of retrieving shapes. In order to retrieve shapes, the observed shapes are decided to be alike or unlike remembered shapes in memory after the comparison of these shapes. To compare the observed and remembered shapes, they must first be appropriately represented so that the points on each shape can be mapped and compared. For this reason, the shape retrieval process needs an appropriate shape representation and shape mapping methods. Moreover, the shape representations should be normalized before the mapping process. However, a normalization process for representations under unpredictable conditions has not yet been established. In this paper, we describe a shape retrieval method that enables us to retrieve shapes under unpredictable conditions with a suitable normalization process. Using curvature partition and angle-length profile, our shape retrieval method normalizes the shape representation before it does the mapping. As a result, unlike the previously proposed methods, it can be used under unpredictable conditions such as when occlusion, geometric distortion, and differences in image resolution occur simultaneously.

With the rapid expansion of applied 3D computational vision, shape descriptors have become increasingly important for a wide variety of applications and objects from molecules to planets. Appropriate shape descriptors are critical for accurate (and efficient) shape retrieval and 3D model classification. Several spectral-based shape descriptors have been introduced by solving various physical equations over a 3D surface model. In this paper, for the first time, we incorporate a specific manifold learning technique, introduced in statistics and machine learning, to develop a global, spectral-based shape descriptor in the computer graphics domain. The proposed descriptor utilizes the Laplacian Eigenmap technique in which the Laplacian eigenvalue problem is discretized using an exponential weighting scheme. As a result, our descriptor eliminates the limitations tied to the existing spectral descriptors, namely dependency on triangular mesh representation and high intra-class quality of 3D models. We also present a straightforward normalization method to obtain a scale-invariant and noise-resistant descriptor. The extensive experiments performed in this study using two standard 3D shape benchmarks—high-resolution TOSCA and McGill datasets—demonstrate that the present contribution provides a highly discriminative and robust shape descriptor under the presence of a high level of noise, random scale variations, and low sampling rate, in addition to the known isometric-invariance property of the Laplace−Beltrami operator. The proposed method significantly outperforms state-of-the-art spectral descriptors in shape retrieval and classification. The proposed descriptor is limited to closed manifolds due to its inherited inability to accurately handle manifolds with boundaries.

This article presents an effective shape descriptor with a property of fast matching. This descriptor, called IDSC-wFW (a weighted Fourier and wavelet-like descriptor based on inner distance shape context), first rewrites shape histograms of IDSC descriptors, changing the histogram belonging to a point to the histogram belonging to a field, and sets the histogram of a field as a one-dimensional signal, then transforms this one-dimensional signal by using a Fourier transform and a transform similar to Haar wavelet. Finally, the two transform results are linearly combined to form a new descriptor. This new descriptor requires only a distance-based measure method during the matching stage. Experimental results on three well-known databases show that this new descriptor not only obtains accurate retrieval results but also runs fast.

The soaring popularity of deep learning in a wide variety of fields ranging from computer vision and speech recognition to self-driving vehicles has sparked a flurry of research interest from both academia and industry. In this paper, we propose a deep learning approach to 3D shape retrieval using a multi-level feature learning paradigm. Low-level features are first extracted from a 3D shape using spectral graph wavelets. Then, mid-level features are generated via the bag-of-features model by employing locality-constrained linear coding as a feature coding method, in conjunction with the biharmonic distance and intrinsic spatial pyramid matching in a bid to effectively measure the spatial relationship between each pair of the bag-of-feature descriptors. Finally, high-level shape features are learned by applying a deep auto-encoder on mid-level features. Extensive experiments on SHREC-2014 and SHREC-2015 datasets demonstrate the much better performance of the proposed framework in comparison with state-of-the-art methods. [ABSTRACT FROM AUTHOR]

The ability to accurately and effectively search for 3D shape is crucial for many applications. In this study, we proposed a novel framework for 3D shape retrieval. We compensate the loss of high frequencies of heat kernel signature from two aspects. One is to introduce the weight for each point to highlight the details of the salient points. The other is to directly capture microgeometry structure through wave kernel's access to high frequencies. Thus, our method can capture geometric features at different frequencies of a shape, which satisfy the property of an ideal descriptor. We conduct shape retrieval experiments on a standard benchmark and compared with another heat kernel-based method. Experimental results demonstrate that the proposed method is effective and accurate. [ABSTRACT FROM AUTHOR]

Sparse features have been successfully used in shape retrieval, by encoding feature descriptors into global shape signatures. We investigate how sparse features based on saliency models affect retrieval and provide recommendations on good saliency models for shape retrieval. Our results show that randomly selecting points on the surface produces better retrieval performance than using any of the evaluated salient keypoint detection, including ground-truth. We discuss the reasons for and implications of this unexpected result. [ABSTRACT FROM AUTHOR]

Manifold learning is the technique that aims for finding a constructive way to embed the data from a highdimensional space into a low-dimensional one based on non-linear approaches. In this paper a supervised manifold learning method for shape recognition is proposed. The approach is based on learning the manifold space for training samples, and maps the test samples to the learned space by a Generalized Regression Neural Network (GRNN). The main goal in this paper is to propose a new feature vector to coincide semantic with Euclidean distances. To accomplish this, the desired topological manifold is learnt by a global distance driven non-linear feature extraction method. The experimental results indicated that the geometrical distances between the samples on the manifold space are more related to their semantic distance. To fuse the results of shape recognition based on contour and region based methods, the final result of shape recognition is based on committee decision in three manifold spaces. The experimental results confirmed the effectiveness and the validity of the proposed method.

In many areas such as commerce, medical investigations, and others, large collections of digital images are being created. Search operations inside these collections of images are usually based on low-level features of objects contained in an image: color, shape, texture. Although such techniques of content-based image retrieval are useful, they are strongly limited by their inability to consider the meaning of images. Moreover, specifying a query in terms of low level features may not be very simple. Image annotation, in which images are associated with keywords describing their semantics, is a more effective way of image retrieval and queries can be naturally specified by the user. The paper presents a combined set of methods for image retrieval, in which both low level features and semantic properties are taken into account when retrieving images. First, it describes some methods for image representation and retrieval based on shape, and proposes a new such method, which overcomes some of the existing limitations. Then, it describes a new method for image semantic annotation based on a genetic algorithm, which is further improved from two points of view: the obtained solution value - using an anticipatory genetic algorithm, and the execution time - using a parallel genetic algorithm.

The retrieval of non-rigid 3D shapes is an important task. A common technique is to simplify this problem to a rigid shape retrieval task by producing a bending-invariant canonical form for each shape in the dataset to be searched. It is common for these techniques to attempt to 'unbend' a shape by applying multidimensional scaling (MDS) to the distances between points on the mesh, but this leads to unwanted local shape distortions. We instead perform the unbending on the skeleton of the mesh, and use this to drive the deformation of the mesh itself. This leads to computational speed-up, and reduced distortion of local shape detail. We compare our method against other canonical forms: our experiments show that our method achieves state-of-the-art retrieval accuracy in a recent canonical forms benchmark, and only a small drop in retrieval accuracy over the state-of-the-art in a second recent benchmark, while being significantly faster. [ABSTRACT FROM AUTHOR]

View-based 3D shape retrieval is a popular branch in 3D shape analysis owing to the high discriminative property of 2D views. However, many previous works do not scale up to large 3D shape databases. We propose a two layer coding (TLC) framework to conduct shape matching much more efficiently. The first layer coding is applied to pairs of views represented as depth images. The spatial relationship of each view pair is captured with so-called eigen-angle, which is the planar angle between the two views measured at the center of the 3D shape. Prior to the second layer coding, the view pairs are divided into subsets according to their eigen-angles. Consequently, view pairs that differ significantly in their eigen-angles are encoded with different codewords, which implies that spatial arrangement of views is preserved in the second layer coding. The final feature vector of a 3D shape is the concatenation of all the encoded features from different subsets, which is used for efficient indexing directly. TLC is not limited to encode the local features from 2D views, but can be also applied to encoding 3D features. Exhaustive experimental results confirm that TLC achieves state-of-the-art performance in both retrieval accuracy and efficiency. [ABSTRACT FROM PUBLISHER]

The medial axis of a 3D shape is widely known for its ability as a compact and complete shape representation. However, there is still lack of a generative description defined over the medial axis directly which limits its actual application to 3D shape analysis such as shape matching and retrieval. In this paper, we propose a new spectral shape descriptor that directly applies spectral analysis to the medial axis of a 3D shape, which we call the medial axis spectrum for a 3D shape. We develop a newly defined Minkowski–Euclidean ratio inspired by the Minkowski inner product to characterize the geometry of the medial axis of a 3D mesh. We then generalize the Laplace–Beltrami operator to the medial axis, and take the solution to a Laplacian eigenvalue problem defined on it as the medial axis spectrum. The medial axis spectrum is invariant under rigid transformation and isometry of the medial axis, and is robust to shape boundary noise as shown by our experiments. The medial axis spectrum is finally used for 3D shape retrieval, and its superiority over previous work is shown by extensive comparisons. [ABSTRACT FROM AUTHOR]

Motivated by the Weber's Law, this paper proposes an efficient and robust shape descriptor based on the perceptual stimulus model, called Weber's Law Shape Descriptor (WLSD). It is based on the theory that human perception of a pattern depends not only on the change of stimulus intensity, but also on the original stimulus intensity. Invariant to scale and rotation is the intrinsic properties of WLSD. As a global shape descriptor, WLSD has far lower computation complexity while is as discriminative as state-of-art shape descriptors. Experimental results demonstrate the strong capability of the proposed method in handling shape retrieval. [ABSTRACT FROM AUTHOR]

In this paper, we propose two novel shape descriptors, angular pattern (AP) and binary angular pattern (BAP), and a multiscale integration of them for shape retrieval. Both AP and BAP are intrinsically invariant to scale and rotation. More importantly, being global shape descriptors, the proposed shape descriptors are computationally very efficient, while possessing similar discriminability as state-of-the-art local descriptors. As a result, the proposed approach is attractive for real world shape retrieval applications. The experiments on the widely used MPEG-7 and TARI-1000 data sets demonstrate the effectiveness of the proposed method in comparison with existing methods. [ABSTRACT FROM PUBLISHER]

Abstract: 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. [Copyright &y& Elsevier]

In this paper, we propose a new shape/object retrieval algorithm, namely, co-transduction. The performance of a retrieval system is critically decided by the accuracy of adopted similarity measures (distances or metrics). In shape/object retrieval, ideally, intraclass objects should have smaller distances than interclass objects. However, it is a difficult task to design an ideal metric to account for the large intraclass variation. Different types of measures may focus on different aspects of the objects: for example, measures computed based on contours and skeletons are often complementary to each other. Our goal is to develop an algorithm to fuse different similarity measures for robust shape retrieval through a semisupervised learning framework. We name our method co-transduction, which is inspired by the co-training algorithm. Given two similarity measures and a query shape, the algorithm iteratively retrieves the most similar shapes using one measure and assigns them to a pool for the other measure to do a re-ranking, and vice versa. Using co-transduction, we achieved an improved result of 97.72% (bull's-eye measure) on the MPEG-7 data set over the state-of-the-art performance. We also present an algorithm called tri-transduction to fuse multiple-input similarities, and it achieved 99.06% on the MPEG-7 data set. Our algorithm is general, and it can be directly applied on input similarity measures/metrics; it is not limited to object shape retrieval and can be applied to other tasks for ranking/retrieval. [ABSTRACT FROM PUBLISHER]

This paper presents a 3-D shape reconstruction algorithm based on the level set method. Multiple dielectric and non-overlapping objects are considered. The level set algorithm is a gradient-type optimization approach that aims to minimize a cost function between measurements and computer-simulated data. The algorithm is capable of retrieving the shape and location of multiple targets made of two different and slightly lossy materials. An appropriate form of the deformation velocity based on the forward and adjoint fields is calculated. The method of moment surface integral equation is implemented to calculate the deformation velocity of the evolving objects. Two sets of Hamilton-Jacobi equations, associated with the two dielectric materials, are solved simultaneously to update the evolving objects. During the inversion scheme, the marching cubes method is employed to restore the surface meshes necessary for the forward solver. The algorithm is tested on corrupted synthetic data with signal-to-noise ratio of 10 dB. [ABSTRACT FROM AUTHOR]

Abstract: Most of the shape recognition measures are rotation, translation and scale (RST) invariant. However, when the shape aspect ratio is changed or the mirror reflection of the object is considered for retrieval, some of these measures are not effectively useful. In consideration of the aforesaid issues, a Fourier descriptor based ‘aspect ratio’ and ‘mirror reflection’ invariant shape matching algorithm is presented here. This algorithm is also RST invariant. [Copyright &y& Elsevier]

Abstract: Boundary-based shape matching has many applications in areas, such as pattern recognition and computer vision. Recently, Dynamic space warping (DSW) has emerged as a very effective tool for matching shapes. However, a central computational difficulty associated with DSW arises when a boundary’s starting point (or rotation angle) is unknown. In this paper, the HopDSW algorithm is proposed to speed up the starting point computation. Rather than performing an exhaustive search for the correct starting point as in classical approaches, the proposed algorithm operates in a coarse-to-fine manner. The coarse search is global and uses a hopping step to exclude points from the search. Then, the search is refined in the neighborhood of the solution of the coarse search. A criterion that governs selecting the hopping step parameter is given, which reduces the number of starting point computations by an order. For shape representation, triangle area signature (TAS) is computed from triangles formed by the boundary points. Experimental results on the MPEG-7 CE-1 database of 1400 shapes show that the proposed algorithm returns the solution of the exhaustive search with a high degree of accuracy and a considerable reduction in the number of computations. [Copyright &y& Elsevier]

Dynamic space warping (DSW) has emerged as a very effective tool for matching shapes. However, a central computational difficulty associated with DSW arises when a boundary's starting point (or rotation angle) is unknown. In this article, the HopDSW algorithm is proposed to speed up the starting point computation. Rather than performing an exhaustive search for the correct starting point as in classical approaches, the proposed algorithm operates in a coarse-to-fine manner. The coarse search is global and uses a hopping step to exclude points from the search. Then the search is refined in the neighborhood of the solution of the coarse search. A criterion that governs selecting the hopping step parameter is given, which reduces the number of starting point computations by an order. For shape representation, a triangle area signature (TAS) is computed from triangles formed by the boundary points. Experimental results on the MPEG-7 CE-1 database of 1400 shapes show that the proposed algorithm returns the solution to an exhaustive search with a high degree of accuracy and a considerable reduction in the number of computations. [ABSTRACT FROM AUTHOR]

This paper describes a method of approximating a shape contour with a polygon. The polygon vertices are extracted from the curvature extremes, through a scale-space description of the contour, via linear diffusion. These vertices are located on the contour points where the sharper changes of the contour directions occur. Using a proper strategy, a set of extremes that result in a given approximation level is chosen. By adding new vertices, the approximation level can be improved, and a scalable representation of the contour is identified. This method results in an approximation that discriminates local from global geometric features and provides a good visual representation of the original contour. This polygonal approximation method is used for scalable encoding of the shape contours. In this regard, an encoding technique suitable for scalable polygonal approximation has been developed. We show that encoding the approximated polygons result in a good relation between the distortion and the bitrate. Finally, we show that in addition to coding this method can be efficiently used for shape comparison and shape retrieval. [ABSTRACT FROM AUTHOR]

Shape similarity and shape retrieval are very important topics in computer vision. The recent progress in this domain has been mostly driven by designing smart shape descriptors for providing better similarity measure between pairs of shapes. In this paper, we provide a new perspective to this problem by considering the existing shapes as a group, and study their similarity measures to the query shape in a graph structure. Our method is general and can be built on top of any existing shape similarity measure. For a given similarity measure, a new similarity is learned through graph transduction. The new similarity is learned iteratively so that the neighbors of a given shape influence its final similarity to the query. The basic idea here is related to PageRank ranking, which forms a foundation of Google Web search. The presented experimental results demonstrate that the proposed approach yields significant improvements over the state-of-art shape matching algorithms. We obtained a retrieval rate of 91.61 percent on the MPEG-7 data set, which is the highest ever reported in the literature. Moreover, the learned similarity by the proposed method also achieves promising improvements on both shape classification and shape clustering. [ABSTRACT FROM AUTHOR]

This paper proposes a novel feature-based invariant descriptor termed Radon composite features (RCFs) for planar shapes. Instead of analyzing shapes directly in the spatial domain, some shape features are extracted from the Radon transform plane using statistical and spectral analysis. The proposed method overcomes the drawbacks of existing shape representation techniques since it accomplishes the invariances to common geometrical transformations without any normalization process, which usually causes inaccuracies. A novel hierarchical strategy with RCFs can achieve low complexity and coarse-to-fine retrieval, and perform accurately when retrieving shapes, while remaining robust against variations. Experiments demonstrate that RCF provides a higher degree of discrimination as compared with several state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel method of using two-level similarity measures for shape-based image retrieval. We first identify the dominant points of a given shape, and then calculate their geometric moments and the distances between two consecutive dominant points. A spectrum representing the normalized geometric moments versus normalized distances is generated, and its area and curve length are computed. We use these two values as similarity features for the indexes in coarse-grained shape retrieval. Furthermore, we use the cross-sectional area and curve length distribution for the indexes in fine-grained shape retrieval. Experimental results show that the proposed method is simple and efficient and can reach the accuracy rate of 95%. [ABSTRACT FROM AUTHOR]

A novel local structural approach, which is a sequel to our previous work, is proposed in this paper for object retrieval in a cluttered and occluded environment without identifying the outlines of an object. It works by first extracting consistent and structurally unique local neighborhood from inputs or models and then voting on the optimal matches employing dynamic programming and a novel hypercube-based indexing structure. The proposed concepts have been tested on a database with thousands of images and compared with the six nearest-neighbors shape description with superior results. [ABSTRACT FROM AUTHOR]

Similarity-based retrieval from shape databases typically employs a pairwise shape matcher and one or more indexing techniques. In this paper, we focus specifically on the design of a pairwise matcher for retrieval of 2-D shape contours. In the past, the matchers used for the one-to-many problem of shape retrieval were often designed for the problem of matching an isolated pair of shapes. This approach fails to exploit two characteristics of the one-to-many matching problem that distinguish it from the one-to-one matching problem. First, the output of shape retrieval systems tends to be dominated by matches to relatively similar shapes. In this paper, we demonstrate that by not expending computational resources on unneeded accuracy of matching, both the speed and the accuracy of retrieval can be increased. Second, the shape database is a large statistical sample of the population of shapes. We introduce a probabilistic model for exploiting that statistical knowledge to further increase retrieval accuracy. The model has several benefits: (1) It does not require class labels on the database shapes, thus supporting unlabeled retrieval. (2) It does not require feature independence. (3) It is parameter-free. (4) It has a fast runtime implementation. The probabilistic model is general and thus potentially applicable to other one-to-many matching problems. [ABSTRACT FROM AUTHOR]

For shapes represented as closed planar contours, we introduce a class of functionals which are invariant with respect to the Euclidean group and which are obtained by performing integral operations. While such integral invariants enjoy some of the desirable properties of their differential counterparts, such as locality of computation (which allows matching under occlusions) and uniqueness of representation (asymptotically), they do not exhibit the noise sensitivity associated with differential quantities and, therefore, do not require presmoothing of the input shape. Our formulation allows the analysis of shapes at multiple scales. Based on integral invariants, we define a notion of distance between shapes. The proposed distance measure can be computed efficiently and allows warping the shape boundaries onto each other; its computation results in optimal point correspondence as an intermediate step. Numerical results on shape matching demonstrate that this framework can match shapes despite the deformation of subparts, missing parts and noise. As a quantitative analysis, we report matching scores for shape retrieval from a database. [ABSTRACT FROM AUTHOR]

In this paper, a new 2D shape Multiscale Triangle-Area Representation (MTAR) method is proposed. This representation utilizes a simple geometric principle, that is, the area of the triangles formed by the shape boundary points. The wavelet transform is used for smoothing and decomposing the shape boundaries into multiscale levels. At each scale level, a TAR image and the corresponding Maxima-Minima lines are obtained. The resulting MTAR is more robust to noise, less complex, and more selective than similar methods such as the curvature scale-space (CSS). Furthermore, the MTAR is invariant to the general affine transformations. The proposed MTAR is tested and compared to the CSS method using MPEG-7 CE-shape-1 part B and Columbia Object Image Library (COIL-20) datasets. The results show that the proposed MTAR outperforms the CSS method for the conducted tests. [ABSTRACT FROM AUTHOR]