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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]

Recent studies on shape retrieval stress for the realization of highly efficient feature descriptors realized with reduced complexity. Accordingly, a simple tessellation operation that geometrically explores the spatial data for realizing efficient and precise shape descriptor is dealt in this paper. The descriptor labelled as Squared-Triangle Tessellation Descriptor (STTD), enforces strict geometrical congruency to facilitate effective feature extraction and representation. STTD dually tessellates the image into square tiles and later decomposes them into triangles. Upon triangle formulation the respective features are capitulated using simple geometrical means which is then transformed into a shape histogram. Then, an auto encoder operates on the constructed feature database and classifies the diverse shapes based on the intra and inter-class relationship that exist amongst the different features. Exhaustive investigations on publicly available dataset namely MPEG7 Part B, Tari-1000 and Kimia's 99 reveal consistent accuracy of 99% offered by STTD across these datasets when compared with its competitors. As majority of the STTD formulation deals with integer arithmetic therefore simple multipliers with less area and power is suffice for its VLSI implementation, thereby, amicable for real-time applications. [ABSTRACT FROM AUTHOR]

The digitalization of manufacturing processes and recent trends, such as the Industrial Metaverse, are continuously increasing in adoption in various critical industries, resulting in a surging demand for 3D CAD models and their exchange. Following this, it becomes necessary to protect the intellectual property of content designers in increasingly decentralized production environments where 3D assets are repeatedly shared online within the ecosystem. CAD models can be protected by traditional security methods such as watermarking, which embeds additional information into the file. Nevertheless, malicious actors may find ways to remove the information from a file. To authenticate and protect 3D models without relying on additional information, we propose a robust 3D perceptual hash generated based on the prevalent geometric features. Furthermore, our geometry-based approach generates compact and tamper-resistant fingerprints for a 3D model by projecting multiple spherical sliced layers of intersection points into cluster distances. The resulting hash links the 3D model to an owner, supporting the detection of counterfeits. The approach was benchmarked for similarity search and evaluated against established state-of-the-art shape retrieval techniques. The results show promising resistance against arbitrary transformations and manipulations, with our approach detecting 25.6% more malicious tampering attacks than the baseline. • A compact geometry-based approach for creating 3D perceptual hashes. • Evaluation of tamper resistance against various 3D mesh manipulations. • Evaluation of rotation and scale resistance against state-of-the-art methods. • Benchmarking of the 3D shape retrieval performance with industrial parts. [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]

Fourier transform profilometry (FTP) is widely used for real-time three-dimensional (3-D) surface shape measurement with a single frame of projection fringe pattern. The band-pass filter is very important to the shape retrieval accuracy of this technique. On the basis of the Hanning band-pass filter, a cross-shaped Hanning filter is developed in the paper to extract the first-order spectrum of deformed fringe pattern, and the effect of fringe angle on the proposed filter is analysed. The phase retrieval results using the proposed filter and Hanning filter are compared in the simulation and measurement experiment. The results show that the cross-shaped Hanning filter coordinating with the fringe pattern of about 45 degrees holds the higher accuracy of 3-D shape retrieval. [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.

In this paper, a bijection, which projects the shape manifold as a linear manifold, is proposed to simplify the nonlinear problems of shape analysis. Shapes are represented by the direction function of discrete curves. These shapes are elements of a finite-dimensional shape manifold. We discuss the shape manifold from three perspectives: extrinsic, intrinsic and global using the reference coordinate system. Then, we construct another manifold, in which the reference frame is the Fourier basis and the associated related coordinate is the Fourier coefficients obtained by Fourier transformation. This transformation ensures a bijection between the local spaces of two manifolds. In the constructed manifold, the nonlinear structure is described by the reference frames. Consequently, we obtain a linear manifold only using the related coordinate. The performance of our method is illustrated by the applications of shape interpolation, transportation of shape deformation and shape retrieval. [ABSTRACT FROM AUTHOR]

The quest for computationally simple, highly accurate and precise shape descriptors supporting retrieval continues to be an active research area in computer vision. In this paper, a simple feature descriptor is realized by blending Modulo Arithmetic (MA) with Local Absolute Pixel Differences (LAPD) labelled as MA-LAPD. MA initially refines edges of images through modulo normalization and later operated by LAPD to capture local texture patterns. Subsequently, LAPD encodes the local intensity transitions in eight directions with regard to center pixel. The two prominent directional indices are converted into unique decimal codes that represent each pixel position, thus, transforming each image into a collection of LAPD codes. The ensuing LAPD image is then fabricated into histograms for characterizing the distribution of local features, used for matching and retrieval. Quantitative and qualitative investigations on Kimia's 99, MPEG-7 Part-B and Tari-1000 datasets reveal consistent Bull's Eye Retrieval (BER) scores above 91%. Also, relative analysis exposes the superiority of MA-LAPD with its predecessors in majority of the datasets. [ABSTRACT FROM AUTHOR]

• Engagement of octagonal lattice-based triangulated feature characterization, which is the first of its kind. • The inherent congruency of the geometrical arrangement makes the descriptor robust to numerous image transformations. • The nature of the second-order derivatives capture keenly high-frequency information such as edges, corners, and points. • Thorough investigations on benchmark shape datasets demonstrate the contribution's superiority. • Complexity analysis reveals the simplicity of the OLTT model signifying its compatibility with real scenarios. Erstwhile shape description schemes lack primarily in establishing trade-offs with accuracy and computational load. Accordingly, a lightweight shape descriptor offering precise definition and compaction of high-frequency features is contributed in this paper using a simple geometrical shape for localization and shape characterization. Initially, the input image is octagonally tessellated and triangularly decomposed into sub-regions whose side-wise differences are evaluated and subjected to second-order differentiation to produce three high-frequency values representing triangle corners. The resultant is processed by the law of sines to yield localized shape features exhibiting congruence and is reiterated on the residual regions, followed by a novel octal encoding scheme encompassing maximal variations in the localized regions. The resulting features are globally fabricated into shape histograms in a non-overlapping manner representing the shape vector. This scheme validated on widely popular benchmark shape datasets demonstrates superior retrieval and recognition accuracies greater than 93% which is lacking in its competitors. [ABSTRACT FROM AUTHOR]

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.

We present a novel spatial hashing based data structure to facilitate 3D shape analysis using convolutional neural networks (CNNs). Our method builds hierarchical hash tables for an input model under different resolutions that leverage the sparse occupancy of 3D shape boundary. Based on this data structure, we design two efficient GPU algorithms namely hash2col and col2hash so that the CNN operations like convolution and pooling can be efficiently parallelized. The perfect spatial hashing is employed as our spatial hashing scheme, which is not only free of hash collision but also nearly minimal so that our data structure is almost of the same size as the raw input. Compared with existing 3D CNN methods, our data structure significantly reduces the memory footprint during the CNN training. As the input geometry features are more compactly packed, CNN operations also run faster with our data structure. The experiment shows that, under the same network structure, our method yields comparable or better benchmark results compared with the state-of-the-art while it has only one-third memory consumption when under high resolutions (i.e., $256^3$ 256 3 ). [ABSTRACT FROM AUTHOR]

The geometric and semantic information of 3D point clouds significantly influence the analysis of 3D point cloud structures. However, semantic learning of 3D point clouds based on deep learning is challenging due to the naturally unordered data structure. In this work, we strive to impart machines with the knowledge of 3D object shapes, thereby enabling them to infer the high-level semantic information from the 3D model. Inspired by the vector of locally aggregated descriptors, we propose indirectly describing the high-level semantic information by associating each point's low-level geometric descriptor with a few visual words. Based on this approach, we design an end-to-end network for 3D shape analysis that combines pointwise low-level geometric and high-level semantic information. The network includes a spatial transform and a uniform operation that make it invariant to input rotation and translation, respectively. Our network also employs pointwise feature extraction and pooling operations to solve the unordered point cloud problem. In a series of experiments with popular 3D shape analysis benchmarks, our network exhibits competitive performance on many important tasks, such as 3D object classification, 3D object part segmentation, semantic segmentation in scenes, and commercial 3D CAD model retrieval. [ABSTRACT FROM AUTHOR]

The representation of 3D data is the key issue for shape analysis. However, most of the existing representations suffer from high computational cost and structure information loss. This paper presents a novel sequential slice representation with an attention-embedding network, named RSSNet, for 3D point cloud recognition and retrieval in road environments. RSSNet has two main branches. Firstly, a sequential slice module is designed to map disordered 3D point clouds to ordered sequence of shallow feature vectors. A gated recurrent unit (GRU) module is applied to encode the spatial and content information of these sequential vectors. The second branch consists of a key-point based graph convolution network (GCN) with an embedding attention strategy to fuse the sequential and global features to refine the structure discriminability. Three datasets were used to evaluate the proposed method, one acquired by our mobile laser scanning (MLS) system and two public datasets (KITTI and Sydney Urban Objects). Experimental results indicated that the proposed method achieved better performance than recognition and retrieval state-of-the-art methods. RSSNet provided recognition rates of 98.08%, 95.77% and 70.83% for the above three datasets, respectively. For the retrieval task, RSSNet obtained excellent mAP values of 95.56%, 87.16% and 69.99% on three datasets, respectively. [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.

• 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]

Shape matching and retrieval is a challenging issue in computer vision owing to the complications in realizing highly accurate descriptors. Herein, a novel shape characterization, representation scheme is presented by blending phase congruency (PC) with histogram of oriented gradients (HOG), labelled as PC-HOG. Firstly, PC is applied on the shapes to obtain contour points that is then operated by HOG to formulate the feature vector. The resulting descriptor is evaluated on shape datasets like MPEG-7 CE shape-1 part B, TARI-1000 and Kimia's 99. Relatively consistent Bull's Eye Retrieval rate of 90% was achieved by the proposed descriptor across the diverse datasets. Also, noise analysis of the proposed descriptor in diverse datasets is performed to signify the scheme's robustness against noise. Furthermore, the inherent nature of PC-HOG makes it to be invariant to different affine transformations. [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]

The consideration of the noise that affects 3D shape recovery is becoming very important for accurate shape reconstruction. In Shape from Focus, when 2D image sequences are obtained, mechanical vibrations, referred as jitter noise, occur randomly along the z‐axis, in each step. To model the noise for real world scenarios, this article uses Lévy distribution for noise profile modeling. Next, focus curves acquired by one of focus measure operators are modeled as Gaussian function to consider the effects of the jitter noise. Finally, since conventional Kalman filter provides good output under Gaussian noise only, a modified Kalman filter, as proposed method, is used to remove the jitter noise. Experiments are carried out using synthetic and real objects to show the effectiveness of the proposed method. At first, the jitter noise and the focus curves are modeled by Lévy distribution and Gaussian functions, respectively. To improve accuracy of the 3D shape recovery, Modified Kalman filtering method for removal of jitter noise, is then proposed. [ABSTRACT FROM AUTHOR]

Abstract Shape information plays an important role in the human visual system, and how to represent the shape accurately is a very challenging issue in shape recognition. In recent years, many shape description approaches have been proposed. However, most of the existing methods are still facing challenges on accuracy and computational efficiency. Fourier descriptor is regarded as a promising shape description method because it has a solid theoretical foundation and at the same time possesses the strength of appealing invariance properties and high computational efficiency. We introduce a novel multiscale Fourier descriptor based on triangular features which is used to identify shapes. The local and global characteristics of a shape are effectively captured by the proposed shape descriptor. Meanwhile, the proposed shape descriptor has good properties, such as the invariant of the geometric transformation and the starting point of an object. We tested this descriptor on four popular benchmarking datasets, including MPEG-7, Swedish leaf, ETH-80, and Flavia leaf. The results confirm that our method is better than comparable-complexity approaches based on Fourier descriptors and does not perform unfavorably with respect to more complex, state-of-the-art, shape descriptors. In particular, our method is far superior to the complex shape description methods in terms of retrieval efficiency and computational complexity. Highlights • We propose a novel multiscale triangle feature signature for Fourier descriptors. • Our method solves the lack of local shape feature of the Fourier descriptors. • The results show the superiority of our method over state-of-the-art descriptors. [ABSTRACT FROM AUTHOR]

In recent decades, the need for efficient and effective image search from large databases has increased. In this paper, we present a novel shape matching framework based on structures common to similar shapes. After representing shapes as medial axis graphs, in which nodes show skeleton points and edges connect nearby points, we determine the critical nodes connecting or representing a shape's different parts. By using the shortest path distance from each skeleton (node) to each of the critical nodes, we effectively retrieve shapes similar to a given query through a transportation-based distance function. To improve the effectiveness of the proposed approach, we employ a unified framework that takes advantage of the feature representation of the proposed algorithm and the classification capability of a supervised machine learning algorithm. A set of shape retrieval experiments including a comparison with several well-known approaches demonstrate the proposed algorithm's efficacy and perturbation experiments show its robustness. [ABSTRACT FROM AUTHOR]

In order to solve the problem that the histogram matching time is long and the engineering application is poor, this paper proposed a method that using EMD-L1 to measure the distance between two feature histograms. EMD-L1 fusioned the L1 norm based on the original EMD and replace the calculation of the ground distance to reduce the number of unknown variables. It achieves shape matching quickly and has a good retrieval performance. With a great deal of experiments in several shape databases, the results show that the performance of novel method is superior to original algorithm. And the matching speed is better than other algorithms under the MNIST data set. [ABSTRACT FROM AUTHOR]

Highlights • A learning framework for shape retrieval based on multi-layers perceptron. • The learning algorithm is used to classify the view images of shape. • The method of sketch-based LBP (SBLBP) descriptor which is extracted from a sketch, is proposed. • Multi-layers perceptron is used to as a classifier. Abstract With the rapid development of 3D technology, the demand to use and retrieve 3D models has become increasingly urgent. In this paper, we present a framework that consists of a sketch-based local binary pattern (SBLBP) feature extraction method, a learning algorithm for the best view of a shape based on multilayer perceptrons (MLPs) and a learning method for shape retrieval based on two Siamese MLP networks. The model is first projected into many multiview images. A transfer learning scheme based on graphic traversal to identify Harris key points is proposed to build relations between view images and sketches. In addition, an MLP classifier is used for classification to obtain the best views of each model. Moreover, we propose a new learning method for shape retrieval that simultaneously uses two Siamese MLP networks to learn SBLBP features. Furthermore, we build a joint Bayesian method to fuse the outputs of the views and sketches. Based on training with many samples, the MLP parameters are effectively fit to perform shape retrieval. Finally, an experiment is conducted to verify the feasibility of the approach, and the results show that the proposed framework is superior to other approaches. [ABSTRACT FROM AUTHOR]

Highlights • Hexagonal grid based triangular tessellation for acute feature characterisation. • Achieving geometrical congruence employing triangle tessellation. • Local-Global approach for realizing acute and simple shape Histograms. • Superior BER scores over its predecessors. • Complexity analysis reveals the simplicity of the proposed intention. Graphical abstract Abstract Shape characterization schemes catering object recognition and retrieval have been undergoing intense study in computer vision. As shape encompasses much of image information, yielding higher retrieval performance with less complexity continues to be a challenging issue. Accordingly, a simple approach, blending hexagonal grid modelling with triangular tessellation for shape matching and retrieval is proposed in this paper. At the onset, a shape image is decomposed into overlapping hexagonal grids that are then divided into six non-overlapping equilateral triangles. Next, the intensity differences of each triangle side is evaluated and the maximum of the three sides is retained. This process is repeated on the remaining triangles that produces six maximum values corresponding to each triangle. These six values, then replace the six corners of the hexagonal subregion to finally produce a feature map that is uniquely packed into feature histograms representing the given shape. Quantitative and qualitative examinations on MPEG-7, TARI-1000 and Kimia's 99 datasets reveals a consistent BER greater than 90%. The superior performance over its competitors can be attributed to the congruent nature of the hexagonal and triangular tessellation. [ABSTRACT FROM AUTHOR]