Princeton Shape Benchmark Research Articles

An assessment of 2-D and 3-D interest point detectors in volumetric images

Many interest point detectors have been designed so far to work in two dimensional (2-D) images. However, expansion of these detectors into the third dimension for three dimensional (3-D) images can refine their representational power. This paper presents how the Harris corner, LoG filtering-based blob, and salient regions detectors can be expanded to find interest points in volumetric images handling multiple slices collectively. Performances of 2-D and 3-D detector implementations were assessed both qualitatively and quantitatively with value combinations of different parameters using metrics such as F1-score, localization error, and repeatability in binary images of twenty 3-D object models from the Princeton Shape Benchmark (PSB). Computation of F1-score and localization error depended on some manually marked ground truth points, while repeatability measurement was according to the proximity of the detected point sets. The 3-D detectors were evaluated as more successful in capturing distinctive and sparse interest points on 3-D object surfaces in qualitative analyses. Despite having greater computational complexities, most of the 3-D detectors yielded better average F1-score, localization accuracy, and repeatability given uniqueness constraint on the matched points in quantitative analyses. Therefore, the 3-D detectors appear preferable when longer working durations or sparser representations would not constitute any disadvantage.

Recognition of 3D Images by Fusing Fractional-Order Chebyshev Moments and Deep Neural Networks.

In order to achieve efficient recognition of 3D images and reduce the complexity of network parameters, we proposed a novel 3D image recognition method combining deep neural networks with fractional-order Chebyshev moments. Firstly, the fractional-order Chebyshev moment (FrCM) unit, consisting of Chebyshev moments and the three-term recurrence relation method, is calculated separately using successive integrals. Next, moment invariants based on fractional order and Chebyshev moments are utilized to achieve invariants for image scaling, rotation, and translation. This design aims to enhance computational efficiency. Finally, the fused network embedding the FrCM unit (FrCMs-DNNs) extracts depth features to analyze the effectiveness from the aspects of parameter quantity, computing resources, and identification capability. Meanwhile, the Princeton Shape Benchmark dataset and medical images dataset are used for experimental validation. Compared with other deep neural networks, FrCMs-DNNs has the highest accuracy in image recognition and classification. We used two evaluation indices, mean square error (MSE) and peak signal-to-noise ratio (PSNR), to measure the reconstruction quality of FrCMs after 3D image reconstruction. The accuracy of the FrCMs-DNNs model in 3D object recognition was assessed through an ablation experiment, considering the four evaluation indices of accuracy, precision, recall rate, and F1-score.

3D Gaussian Geometric Moment Invariants

ABSTRACT 3D moment invariants are important tools for 3D image feature representation. In this paper, we introduced a novel approach for constructing 3D moment invariants using Gaussian geometric moments. Our proposed method demonstrated invariance under translation, rotation, and scale transformations. The numerical experiments validate the invariance and robustness of the proposed method, comparing it with traditional 3D geometric moments and revealing superior performance in the presence of noise and transformations. Additionally, the method is applied to content-based 3D image retrieval, exhibiting promising results through Minkowski distance-based retrieval on the Princeton Shape Benchmark (PSB) database.

Robust registration and learning using multi-radii spherical polar Fourier transform

This paper presents effective methods using spherical polar Fourier transform data for two different applications, with active areas of research, one as a conventional volumetric registration algorithm and other as a machine learning classification network. For registration purposes the proposed method has the following advantageous features: (i) it is a unique and effective technique for estimating up to 7 degrees of freedom for 3D volumetric registration, that has a closed-form solution for 3D rotation estimation, and which does not resort to recurrence relations or search for point correspondences between two objects/volumes, (ii) it allows for robust rotation estimation determined simultaneously on multiple spectral spheres, therefore complete stack of such spherical layers can be processed concurrently to obtain accurate and optimal all three angles, and (iii) it has the ability to handle arbitrary large rotation angles, is shown to be robust against the presence of noise, holes/missing data, and partial overlaps. We demonstrate the effectiveness of our solution with extensive experimentation, including a set of scanned MRI images, a crashed car parking dataset, and the Princeton shape benchmark dataset with hundreds of 3D objects. For the classification solution we modify and adapt an existing network in the literature, a type of spherical convolutional network, that is suitable for processing multi-radii spectral spherical data, and showcase the resulting robustness achieved in classification of objects from the ModelNet40 dataset, especially in the presence of outliers, additive noise, and missing data.

Integral spin images usage in deep learning algorithms for 3D model classification

We are investigating a problem of 3D model classification using deep learning algorithms. We propose integral spin images usage as 3D model representation. A number of computational experiments were made to build spin images for 3D models of Princeton Shape Benchmark and use them to train LeNet-5, AlexNet and ResNet deep neural networks. The results showed that integral spin images can be used in conjunction with deep learning algorithms in 3D model classification problem. However, with greater number of classes classification accuracy tends to decrease. It is expected that designing a more complex neural network architecture and expanding number of data characteristics can increase accuracy.

Multi-feature 3D model retrieval using view-based techniques

ABSTRACT Most research on 3D model retrieval focus on shape as the main feature used for search and retrieval. In this paper, we explore augmenting 3D shape-based similarity measures by combining shape with color features. There are already numerous techniques for content-based 3D model retrieval utilizing shape, some use global shape features, shape distributions, or view-based methods. This paper uses a view-based approach using 2D projections of 3D models taken from different viewpoints. The main problem with view-based techniques is how to normalize the rotation of the mesh in 3D space to properly align the model to the projection planes. In our work, we use Normal-vectors PCA (NPCA). The 3D model is first projected onto three planes using their normal vectors and gray-level images (inner elevations) that describe the depth information are generated. The angular radial transform (ART) from MPEG-7 is then used on these inner elevations to extract a feature descriptor. These descriptors are called the inner elevation descriptor (IED) and are used to match the query with the database object. This shape feature is then augmented using color histograms considering perceptual color similarity. It is then tested on the Princeton Shape Benchmark and compared to well-known approaches.

Hypergraph-Induced Convolutional Networks for Visual Classification.

At present, convolutional neural networks (CNNs) have become popular in visual classification tasks because of their superior performance. However, CNN-based methods do not consider the correlation of visual data to be classified. Recently, graph convolutional networks (GCNs) have mitigated this problem by modeling the pairwise relationship in visual data. Real-world tasks of visual classification typically must address numerous complex relationships in the data, which are not fit for the modeling of the graph structure using GCNs. Therefore, it is vital to explore the underlying correlation of visual data. Regarding this issue, we propose a framework called the hypergraph-induced convolutional network to explore the high-order correlation in visual data during deep neural networks. First, a hypergraph structure is constructed to formulate the relationship in visual data. Then, the high-order correlation is optimized by a learning process based on the constructed hypergraph. The classification tasks are performed by considering the high-order correlation in the data. Thus, the convolution of the hypergraph-induced convolutional network is based on the corresponding high-order relationship, and the optimization on the network uses each data and considers the high-order correlation of the data. To evaluate the proposed hypergraph-induced convolutional network framework, we have conducted experiments on three visual data sets: the National Taiwan University 3-D model data set, Princeton Shape Benchmark, and multiview RGB-depth object data set. The experimental results and comparison in all data sets demonstrate the effectiveness of our proposed hypergraph-induced convolutional network compared with the state-of-the-art methods.

Rotation Scaling and Translation Invariants of 3D Radial Shifted Legendre Moments

This paper proposes a new set of 3D rotation scaling and translation invariants of 3D radially shifted Legendre moments. We aim to develop two kinds of transformed shifted Legendre moments: a 3D substituted radial shifted Legendre moments (3DSRSLMs) and a 3D weighted radial one (3DWRSLMs). Both are centered on two types of polynomials. In the first case, a new 3D radial complex moment is proposed. In the second case, new 3D substituted/weighted radial shifted Legendre moments (3DSRSLMs/3DWRSLMs) are introduced using a spherical representation of volumetric image. 3D invariants as derived from the suggested 3D radial shifted Legendre moments will appear in the third case. To confirm the proposed approach, we have resolved three issues. To confirm the proposed approach, we have resolved three issues: rotation, scaling and translation invariants. The result of experiments shows that the 3DSRSLMs and 3DWRSLMs have done better than the 3D radial complex moments with and without noise. Simultaneously, the reconstruction converges rapidly to the original image using 3D radial 3DSRSLMs and 3DWRSLMs, and the test of 3D images are clearly recognized from a set of images that are available in Princeton shape benchmark (PSB) database for 3D image.

Radial Hahn Moment Invariants for 2D and 3D Image Recognition

Recently, orthogonal moments have become efficient tools for two-dimensional and three-dimensional (2D and 3D) image not only in pattern recognition, image vision, but also in image processing and applications engineering. Yet, there is still a major difficulty in 3D rotation invariants. In this paper, we propose new sets of invariants for 2D and 3D rotation, scaling and translation based on orthogonal radial Hahn moments. We also present theoretical mathematics to derive them. Thus, this paper introduces in the first case new 2D radial Hahn moments based on polar representation of an object by one-dimensional orthogonal discrete Hahn polynomials, and a circular function. In the second case, we present new 3D radial Hahn moments using a spherical representation of volumetric image by one-dimensional orthogonal discrete Hahn polynomials and a spherical function. Further 2D and 3D invariants are derived from the proposed 2D and 3D radial Hahn moments respectively, which appear as the third case. In order to test the proposed approach, we have resolved three issues: the image reconstruction, the invariance of rotation, scaling and translation, and the pattern recognition. The result of experiments show that the Hahn moments have done better than the Krawtchouk moments, with and without noise. Simultaneously, the mentioned reconstruction converges quickly to the original image using 2D and 3D radial Hahn moments, and the test images are clearly recognized from a set of images that are available in COIL-20 database for 2D image, and Princeton shape benchmark (PSB) database for 3D image.

Robust Reconstruction and Generalized Dual Hahn Moments Invariants Extraction for 3D Images

In this paper, we introduce a new set of 3D weighed dual Hahn moments which are orthogonal on a non-uniform lattice and their polynomials are numerically stable to scale, consequent, producing a set of weighted orthonormal polynomials. The dual Hahn is the general case of Tchebichef and Krawtchouk, and the orthogonality of dual Hahn moments eliminates the numerical approximations. The computational aspects and symmetry property of 3D weighed dual Hahn moments are discussed in details. To solve their inability to invariability of large 3D images, which cause to overflow issues, a generalized version of these moments noted 3D generalized weighed dual Hahn moment invariants are presented where whose as linear combination of regular geometric moments. For 3D pattern recognition, a generalized expression of 3D weighted dual Hahn moment invariants, under translation, scaling and rotation transformations, have been proposed where a new set of 3D-GWDHMIs have been provided. In experimental studies, the local and global capability of free and noisy 3D image reconstruction of the 3D-WDHMs has been compared with other orthogonal moments such as 3D Tchebichef and 3D Krawtchouk moments using Princeton Shape Benchmark database. On pattern recognition using the 3D-GWDHMIs like 3D object descriptors, the experimental results confirm that the proposed algorithm is more robust than other orthogonal moments for pattern classification of 3D images with and without noise.

A novel 3D model retrieval system based on three-view sketches

© 2016 - IOS Press and the authors. All rights reserved.3D models can be used in 3D printing and many other areas. At present, there are a lot of researches on 3D model retrieval and sketch is considered to be important for 3D model retrieval. In this paper, we develop a new 3D model retrieval prototype system based on style-sensitive 3D model retrieval method and three-view user sketches. We also implement user-friendly graphic interfaces for the 3D model retrieval system. We explore the performance of the system by conducting a series of 3D model retrieval experiments on the Princeton shape benchmark data set. Experimental results show that the new retrieval system can obtain satisfactory retrieval results. And some results of the new method are superior to some content-based 3D model retrieval methods, in terms of both quantitative search performance metrics and qualitatively measured user search experiences.

OBJECT CLASSIFICATION VIA PLANAR ABSTRACTION

Abstract. We present a supervised machine learning approach for classification of objects from sampled point data. The main idea consists in first abstracting the input object into planar parts at several scales, then discriminate between the different classes of objects solely through features derived from these planar shapes. Abstracting into planar shapes provides a means to both reduce the computational complexity and improve robustness to defects inherent to the acquisition process. Measuring statistical properties and relationships between planar shapes offers invariance to scale and orientation. A random forest is then used for solving the multiclass classification problem. We demonstrate the potential of our approach on a set of indoor objects from the Princeton shape benchmark and on objects acquired from indoor scenes and compare the performance of our method with other point-based shape descriptors.

OBJECT CLASSIFICATION VIA PLANAR ABSTRACTION

We present a supervised machine learning approach for classification of objects from sampled point data. The main idea consists in first abstracting the input object into planar parts at several scales, then discriminate between the different classes of objects solely through features derived from these planar shapes. Abstracting into planar shapes provides a means to both reduce the computational complexity and improve robustness to defects inherent to the acquisition process. Measuring statistical properties and relationships between planar shapes offers invariance to scale and orientation. A random forest is then used for solving the multiclass classification problem. We demonstrate the potential of our approach on a set of indoor objects from the Princeton shape benchmark and on objects acquired from indoor scenes and compare the performance of our method with other point-based shape descriptors.

A 3D shape descriptor based on spherical harmonics through evolutionary optimization

This paper proposes an optimization approach based on a newly designed parameter set self-evolutionary process. This method improves the discriminability of the original shape descriptor of a 3D model based on spherical harmonics while retaining the efficiency and simplicity of the original shape descriptor. This method captures the critical characteristics, such as the distance, area, and normal distributions of a 3D model extracted along the latitude–longitude directions after the 3D model is normalized in the uniform coordinate frame, and obtains the 3D model׳s features using a spherical harmonics transform. In order to determine the spherical harmonic basis function relationship, an additional weight (0,1) of each spherical harmonic coefficient as random variable is used to search for the optimal variables based on genetic optimization. The resulting transformed features for these random variables are then used as modified shape descriptors. Retrieval performance is examined using the public benchmarks: the Princeton Shape Benchmark, CCCC and NTU databases, and experiments have shown that the optimized additional weight for shape descriptors based on spherical harmonics results in a significant improvement in discriminability.

Sparse Contextual Activation for Efficient Visual Re-Ranking.

In this paper, we propose an extremely efficient algorithm for visual re-ranking. By considering the original pairwise distance in the contextual space, we develop a feature vector called sparse contextual activation (SCA) that encodes the local distribution of an image. Hence, re-ranking task can be simply accomplished by vector comparison under the generalized Jaccard metric, which has its theoretical meaning in the fuzzy set theory. In order to improve the time efficiency of re-ranking procedure, inverted index is successfully introduced to speed up the computation of generalized Jaccard metric. As a result, the average time cost of re-ranking for a certain query can be controlled within 1 ms. Furthermore, inspired by query expansion, we also develop an additional method called local consistency enhancement on the proposed SCA to improve the retrieval performance in an unsupervised manner. On the other hand, the retrieval performance using a single feature may not be satisfactory enough, which inspires us to fuse multiple complementary features for accurate retrieval. Based on SCA, a robust feature fusion algorithm is exploited that also preserves the characteristic of high time efficiency. We assess our proposed method in various visual re-ranking tasks. Experimental results on Princeton shape benchmark (3D object), WM-SRHEC07 (3D competition), YAEL data set B (face), MPEG-7 data set (shape), and Ukbench data set (image) manifest the effectiveness and efficiency of SCA.

A powerful 3D model classification mechanism based on fusing multi-graph

Recently, integrating several feature descriptors to be a powerful one has become a hot issue in the field of 3D object understanding. The fusing mechanism is so crucial that can significantly affect the performance of 3D model classification. In this paper, a powerful model for 3D model classification, which can novelly integrate several graphs, is proposed. This mechanism is based on graph fusion and modifies each graph׳s weight in a boost manner. Each graph׳s weight in the fusion graph can be dynamically calculated according to its performance. Finally, a fusion graph is acquired to 3D model classification. We conduct the experiments on the publicly available 3D model databases: Princeton shape benchmark (PSB) and SHREC׳09, and the experimental results demonstrate the powerful performance of the proposed method.

A 3D model recognition mechanism based on deep Boltzmann machines

The effectiveness of 3D model recognition generally depends on the feature representations and classification methods. Previous algorithms have not shown good capacities to detect 3D model׳s feature, thus, they seem not to be competent to recognize 3D model. Meanwhile, recent efforts have illustrated that Deep Boltzmann Machines (DBM) have great power to approximate the distributions of input data, and can archive state-of-the-arts results. In this paper, we propose a novel 3D model recognition mechanism based on DBM, which can be divided into two parts: one is feature detecting based on DBM, and the other is classification based on semi-supervised learning method. During the first part, the high-level abstraction representation can be obtained from a well-trained DBM, and the feature is used in semi-supervised classification method in the second part. The experiments are conducted on publicly available 3D model data sets: Princeton Shape Benchmark (PSB), SHREC׳09 and National Taiwan University (NTU). The proposed method is compared with several state-of-the-art methods in terms of several popular evaluation criteria, and the experimental results show better performance of the proposed model.

3-D object retrieval using topic model

In the last few years, extensive effort has been spent to develop better performed 3-D object retrieval methods. View-based methods have attracted a significant amount of attention, not only because their state-of-art performance, but also they merely require some of a 3-D object's 2-D view images. However, most recent approaches only deal with the images' primordial-extracted features and ignore their hidden relationships. Considering these latent characters, a visual-topic-model 3-D object retrieval approach is introduced in this paper. In this framework, dense scale invariant feature transform(dense-SIFT) descriptors are extracted from a set of views of each 3-D object, and all the dense-SIFT descriptors are grouped into bag-of-word features using k-means clustering. Then, the topic distribution of a 3-D object is generated via latent dirichlet allocation (LDA) given its bag-of-word features. Gibbs sampling is applied in the learning and inference processing of LDA. We conduct experiments on the Princeton Shape Benchmark (PSB) and National Taiwan University 3D model database (NTU), and the experimental results demonstrate that the proposed method can achieve better retrieval effectiveness than the state-of-the-art methods under several standard evaluation measures.

3D Shape Partition via Multi-class Spectral Graph Clustering

This paper proposes a new 3D shape partition algorithm. The main idea of our method is to represent 3D shape as a weighted graph whose nodes denote each face in the shape and the weights on the edges encode the similarities between faces. We then extract a set of geometric features from shape to build an affinity matrix for weighted graph and use multi-class spectral clustering method to find an optimal partition. We compute the generalized eigenvalue problems of the affinity matrix to group the most similar faces into the same semantic part and apply the graph cut method to refine the boundaries between the partition parts. Finally we evaluate our approach on the Princeton shape benchmark. The experiment shows that our method can successfully segment different classes of 3D shapes and can achieve more meaningful segmentation results compared to other leading single shape partition algorithms.

3D shape retrieval using viewpoint information‐theoretic measures

AbstractIn this paper, we present an information‐theoretic framework to compute the shape similarity between 3D polygonal models. Given a 3D model, an information channel between a sphere of viewpoints around the model and its polygonal mesh is defined to compute the specific information associated with each viewpoint. The obtained information sphere can be seen as a shape descriptor of the model. Then, given two models, their similarity is obtained by performing a registration process between the corresponding information spheres. The distance between the information histograms is also defined as a coarse measure of similarity, as well as the scalar value given by the mutual information of the channel. The performance of all these measures is tested using the Princeton Shape Benchmark database. Copyright © 2013 John Wiley & Sons, Ltd.