Scale-invariant Heat Kernel Signature Research Articles

Ventricle shape analysis using modified WKS for atrophy detection.

Brain ventricle is one of the biomarkers for detecting neurological disorders. Studying the shape of the ventricles will aid in the diagnosis process of atrophy and other CSF-related neurological disorders, as ventricles are filled with CSF. This paper introduces a spectral analysis algorithm based on wave kernel signature. This shape signature was used for studying the shape of segmented ventricles from the brain images. Based on the shape signature, the study groups were classified as normal subjects and atrophy subjects. The proposed algorithm is simple, effective, automated, and less time consuming. The proposed method performed better than the other methods heat kernel signature, scale invariant heat kernel signature, wave kernel signature, and spectral graph wavelet signature, which were used for validation purpose, by producing 94-95% classification accuracy by classifying normal and atrophy subjects correctly for CT, MR, and OASIS datasets.

Multiscale persistent topological descriptor for porous structure retrieval

Porous structures play an important role in applications such as materials science and chemistry. The development of synthesized porous materials requires novel descriptors to quantify the geometric and topological features of pore surfaces. Persistent homology provides a stable tool to capture the changes in topological invariants from a manifold filtered by a real-valued function. In this study, a framework is proposed on the basis of a real-valued function evolving with a parameter on a surface to generate a multiscale persistent topological descriptor. It is obtained by approximating the Betti number curves that are produced from a collection of persistence barcodes through a B-spline surface. A vectorizing descriptor is constructed by reshaping the control points of the B-spline surface. In our experiments, scale invariant heat kernel signature (SI-HKS) is employed as a real-valued function defined on a surface to compute the descriptor. Retrieval tasks on a synthetic porous data set and a zeolite data set show the competitiveness of the proposed method compared with the descriptors based on SI-HKS and advanced topological descriptors.

Approach for 3D Cultural Relic Classification Based on a Low-Dimensional Descriptor and Unsupervised Learning

Computer-aided classification serves as the basis of virtual cultural relic management and display. The majority of the existing cultural relic classification methods require labelling of the samples of the dataset; however, in practical applications, there is often a lack of category labels of samples or an uneven distribution of samples of different categories. To solve this problem, we propose a 3D cultural relic classification method based on a low dimensional descriptor and unsupervised learning. First, the scale-invariant heat kernel signature (Si-HKS) was computed. The heat kernel signature denotes the heat flow of any two vertices across a 3D shape and the heat diffusion propagation is governed by the heat equation. Secondly, the Bag-of-Words (BoW) mechanism was utilized to transform the Si-HKS descriptor into a low-dimensional feature tensor, named a SiHKS-BoW descriptor that is related to entropy. Finally, we applied an unsupervised learning algorithm, called MKDSIF-FCM, to conduct the classification task. A dataset consisting of 3D models from 41 Tang tri-color Hu terracotta Eures was utilized to validate the effectiveness of the proposed method. A series of experiments demonstrated that the SiHKS-BoW descriptor along with the MKDSIF-FCM algorithm showed the best classification accuracy, up to 99.41%, which is a solution for an actual case with the absence of category labels and an uneven distribution of different categories of data. The present work promotes the application of virtual reality in digital projects and enriches the content of digital archaeology.

Long-distance deformation object recognition by integrating contour structure and scale-invariant heat kernel signature

The tough challenges of object recognition in long-distance scene involves contour shape deformation invariant features construction. In this work, an effective contour shape descriptor integrating critical points structure and Scale-invariant Heat Kernel Signature (SI-HKS) is proposed for long-distance object recognition. We firstly propose a general feature fusion model. Then, we capture the object contour structure feature with Critical-points Inner-distance Shape Context (CP-IDSC). Meanwhile, we pull-in the SI-HKS for capturing the local deformation-invariant properties of 2D shape. Based on the integration of the above two feature descriptors, the fusion descriptor is compacted by mapping into a low dimensional subspace using the bags-of-features, allowing for an efficient Bayesian classifier recognition. The extensive experiments on synthetic turbulence-degraded shapes and real-life infrared image show that the proposed method outperformed other compared approaches in terms of the recognition precision and robustness.

Dempster–Shafer evidence theory‐based multi‐feature learning and fusion method for non‐rigid 3D model retrieval

This study introduces a novel multi‐feature‐based non‐rigid three‐dimensional (3D) model retrieval method. First, for each 3D model, compute the scale‐invariant heat kernel signature (SI‐HKS) descriptor and the wave kernel signature (WKS) descriptor of each vertex. Then, the normalised weighted bags of phrases feature is obtained and they are fed to the convolutional neural networks. The trust degree of each kind of descriptor is computed, and the total trust degree can be obtained. Finally, the fusion network is trained and the retrieval results can be obtained according to the ranking of the total trust degrees. For the training phase and the testing phase, the authors define different computation methods of the trust degrees and the total trust degrees. The Dempster–Shafer (DS) evidence‐based total trust degrees are used not only in the feature layer but also in the decision layer. The final decision results of the total trust degrees are used in the process of the network learning. So the proposed method can make full use of the complementary information of the SI‐HKS descriptor and the WKS descriptor. Extensive experiments have shown that the proposed multi‐feature fusion method has better performance than a single feature‐based method, and also outperforms other existing state‐of‐the‐art methods.

Automatic human body feature extraction and personal size measurement

It is a pervasive problem to automatically obtain the size of a human body without contacting for applications like virtual try-on. In this paper, we propose a novel approach to calculate human body size, such as width of shoulder, girths of bust, hips and waist. First, a depth camera as the 3D model acquisition device is used to get the 3D human body model. Then an automatic extraction method of focal features on 3D human body via random forest regression analysis of geodesic distances is used to extract the predefined feature points and lines. Finally, the individual human body size is calculated according to these feature points and lines. The scale-invariant heat kernel signature is exploited to serve as feature proximity. So our method is insensitive to postures and different shapes of 3D human body. These main advantages of our method lead to robust and accurate feature extraction and size measurement for 3D human bodies in various postures and shapes. The experiment results show that the average error of feature points extraction is 0.0617cm, the average errors of shoulder width and girth are 1.332 cm and 0.7635 cm, respectively. Overall, our algorithm has a better detection effect for 3D human body size, and it is stable with better robustness than existing methods.

Invariant probabilistic sensitivity analysis for building energy models

One of the key challenges in the field of building-performance analysis is to identify the key source of input parameter/s that has/have largest effect on the energy efficiency of the buildings. Critical input parameters can be identified through the use of sensitivity analysis models. In this paper, we outline an invariant probabilistic sensitivity analysis technique to enable screening of the most important parameters in the building energy models. The proposed probabilistic sensitivity analysis method measures the average distance between unconditional probability distribution and conditional (on an input) probability distribution of an output. The distribution's description is based on the scale-invariant heat kernel signature (SI-HKS). In this paper, SI-HKS method is extended for invariant probabilistic sensitivity analysis. We demonstrate the application of the proposed method through the use of Energy Plus building-performance modelling tool.

A non-rigid 3D model retrieval method based on scale-invariant heat kernel signature features

The number of non-rigid 3D models increases steadily in various areas. It is imperative to develop efficient retrieval system for 3D non-rigid models. As we know, global features fail to consistently describe the intra-class variability of non-rigid 3D models, the local features are more effective than global features for the retrieval of non-rigid 3D models. In this paper, we use Heat Kernel Signature (HKS) as the local features to represent non-rigid 3D models and further propose the retrieval method based on scale-invariant local features. Firstly, we extract key-points at multiple scales automatically. Then, the HKS local features are computed for each key-point. However, the HKS features are sensitive to scale. In order to solve this problem, we convert the scale problem into the translation problem using the diffusion Wavelets transform. To solve the translation problem, we use a kind of histogram equalization technique. Finally, we use the bipartite graph matching algorithm to compute similarity between the 3D models. Experimental results on two public benchmarks show that our method outperforms state-of-the-art methods for non-rigid 3D models retrieval.

Learning a discriminative deformation-invariant 3D shape descriptor via many-to-one encoder

Recent advances in 3D acquisition techniques have led to a rapid increase in the size of database of three dimensional (3D) models across areas as diverse as engineering, medicine and biology, etc. Therefore, developing an efficient shape retrieval method has been attracting more and more attention in recent years. In this paper, we have developed a novel learning paradigm for extracting a concise data-driven shape descriptor to address challenging issues posed by structural deformation variations and noise present in 3D models. First, we use the scale invariant heat kernel signature (SIHKS) to describe the vertex of the shape. The locality-constrained linear coding (LLC) is employed to encode each vertex of the shape to form the global shape representation. Then we develop a discriminative shape descriptor for retrieval using many-to-one encoder. Our proposed shape descriptor is extensively evaluated on three well-known benchmark datasets including McGill, SHREC’10 ShapeGoogle and SHREC’14 human. Experimental results on 3D shape retrieval demonstrate the superior performance of our proposed method over the state-of-the-art methods and is robust to large deformations.

Intrinsic spatial pyramid matching for deformable 3D shape retrieval

In this paper, we present an intrinsic spatial pyramid matching approach for 3D shape retrieval. Motivated by the fact that the second eigenfunction of Laplace–Beltrami operator not only can capture the global topological structure information, but also is intrinsic, we propose to adopt its level sets as cuts to perform surface partition. The resulting matching scheme is able to consistently estimate the approximate global geometric correspondence among 3D shapes. In particular, we can leverage recent developments in intrinsic shape analysis and perform intrinsic spatial pyramid matching based on dense spectral shape descriptors such as scale-invariant heat kernel signature. Our experiments demonstrate a significant improvement of 3D shape retrieval on two standard benchmarks.

Spatially aggregating spectral descriptors for nonrigid 3D shape retrieval: a comparative survey

This paper presents a comprehensive review and analysis of recent spectral shape descriptors for nonrigid 3D shape retrieval. More specifically, we compare the latest spectral descriptors based on the Laplace---Beltrami (LB) operator, including ShapeDNA, heat kernel signature, scale invariant heat kernel signature, heat mean signature, wave kernel signature, and global point signature. We also include the eigenvalue descriptor (EVD), which is a geodesic distance-based shape signature. The global descriptors ShapeDNA and EVD are compared via the chi-squared distance, while all local descriptors are compared using the codebook model. Moreover, we investigate the ambiguity modeling of codebook for the densely distributed low-level shape descriptors. Inspired by the ability of spatial cues to improve discrimination between shapes, we also propose to adopt the isocontours of the second eigenfunction of the LB operator to perform surface partition, which can significantly ameliorate the retrieval performance of the time-scaled local descriptors. In addition, we introduce an intrinsic spatial pyramid matching approach in a bid to further enhance the retrieval accuracy. Extensive experiments are carried out on two 3D shape benchmarks to assess the performance of the spectral descriptors. Our proposed approach is shown to provide the best performance.