The importance of wild video based image set recognition is becoming monotonically increasing. However, the contents of these collected videos are often complicated, and how to efficiently perform set modeling and feature extraction is a big challenge for set-based classification algorithms. In recent years, some proposed image set classification methods have made a considerable advance by modeling the original image set with covariance matrix, linear subspace, or Gaussian distribution. As a matter of fact, most of them just adopt a single geometric model to describe each given image set, which may lose some other useful information for classification. To tackle this problem, we propose a novel algorithm to model each image set from a multi-geometric perspective. Specifically, the covariance matrix, linear subspace, and Gaussian distribution are applied for set representation simultaneously. In order to fuse these multiple heterogeneous Riemannian manifoldvalued features, the well-equipped Riemannian kernel functions are first utilized to map them into high dimensional Hilbert spaces. Then, a multi-kernel metric learning framework is devised to embed the learned hybrid kernels into a lower dimensional common subspace for classification. We conduct experiments on four widely used datasets corresponding to four different classification tasks: video-based face recognition, set-based object categorization, video-based emotion recognition, and dynamic scene classification, to evaluate the classification performance of the proposed algorithm. Extensive experimental results justify its superiority over the state-of-the-art.
A novel efficient method for content-based image retrieval (CBIR) is developed in this paper using both texture and color features. Our motivation is to represent and characterize an input image by a set of local descriptors extracted at characteristic points (i.e. keypoints) within the image. Then, dissimilarity measure between images is calculated based on the geometric distance between the topological feature spaces (i.e. manifolds) formed by the sets of local descriptors generated from these images. In this work, we propose to extract and use the local extrema pixels as our feature points.…
School of IoT Engineering, Jiangnan University（江南大学物联网工程学院）
In the domain of pattern recognition, using the CovDs (Covariance Descriptors) to represent data and taking the metrics of the resulting Riemannian manifold into account have been widely adopted for the task of image set classification. Recently, it has been proven that infinite-dimensional CovDs are more discriminative than their low-dimensional counterparts. However, the form of infinite-dimensional CovDs is implicit and the computational load is high. We propose a novel framework for representing image sets by approximating infinite-dimensional CovDs in the paradigm of the Nyström method ba…
Covariance Descriptors Meet General Vision Encoders: Riemannian Deep Learning for Medical Image Classification
1 School of Computation, Information；Technology, Technical University of Munich, Germany 2 Munich Center for Machine Learning (MCML), Germany 3 Institute of Machine Learning in Biomedical Imaging, Helmholtz Munich, Germany 4 School of Biomedical Engineering；Imaging Sciences, King’s College London, UK
In this paper we present an efficient method for aggregating binary feature descriptors to allow compact representation of 3D scene model in incremental structure-from-motion and SLAM applications. All feature descriptors linked with one 3D scene point or landmark are represented by a single low-dimensional real-valued vector called a \emph{prototype}. The method allows significant reduction of memory required to store and process feature descriptors in large-scale structure-from-motion applications. An efficient approximate nearest neighbours search methods suited for real-valued descriptors,…
In the domain of pattern recognition, using the SPD (Symmetric Positive Definite) matrices to represent data and taking the metrics of resulting Riemannian manifold into account have been widely used for the task of image set classification. In this paper, we propose a new data representation framework for image sets named CSPD (Component Symmetric Positive Definite). Firstly, we obtain sub-image sets by dividing the image set into square blocks with the same size, and use traditional SPD model to describe them. Then, we use the results of the Riemannian kernel on SPD matrices as similarities …
Laboratory for Mathematical and Numerical Modeling in Engineering Science（工程科学数学与数值建模实验室）；National Engineering School at Tunis（突尼斯国立工程师学院）；ENIT-LAMSIN（突尼斯国立工程师学院-工程科学数学与数值建模实验室）
We present a novel approach for the derivation of PDE modeling curvature-driven flows for matrix-valued data. This approach is based on the Riemannian geometry of the manifold of Symmetric Positive Definite Matrices Pos(n).
NICTA, PO Box 6020, St Lucia, QLD 4067, Australia（澳大利亚国家信息与通信技术研究院，地址：澳大利亚昆士兰州圣卢西亚，邮编 4067，邮政信箱 6020）；University of Queensland, School of ITEE, QLD 4072, Australia（澳大利亚昆士兰大学信息技术与电气工程学院，地址：澳大利亚昆士兰州，邮编 4072）
For covariance-based image descriptors, taking into account the curvature of the corresponding feature space has been shown to improve discrimination performance. This is often done through representing the descriptors as points on Riemannian manifolds, with the discrimination accomplished on a tangent space. However, such treatment is restrictive as distances between arbitrary points on the tangent space do not represent true geodesic distances, and hence do not represent the manifold structure accurately. In this paper we propose a general discriminative model based on the combination of sev…
This paper is devoted to the problem of blob detection in manifold-valued images. Our solution is based on new definitions of blob response functions. We define the blob response functions by means of curvatures of an image graph, considered as a submanifold. We call the proposed framework Riemannian blob detection. We prove that our approach can be viewed as a generalization of the grayscale blob detection technique. An expression of the Riemannian blob response functions through the image Hessian is derived. We provide experiments for the case of vector-valued images on 2D surfaces: the prop…
Shanghai Jiao Tong University（上海交通大学）；G60 Yun Zhi AI Innovation and Application Research Center（G60云智人工智能创新应用研究中心）；Midea Corporate Research Center（美的集团中央研究院）
We introduce a lightweight network to improve descriptors of keypoints within the same image. The network takes the original descriptors and the geometric properties of keypoints as the input, and uses an MLP-based self-boosting stage and a Transformer-based cross-boosting stage to enhance the descriptors. The boosted descriptors can be either real-valued or binary ones. We use the proposed network to boost both hand-crafted (ORB, SIFT) and the state-of-the-art learning-based descriptors (SuperPoint, ALIKE) and evaluate them on image matching, visual localization, and structure-from-motion tas…
University of Wollongong（卧龙岗大学）；National University of Defense Technology（国防科技大学）
Being symmetric positive-definite (SPD), covariance matrix has traditionally been used to represent a set of local descriptors in visual recognition. Recent study shows that kernel matrix can give considerably better representation by modelling the nonlinearity in the local descriptor set. Nevertheless, neither the descriptors nor the kernel matrix is deeply learned. Worse, they are considered separately, hindering the pursuit of an optimal SPD representation. This work proposes a deep network that jointly learns local descriptors, kernel-matrix-based SPD representation, and the classifier via…
Feature descriptors play a crucial role in a wide range of geometry analysis and processing applications, including shape correspondence, retrieval, and segmentation. In this paper, we introduce Geodesic Convolutional Neural Networks (GCNN), a generalization of the convolutional networks (CNN) paradigm to non-Euclidean manifolds. Our construction is based on a local geodesic system of polar coordinates to extract "patches", which are then passed through a cascade of filters and linear and non-linear operators. The coefficients of the filters and linear combination weights are optimization vari…
NICTA（澳大利亚国家信息与通信技术研究院）；Australian National University（澳大利亚国立大学）
Vectors of Locally Aggregated Descriptors (VLAD) have emerged as powerful image/video representations that compete with or even outperform state-of-the-art approaches on many challenging visual recognition tasks. In this paper, we address two fundamental limitations of VLAD: its requirement for the local descriptors to have vector form and its restriction to linear classifiers due to its high-dimensionality. To this end, we introduce a kernelized version of VLAD. This not only lets us inherently exploit more sophisticated classification schemes, but also enables us to efficiently aggregate non…
We propose a new action and gesture recognition method based on spatio-temporal covariance descriptors and a weighted Riemannian locality preserving projection approach that takes into account the curved space formed by the descriptors. The weighted projection is then exploited during boosting to create a final multiclass classification algorithm that employs the most useful spatio-temporal regions. We also show how the descriptors can be computed quickly through the use of integral video representations. Experiments on the UCF sport, CK+ facial expression and Cambridge hand gesture datasets i…
College of Engineering and Computer Science, Australian National University（澳大利亚国立大学工程与计算机科学学院）；NICTA
In this paper, we develop an approach to exploiting kernel methods with manifold-valued data. In many computer vision problems, the data can be naturally represented as points on a Riemannian manifold. Due to the non-Euclidean geometry of Riemannian manifolds, usual Euclidean computer vision and machine learning algorithms yield inferior results on such data. In this paper, we define Gaussian radial basis function (RBF)-based positive definite kernels on manifolds that permit us to embed a given manifold with a corresponding metric in a high dimensional reproducing kernel Hilbert space. These …
School of Computer Science & Engineering, UESTC（电子科技大学计算机科学与工程学院）
At present, the great achievements of convolutional neural network(CNN) in feature and metric learning have attracted many researchers. However, the vast majority of deep network architectures have been used to represent based on real values. The research of complex-valued networks is seldom concerned due to the absence of effective models and suitable distance of complex-valued vector. Motived by recent works, complex vectors have been shown to have a richer representational capacity and efficient complex blocks have been reported, we propose a new approach for learning image descriptors with…
Nanyang Technological University（南洋理工大学）；DSO National Laboratories（DSO国家实验室）
Robust visual tracking for long video sequences is a research area that has many important applications. The main challenges include how the target image can be modeled and how this model can be updated. In this paper, we model the target using a covariance descriptor, as this descriptor is robust to problems such as pixel-pixel misalignment, pose and illumination changes, that commonly occur in visual tracking. We model the changes in the template using a generative process. We introduce a new dynamical model for the template update using a random walk on the Riemannian manifold where the cov…
Key Lab of Intelligent Information Processing of Chinese Academy of Sciences (CAS)（中国科学院智能信息处理重点实验室）；Institute of Computing Technology, CAS（中国科学院计算技术研究所）
Human action recognition remains a challenging task due to the various sources of video data and large intra-class variations. It thus becomes one of the key issues in recent research to explore effective and robust representation to handle such challenges. In this paper, we propose a novel representation approach by constructing mid-level words in videos and encoding them on Riemannian manifold. Specifically, we first conduct a global alignment on the densely extracted low-level features to build a bank of corresponding feature groups, each of which can be statistically modeled as a mid-level…
Beyond First-Order: Learning Riemannian Geometries for Invariant Visual Place Recognition
The Hong Kong University of Science and Technology, Hong Kong, China（香港科技大学）；University of Macau, Macau, China（澳门大学）；University of Science and Technology Beijing, Beijing, China（北京科技大学）
Jiangnan University（江南大学）；University of Surry（萨里大学）
We consider a family of structural descriptors for visual data, namely covariance descriptors (CovDs) that lie on a non-linear symmetric positive definite (SPD) manifold, a special type of Riemannian manifolds. We propose an improved version of CovDs for image set coding by extending the traditional CovDs from Euclidean space to the SPD manifold. Specifically, the manifold of SPD matrices is a complete inner product space with the operations of logarithmic multiplication and scalar logarithmic multiplication defined in the Log-Euclidean framework. In this framework, we characterise covariance …
Washington University in St. Louis（圣路易斯华盛顿大学）；NVIDIA Research（英伟达研究院）
Covariance and histogram image descriptors provide an effective way to capture information about images. Both excel when used in combination with special purpose distance metrics. For covariance descriptors these metrics measure the distance along the non-Euclidean Riemannian manifold of symmetric positive definite matrices. For histogram descriptors the Earth Mover's distance measures the optimal transport between two histograms. Although more precise, these distance metrics are very expensive to compute, making them impractical in many applications, even for data sets of only a few thousand …
Cooperative Medianet Innovation Center, Shanghai Jiao Tong University（上海交通大学协同媒体创新中心）
With the explosive growth of image databases, deep hashing, which learns compact binary descriptors for images, has become critical for fast image retrieval. Many existing deep hashing methods leverage quantization loss, defined as distance between the features before and after quantization, to reduce the error from binarizing features. While minimizing the quantization loss guarantees that quantization has minimal effect on retrieval accuracy, it unfortunately significantly reduces the expressiveness of features even before the quantization. In this paper, we show that the above definition of…
University of Florida（佛罗里达大学）；GE Healthcare（通用电气医疗集团）
Manifold-valued datasets are widely encountered in many computer vision tasks. A non-linear analog of the PCA, called the Principal Geodesic Analysis (PGA) suited for data lying on Riemannian manifolds was reported in literature a decade ago. Since the objective function in PGA is highly non-linear and hard to solve efficiently in general, researchers have proposed a linear approximation. Though this linear approximation is easy to compute, it lacks accuracy especially when the data exhibits a large variance. Recently, an alternative called exact PGA was proposed which tries to solve the optim…
The analysis of manifold-valued data requires efficient tools from Riemannian geometry to cope with the computational complexity at stake. This complexity arises from the always-increasing dimension of the data, and the absence of closed-form expressions to basic operations such as the Riemannian logarithm. In this paper, we adapt a generic numerical scheme recently introduced for computing parallel transport along geodesics in a Riemannian manifold to finite-dimensional manifolds of diffeomorphisms. We provide a qualitative and quantitative analysis of its behavior on high-dimensional manifol…
