Edge features contain important information about graphs. However, current state-of-the-art neural network models designed for graph learning, \eg, graph convolutional networks (GCN) and graph attention networks (GAT), inadequately utilize edge features, especially multi-dimensional edge features. In this paper, we build a new framework for a family of new graph neural network models that can more sufficiently exploit edge features, including those of undirected or multi-dimensional edges. The proposed framework can consolidate current graph neural network models, e.g., GCN and GAT. The proposed framework and new models have the following novelties: First, we propose to use doubly stochastic normalization of graph edge features instead of the commonly used row or symmetric normalization approaches used in current graph neural networks. Second, we construct new formulas for the operations in each individual layer so that they can handle multi-dimensional edge features. Third, for the proposed new framework, edge features are adaptive across network layers. As a result, our proposed new framework and new models are able to exploit a rich source of graph edge information. We apply our new models to graph node classification on several citation networks, whole graph classification, and regression on several molecular datasets. Compared with the current state-of-the-art methods, i.e., GCNs and GAT, our models obtain better performance, which testify to the importance of exploiting edge features in graph neural networks.

Accurate head pose estimation is significant for many applications such as face recognition and human-computer interaction. In this paper, we treat the head pose estimation as a classification problem and employ the Lie Algebrized Gaussians (LAG) feature as the representation approach for head image. The LAG feature, which is built on Gausssian Mixture Model (GMM), has the capability to preserve the structure of Gaussian components in the original Lie group manifold. Moreover, to keep more spatial structure information of the image, LAG is operated on many subregions of the image. As a result, these properties of LAG enable it to reflect the pose characteristic of the head image well and possess powerful discriminative ability in pose classification. Experiments on CMU Pose, Illumination, and Expression (PIE) and Pointing'04 benchmarks show state-of-the-art performance and demonstrate that LAG represents the head pose characteristic well.

This paper introduces a feature descriptor called Shape of Gaussian (SOG), which is based on a general feature descriptor design framework called Shape of Signal Probability Density Function (SOSPDF). SOSPDF takes the shape of a signal's probability density function (pdf) as its feature. Under such a view, both histogram and region covariance often used in computer vision are SOSPDF features. Histogram describes SOSPDF by a discrete approximation way. Region covariance describes SOSPDF as an incomplete parameterized multivariate Gaussian distribution. Our proposed SOG descriptor is a full parameterized Gaussian, so it has all the advantages of region covariance and is more effective. Furthermore, we identify that SOGs form a Lie group. Based on Lie group theory, we propose a distance metric for SOG. We test SOG features in tracking problem. Experiments show better tracking results compared with region covariance. Moreover, experiment results indicate that SOG features attempt to harvest more useful information and are less sensitive against noise.

Spatiograms were generalization of histograms, which can harvest spatial information of images. The similarity measure is important when applying spatiograms to various computer vision problems such as tracking and image retrieval. The original proposed measures use Mahalanobis distance of coordinate mean to measure spatial information in spatiograms. However, spatial information which is described by spatiograms does not lie on vector space. Measures for vector space such as Mahalanobis distance are not effective measures for them. In this paper, We model spatial information as Gaussian approximation of coordinate distributions. Then we parameterize them as a Lie group. Based on Lie group theory, we analyze function space structure of Gaussian pdfs (probability density function) and propose an effective spatiogram similarity measure. We test our measure in object tracking scenarios. Experiments show better tracking results compared with previously proposed measures.