Riemannian level-set methods for tensor-valued data

Multiple Riemannian Manifold-valued Descriptors based Image Set Classification with Multi-Kernel Metric Learning

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, whic…

A Riemanian Approach to Blob Detection in Manifold-Valued Images

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…

黎曼梯度与海森矩阵的算子值公式及可处理度量族

Operator-valued formulas for Riemannian Gradient and Hessian and families of tractable metrics

本文提出一种算子值公式方法，用于计算一类商流形的黎曼梯度与海森矩阵，并将其应用于斯蒂费尔流形、旗流形及固定秩半正定矩阵流形，扩展了流形优化和机器学习中可用的度量族。