Combing multiple manifold-valued descriptors for improved object recognition

Paper: Combing multiple manifold-valued descriptors for improved object recognition (Mehrtasg Harandi)

A learning method for classification using multiple manifold-valued features

1、Feature combination： Combing HOG and Region Convariance descriptors that reside on two different manifolds.

2、A kernel on the n-dimensional unit sphere

一些非向量空间的描述子有：

Normalized histogram vectors、Convariance descriptors （object recognition）

Diffusion tensors (biomedical image analysis)

3D rotation matrices (geometrical computer vision)

Linear subspaces of the n-dimensional Euclidean space (video vision)

分析这种非向量空间描述子的方法是利用黎曼几何~

把欧式算法推广到黎曼流形的方法：

一是，obtain a Euclidean represenration of the manifold-valued data by approximating the manifold by the tangent space. (log and exp maps)

 二是，embed the manifold in the high dimensional Reproducing Kernel Hilbert space (RKHS) using a positive definite kernel.

Combining multiple manifold-valued descriptor via RKHS embedding.