Combining multiple manifold-valued descriptors for improved object recognitionwen
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分析paper:Combining multiple manifold-valued descriptors for improved object recognition
From Mehrtash harandi
Classification using multiple manifold-valued features.
Riemannnian Geometry
Combining the HOG + Region Covariance on two different manifolds
通常把欧式空间的算法应用到黎曼流形,是通过切空间近似,来获得一个欧式表示。
但是切空间投影度量等,是在一个临近区域内,当数据分布非常远时,投影到切空间边失去了意义。
Mehrtash一直主张,通过正定kernel投影,把流形空间嵌入到高维的Reproducing Kernel Hilbert Space.
联合HOG特征和区域协方差特征,他们分别处于两种特定的流形上,单位球 和 黎曼流形。
1、单位球 (The unit n-sphere)
定义:The n-dimensional sphere that has unit radius and is centered at the origin of the n+1 dimensional Euclidean space, denoted by S^n.
度量:
其中HOG特征通过L2规则化。
2、黎曼流形 (SPD矩阵)
度量:
0 0
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