一种基于张量和洛仑兹几何的降维方法

唐科威; 刘日升; 杜慧; 苏志勋

doi:10.3724/SP.J.1004.2011.01151

一种基于张量和洛仑兹几何的降维方法

doi: 10.3724/SP.J.1004.2011.01151

唐科威¹,
刘日升^1,3,
杜慧¹,
苏志勋^1,2, ,

1.
大连理工大学数学科学学院大连 116024;
2.
特拉华州立大学应用数学研究中心美国 19901;
3.
卡内基梅隆大学机器人研究所美国 15213

详细信息

通讯作者:
苏志勋大连理工大学数学科学学院教授.1987年获得吉林大学数学系学士学位,1990年获得南开大学计算机系硕士学位,1993年获得大连理工大学数学科学学院博士学位.主要研究方向为计算机图形学,图像处理,计算几何和计算机视觉等.E-mail:zxsu@gmail.com

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出版历程
- 收稿日期: 2010-03-04
- 修回日期: 2011-03-22
- 刊出日期: 2011-09-20

A Novel Dimensionality Reduction Method Based on Tensor and Lorentzian Geometry

TANG Ke-Wei¹,
LIU Ri-Sheng^1,3,
DU Hui¹,
SU Zhi-Xun^{1,2
, ,}

1.
Dalian University of Technology School of Mathematical Sci- ences, Dalian 116024, P.R. China;
2.
Delaware State University of Mathematical Sciences, Dover 19901, USA;
3.
Robotics Institute, Carnegie Mellon University, Pittsburgh 15213, USA

摘要

摘要: 统的基于向量的降维算法,将大小为m×n的灰度图像,作为Rm×n中的向量进行处理.但这种表示方法往往造成图像像素空间局部信息的丢失,因此不能很好地描述图像的结构信息.本质上,灰度图像可以看成是一个二阶张量,而图像的各种特征(如Gabor和LBP特征等)往往需要用更高阶的张量来描述.本文从图像特征的张量表示出发,将新近提出的洛仑兹投影判别法(Lorentziandiscriminant projection, LDP)推广到张量空间中,提出张量LDP.对于灰度图像,该方法直接利用图像的灰度矩阵(二阶张量)进行运算,从而很好地保持了图像像素的局部结构信息.另外,该方法还可以自然地推广到高维张量空间来处理更复杂的图像特征,如Gabor和LBP特征等.经人脸和纹理识别实验的验证,该算法效率高且能达到较高的识别率.
- 张量 /
- 数据降维 /
- 洛仑兹几何 /
- 人脸识别 /
- 纹理识别
Abstract: Traditional vector-based dimensionality reduction algorithms consider an m×n image as a high dimensional vector in Rm×n. However, because this representation usually causes the lost of the local spatial information, it can not describe the image well. Intrinsically, an image is a 2D tensor and some feature extracted from the image (e.g. Gabor feature, LBP feature) may be a higher tensor. In this paper, we consider the nature of the image feature and propose the tensor Lorentzian discriminant projection algorithm, which can be considered as the tensor generation of the newly proposed Lorentzian discriminant projection (LDP). With regard to an image, this algorithm directly uses the hue matrix to compute, so it keeps the local spatial information well. In addition, this method can be naturally extended to the higher tensor space to deal with more complicated image features, such as Gabor feature and LBP feature. The experimental results on face and texture recognition show that our algorithm achieves better recognition accuracy while being much more efficient.
- Tensor /
- dimensionality reduction /
- Lorentzian ge-ometry /
- face recognition /
- texture recognition

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参考文献(1)

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