基于流形学习和流形高阶近似的图像距离度量

为克服切距离方法的不足,提出了流形高阶近似距离（HMD）.HMD度量方法通过最大差异延展方法（MVU）学习出非线性图像流形的内蕴变量,然后在原型图像处用基于流形高阶泰勒展开式的非线性曲面来局部近似图像流形.HMD定义为待识别图像与图像流形的高阶近似曲面间的最小距离,通过计算待识别图像与图像流形上多个基准图像间的HMD距离能够实现图像的分类和识别.人脸识别和手写数字识别的结果表明：HMD距离在识别精度和稳定性上要优于切距离和当前一些典型的图像距离度量方法.

Image distance measurement based on manifold learning and manifold high-order approximation

To overcome the shortcomings of tangent distance,an image distance high-order approximated manifold distance(HMD) was proposed.In HMD metric intrinsic variables of nonlinear image manifold were revealed by maximum variance unfolding(MVU) and image manifold was locally approximated at prototype by curved surface based on high-order Taylor expansions with respect to intrinsic variables.HMD was defined as the minimum distance between the query image and the approximated curved surface of image manifold.The image classification and recognition can be achieved by computing HMD distances between the query image and the landmarks of image manifold.A series of face recognition and handwritten digit recognition experiments demonstrate that HMD can not only achieve higher recognition accuracy but also has more stability of classification than several state-of-the-art distance metrics.