【摘要】 利用拓扑理论中的单形定义,本文提出了一种针对人脸图像本征维数的估计方法。首先给出一个简单的几何模型,说明在不同的姿态和光照条件下人脸图像可看成一个弯曲流形;然后把人脸流形模型近似为一个单纯复形,获得相应的单形数目;最后,利用单纯复形中单形的最大维数是单纯复形的维数的性质,从而估计出人脸图像的本征维数。实验结果表明,本文方法跟经典方法,如分形方法、熵估计方法及k-近邻图方法等相比较,在人脸图像本征维数估计方面是有效的和准确的。更多还原

【Abstract】 To estimate the intrinsic dimension of human face image, a novel algorithm is proposed by using the simplex definition of topological theory. Firstly, a simple geometry model is built to show that human face images under varying poses and lightings can form a curved manifold and classification of the manifold can be transferred onto its coordinate charts. Secondly, the face manifold is modeled as an approximating simplicial complex that the number of its simplex is obtained. Finally, utilizing the property that the maximal dimension of simplex in simplicial complex is equal to the dimension of simplicial complex, the intrinsic dimension of human face images is estimated. Experimental results show that the proposed method of estimation of intrinsic dimension in human face images is effective and accurate compared with other classical methods, such as fractal-based method, entropy estimation method, k-nearest neighbor graphs method, and so on.更多还原