中文摘要：

图像非刚性配准在计算机视觉和医学图像有着重要的作用．然而存在的非刚性配准算法对严重扭曲变形的图像配准精度和效率都比较低．针对该问题，提出基于Nystrom低阶近似和谱特征的图像非刚性配准算法．算法首先提取像素的谱特征，并将谱特征与空间特征、灰度特征融合形成具有扭曲不变性的全局谱特征；然后在微分同胚配准的框架内使用全局谱匹配，确保算法产生的变形场具有光滑性、可逆性、可微性，以提高配准的精度；其次采用Nystrom抽样方法，随机抽取拉普拉斯矩阵的行与列，低阶逼近该矩阵，降低高维矩阵谱分解的时间，从而提高配准的效率；最后提出基于小波分解的多分辨率图像配准方法，进一步提高配准的精度和效率．理论分析和实验结果均表明，该算法的配准精度和配准效率都有明显的提高．

英文摘要：

Non-rigid image registration plays an important role in computer vision and medical image. However, the typical non-rigid registration algorithms for seriously distorted deformation images lead to a poor registration precision and low efficiency. Therefore, we introduce a new non-rigid image registration algorithm based on low-rank NystrSm approximation method and spectral feature. Firstly, we extract the spectral feature of pixel, and combine spatial feature and gray feature to form global spectral feature which is invariant to distortion. Then the spectral match method is used within the diffeomorphic registration framework so that the deformation field generated by the algorithm is smooth, reversible, and differentiable, with an improved registration precision. Secondly, we use Nystrom sampling method to speed up high dimension matrix spectral decomposition by generating a low-rank approximation matrix via randomly selected rows and columns of the Laplace matrix. Finally, we put forward an image registration method based on wavelet decomposition, to improve the accuracy and efficiency of registration. The theoretic analysis and experimental results show that our algorithm can improve registration precision as well as efficiency.