基于Riemann度量的张量值图像各向异性插值

张量值图像在数字图像处理中有很重要的作用,传统的线性插值方法只考虑了被插值点与采样点的位置关系,没有考虑采样点张量自身信息,在插值过程中容易造成边缘模糊。该文提出了一种Riemann度量框架下的各向异性插值方法,由张量场的梯度信息得到局部结构张量,用来确定邻域采样点的权重,依此构建自适应插值核函数,在Rie-mann度量框架下对邻域采样点加权求和得到被插值点张量值。该方法容易实现且效率高,这在含大量数据的张量值图像处理中显得尤为重要。实验结果表明,该方法既能保持张量值图像边缘特征和细节特征,又能保证插值后张量满足正定性条件。此外,各向异性的处理框架为张量值图像滤波、分割和配准等问题提供了新的解决方法。

Anisotropic interpolation method for tensor valued images based on a Riemannian metric framework

The interpolation of tensor valued images is an essential step in various digital image processing applications.Traditional linear interpolation for tensor field images only considers the positional relationship between the interpolation points and sample points,while ignoring the tensor information.This study presents an anisotropic interpolation technique for tensor valued images based on a Riemannian metric framework.The method uses the local structure tensor as a metric to compute the distance between the sample and the interpolation points.Then,the weighted sum is calculated by an adaptive interpolation kernel function for the Riemannian metric framework.The method can be easily implemented and is very efficient,which is important in processing tensor valued images that contain vast amounts of data.Tests show that this method preserves the boundaries as well as the positive definite constraint in a new framework for anisotropic tensor valued image processing,including applications for filtering,registration and segmentation.