改进非线性结构张量的含噪图像边缘检测

Edge Detection in Images Corrupted with Noise Based on Improved Nonlinear Structure Tensor

现有的边缘检测方法在含噪图像中的检测性能不佳。针对含噪图像的边缘检测问题,提出了利用引导核改进基于非线性结构张量的含噪图像边缘检测方法。首先,计算含噪图像的张量积。然后,根据图像梯度对张量积进行扩散,图像梯度依赖张量积本身。扩散方程中的扩散矩阵包含张量积,该张量积是通过各向异性的引导核进行空间自适应平均,而不是通过各向同性的高斯核进行平均。最后计算扩散张量积的特征值和特征向量,并基于此检测图像的边缘。将所提方法与基于线性结构张量的边缘检测方法、基于张量梯度扩散的非线性结构张量的边缘检测方法、基于图像梯度扩散的非线性结构张量的边缘检测方法进行比较,实验结果表明,所提方法可以得到更为清晰的边缘,并且检测结果中噪声较少。

The performance of existing edge detection methods in images corrupted by noise is not satisfying.Aiming at the edge detection problem in images corrupted by moderate noise,an image edge detection method based on improved nonlinear structure tensor using steering kernel is proposed.First the tensor products of the noisy image are computed.Then the tensor products are diffused according to the derivatives of the image which depends on the tensor product itself.The diffusivity matrix in the diffusion equation is composed of the tensor products which are spatially adaptive averaged using a steering kernel instead of isotropic filtered using a gaussian kernel.Finally,the eigenvalues and eigenvectors of the diffused tensor products are computed in order to detect the image edge.Experimental results show that,compared with image edge detection methods based on linear structure tensor,nonlinear structure tensor diffused according to the derivatives of the tensor,nonlinear structure tensor diffused according to the derivatives of the image,the proposed method can get clearer edges with smaller amount of noise.