论文标题
一些纹理细分理论
Some Theory for Texture Segmentation
论文作者
论文摘要
在图像中的纹理分割的上下文中，并为原型方法提供了一些理论保证，该方法包括在像素附近提取本地特征，然后应用群集算法以根据这些功能对像素进行分组。一方面，对于我们使用高斯马尔可夫随机字段进行建模的固定纹理，我们通过计算其邻域贴片的样品协方差矩阵并通过应用K-均值将协方差矩阵构造样品协方差矩阵来构造每个像素的功能。我们证明这种通用方法是一致的。另一方面，对于非平稳字段，我们将像素的位置作为附加功能，并应用单链群集。我们再次表明，这种通用和象征的方法是一致的。我们通过对生成和自然纹理进行的一些数值实验来补充理论。
In the context of texture segmentation in images, and provide some theoretical guarantees for the prototypical approach which consists in extracting local features in the neighborhood of a pixel and then applying a clustering algorithm for grouping the pixel according to these features. On the one hand, for stationary textures, which we model with Gaussian Markov random fields, we construct the feature for each pixel by calculating the sample covariance matrix of its neighborhood patch and cluster the pixels by an application of k-means to group the covariance matrices. We show that this generic method is consistent. On the other hand, for non-stationary fields, we include the location of the pixel as an additional feature and apply single-linkage clustering. We again show that this generic and emblematic method is consistent. We complement our theory with some numerical experiments performed on both generated and natural textures.
