In this work, we propose a new Bayesian model for unsupervised image segmentation based on a combination of the spatially varying finite mixture models (SVFMMs) and the non-local means (NLM) framework. The probabilistic NLM weighting function is successfully integrated into a varying Gauss–Markov random field, yielding a prior density that adaptively imposes a local regularization to simultaneously preserve edges and enforce smooth constraints in homogeneous regions of the image. Two versions of our model are proposed: a pixel-based model and a patch-based model, depending on the design of the probabilistic NLM weighting function. Contrary to previous methods proposed in the literature, our approximation does not introduce new parameters to be estimated into the model, because the NLM weighting function is completely known once the neighborhood of a pixel is fixed. The proposed model can be estimated in closed-form solution via a maximum a posteriori (MAP) estimation in an expectation–maximization scheme. We have compared our model with previously proposed SVFMMs using two public datasets: the Berkeley Segmentation dataset and the BRATS 2013 dataset. The proposed model performs favorably to previous approaches in the literature, achieving better results in terms of Rand Index and Dice metrics in our experiments.

在这项工作中，我们基于空间变化的有限混合模型（SVFMM）和非局部均值（NLM）框架的组合，提出了一种用于无监督图像分割的新贝叶斯模型。概率NLM加权函数已成功集成到变化的高斯-马尔可夫随机场中，从而产生先验密度，该密度自适应地施加局部正则化，以同时保留边缘并在图像的均匀区域中实施平滑约束。根据概率NLM加权函数的设计，提出了两种版本的模型：基于像素的模型和基于补丁的模型。与文献中提出的先前方法相反，我们的近似方法并未在模型中引入要估算的新参数，因为一旦固定了像素的邻域，就完全可以知道NLM加权函数。可以通过期望最大化方案中的最大后验（MAP）估计，在闭式解决方案中估计提出的模型。我们使用两个公共数据集（伯克利细分数据集和BRATS 2013数据集）将我们的模型与先前提出的SVFMM进行了比较。所提出的模型比文献中的先前方法具有更好的性能，在我们的实验中就兰德指数和骰子指标而言获得了更好的结果。伯克利细分数据集和BRATS 2013数据集。所提出的模型比文献中的先前方法具有更好的性能，在我们的实验中就兰德指数和骰子指标而言获得了更好的结果。伯克利细分数据集和BRATS 2013数据集。所提出的模型比文献中的先前方法具有更好的性能，在我们的实验中就兰德指数和骰子指标而言获得了更好的结果。