Non-local dependency is a very important prior for many image segmentation tasks. Generally, convolutional operations are building blocks that process one local neighborhood at a time which means the convolutional neural networks(CNNs) usually do not explicitly make use of the non-local prior on image segmentation tasks. Though the pooling and dilated convolution techniques can enlarge the receptive field to use some nonlocal information during the feature extracting step, there is no nonlocal priori for feature classification step in the current CNNs' architectures. In this paper, we present a non-local total variation (TV) regularized softmax activation function method for semantic image segmentation tasks. The proposed method can be integrated into the architecture of CNNs. To handle the difficulty of back-propagation for CNNs due to the non-smoothness of nonlocal TV, we develop a primal-dual hybrid gradient method to realize the back-propagation of nonlocal TV in CNNs. Experimental evaluations of the non-local TV regularized softmax layer on a series of image segmentation datasets showcase its good performance. Many CNNs can benefit from our proposed method on image segmentation tasks.

中文翻译：

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非局部正则CNN用于图像分割

对于许多图像分割任务而言，非本地依赖性是非常重要的先决条件。通常，卷积运算是一次处理一个局部邻域的构造块，这意味着卷积神经网络（CNN）通常不会在图像分割任务上显式地利用非局部先验。尽管池化和膨胀卷积技术可以在特征提取步骤中扩大接收区域以使用一些非局部信息，但是在当前的CNN架构中，没有非局部先验特征分类步骤。在本文中，我们提出了一种用于语义图像分割任务的非局部总变异（TV）正则化softmax激活函数方法。所提出的方法可以集成到CNN的体系结构中。为了解决由于非本地电视不平滑导致的CNN反向传播的困难，我们开发了一种原始对偶混合梯度方法来实现CNNs在非本地电视中的反向传播。在一系列图像分割数据集上对非本地TV正则化softmax图层进行的实验评估证明了其良好的性能。许多CNN都可以从我们提出的图像分割任务方法中受益。