Image segmentation is the task of partitioning an image into individual objects, and has many important applications in a wide range of fields. The majority of segmentation methods rely on image intensity gradient to define edges between objects. However, intensity gradient fails to identify edges when the contrast between two objects is low. In this paper we aim to introduce methods to make such weak edges more prominent in order to improve segmentation results of objects of low contrast. This is done for two kinds of segmentation models: global and local. We use a combination of a reproducing kernel Hilbert space and approximated Heaviside functions to decompose an image and then show how this decomposition can be applied to a segmentation model. We show some results and robustness to noise, as well as demonstrating that we can combine the reconstruction and segmentation model together, allowing us to obtain both the decomposition and segmentation simultaneously.

中文翻译：

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基于可再生内核希尔伯特空间的全局和局部图像分割

图像分割是将图像划分为单个对象的任务，并且在广泛的领域中具有许多重要的应用。大多数分割方法依靠图像强度梯度来定义对象之间的边缘。但是，当两个对象之间的对比度较低时，强度梯度无法识别边缘。在本文中，我们旨在介绍使这些弱边缘更加突出的方法，以改善低对比度对象的分割结果。这是针对两种细分模型完成的：全局和局部。我们结合使用可再生内核Hilbert空间和近似的Heaviside函数来分解图像，然后说明如何将此分解应用于分割模型。我们显示了一些结果以及对噪声的鲁棒性，