It has been demonstrated that the segmentation performance is highly dependent on both subspace preservation and graph connectivity. In the literature, the full connectivity method linearly represents each data point ( e.g., a pixel in one image) by all data points for achieving subspace preservation, while the sparse connectivity method was designed to linearly represent each data point by a set of data points for achieving graph connectivity. However, previous methods only focused on either subspace preservation or graph connectivity. In this article, we propose a Sparse Graph Connectivity (SGC) method for image segmentation to automatically learn the affinity matrix from the low-dimensional space of original data, which aims at simultaneously achieving subspace preservation and graph connectivity. To do this, the proposed SGC simultaneously learns a self-representation affinity matrix for subspace preservation and a sparse affinity matrix for graph connectivity, from the intrinsic low-dimensional feature space of high-dimensional original data. Meanwhile, the self-representation affinity matrix is pushed to be similar to the sparse affinity as well as be the final segmentation results. Experimental result on synthetic and real-image datasets showed that our SGC method achieved the best segmentation performance, compared to state-of-the-art segmentation methods.

中文翻译：

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用于图像分割的稀疏图连接

已经证明，分割性能高度依赖于子空间的保存和图的连通性。在文献中，全连接方法线性表示每个数据点（例如，一个图像中的一个像素）通过所有数据点来实现子空间保存，而稀疏连通性方法旨在通过一组数据点线性表示每个数据点以实现图形连通性。然而，以前的方法只关注子空间保存或图连接。在本文中，我们提出了一种用于图像分割的稀疏图连接（SGC）方法，从原始数据的低维空间中自动学习亲和矩阵，旨在同时实现子空间保存和图连接。为此，所提出的 SGC 从高维原始数据的固有低维特征空间中同时学习用于子空间保存的自表示亲和矩阵和用于图连接的稀疏亲和矩阵。同时，将自表示亲和矩阵推到与稀疏亲和矩阵相似，并作为最终的分割结果。合成和真实图像数据集的实验结果表明，与最先进的分割方法相比，我们的 SGC 方法实现了最佳分割性能。