IEEE Trans Image Process. 2012 Oct;21(10):4498-502. doi: 10.1109/TIP.2012.2206038. Epub 2012 Jun 26.
Crumpled sheets of paper tend to exhibit a specific and complex structure, which is described by physicists as ridge networks. Existing literature shows that the automation of ridge network detection in crumpled paper is very challenging because of its complex structure and measuring distortion. In this paper, we propose to model the ridge network as a weighted graph and formulate the ridge network detection as an optimization problem in terms of the graph density. First, we detect a set of graph nodes and then determine the edge weight between each pair of nodes to construct a complete graph. Next, we define a graph density criterion and formulate the detection problem to determine a subgraph with maximal graph density. Further, we also propose to refine the graph density by including a pairwise connectivity into the criterion to improve the connectivity of the detected ridge network. Our experimental results show that, with the density criterion, our proposed method effectively automates the ridge network detection.
皱纸往往呈现出一种特定而复杂的结构，物理学家将其描述为脊网络。现有文献表明，由于皱纸结构复杂且存在测量变形，其脊网络的自动化检测极具挑战性。在本文中，我们将脊网络建模为加权图，并将脊网络检测表述为图密度意义下的优化问题。首先，我们检测一组图节点，然后确定每对节点之间的边权重，以构建完全图。接下来，我们定义图密度准则，并将检测问题表述为确定具有最大图密度的子图。此外，我们还建议通过将节点间连通性纳入准则，来细化图密度，以提高检测到的脊网络的连通性。实验结果表明，利用密度准则，我们的方法能够有效地实现脊网络的自动化检测。
