Ridge surfaces represent important features for the analysis of 3-dimensional (3D) datasets in diverse applications and are often derived from varying underlying data including flow fields, geological fault data, and point data, but they can also be present in the original scalar images acquired using a plethora of imaging techniques. Our work is motivated by the analysis of image data acquired using micro-computed tomography (Micro-CT) of ancient, rolled and folded thin-layer structures such as papyrus, parchment, and paper as well as silver and lead sheets. From these documents we know that they are 2-dimensional (2D) in nature. Hence, we are particularly interested in reconstructing 2D manifolds that approximate the document's structure. The image data from which we want to reconstruct the 2D manifolds are often very noisy and represent folded, densely-layered structures with many artifacts, such as ruptures or layer splitting and merging. Previous ridge-surface extraction methods fail to extract the desired 2D manifold for such challenging data. We have therefore developed a novel method to extract 2D manifolds. The proposed method uses a local fast marching scheme in combination with a separation of the region covered by fast marching into two sub-regions. The 2D manifold of interest is then extracted as the surface separating the two sub-regions. The local scheme can be applied for both automatic propagation as well as interactive analysis. We demonstrate the applicability and robustness of our method on both artificial data as well as real-world data including folded silver and papyrus sheets.

翻译：脊面是三维数据集分析中的重要特征，广泛应用于多种场景，通常源于流场、地质断层数据和点云数据等底层数据，也可通过多种成像技术直接获取的标量图像中提取。本研究受微型计算机断层扫描（Micro-CT）获取的古代卷曲折叠薄层结构（如莎草纸、羊皮纸、纸张以及银箔和铅片）图像分析需求驱动。基于这些文献的二维本质特征，我们特别关注重建近似文档结构的二维流形。待重建二维流形的源图像数据常存在严重噪声，呈现包含大量伪影（如破裂、层裂与合并）的折叠密集层状结构。针对此类具有挑战性的数据，现有脊面提取方法无法有效获取目标二维流形。为此，我们提出一种新颖的二维流形提取方法。该方法采用局部快速行进算法，并结合区域分割策略将快速行进覆盖区域划分为两个子区域，目标二维流形即作为分隔这两个子区域的界面被提取。局部方案既支持自动传播也适用于交互式分析。通过在人工合成数据与包含折叠银箔和莎草纸的真实数据上的实验，验证了该方法的适用性与鲁棒性。