Subvoxel accurate graph search using non-Euclidean graph space

• Published in: PloS one Vol. 9; no. 10; p. e107763
• Main Authors: Abràmoff, Michael D, Wu, Xiaodong, Lee, Kyungmoo, Tang, Li
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 14.10.2014; Public Library of Science (PLoS)
• Subjects: Accuracy; Algorithms; Angiography; Automation; Biology and Life Sciences; Computer and Information Sciences; Computer applications; Computer engineering; Computing time; Data acquisition; Equipment costs; Euclidean geometry; Euclidean space; Graph representations; Graph theory; Humans; Image acquisition; Image processing; Image segmentation; Imaging, Three-Dimensional; Magnetic Resonance Imaging; Medical imaging; Medicine and Health Sciences; NMR; Nodes; Nuclear magnetic resonance; Optic nerve; Optical Coherence Tomography; Optics; Optimization; Physical Sciences; Quantitative analysis; Research and Analysis Methods; Retina; Retina - diagnostic imaging; Run time (computers); Science; Searching; Statistical analysis; Tissues; Tomography; Tomography, Optical Coherence; United States > US; Iowa; Iowa City Iowa
• DOI: 10.1371/journal.pone.0107763
• ISSN: 1932-6203

Graph search is attractive for the quantitative analysis of volumetric medical images, and especially for layered tissues, because it allows globally optimal solutions in low-order polynomial time. However, because nodes of graphs typically encode evenly distributed voxels of the volume with arcs connecting orthogonally sampled voxels in Euclidean space, segmentation cannot achieve greater precision than a single unit, i.e. the distance between two adjoining nodes, and partial volume effects are ignored. We generalize the graph to non-Euclidean space by allowing non-equidistant spacing between nodes, so that subvoxel accurate segmentation is achievable. Because the number of nodes and edges in the graph remains the same, running time and memory use are similar, while all the advantages of graph search, including global optimality and computational efficiency, are retained. A deformation field calculated from the volume data adaptively changes regional node density so that node density varies with the inverse of the expected cost. We validated our approach using optical coherence tomography (OCT) images of the retina and 3-D MR of the arterial wall, and achieved statistically significant increased accuracy. Our approach allows improved accuracy in volume data acquired with the same hardware, and also, preserved accuracy with lower resolution, more cost-effective, image acquisition equipment. The method is not limited to any specific imaging modality and readily extensible to higher dimensions.